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Boris Krumov

Dreamer

875 4

  • Dreams 85
  • Following 14
  • Followers 5
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Vibrant Fractal Design with Swirling Patterns and Colors
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    Intricate 3D Fractal with Ethereal Details

    • Model: AIVision

    • Size: 1536 X 1536 (2.36 MP)

    • Used settings:

      • Prompt: An image of a highly detailed, symmetrical 3D fractal structure resembling a modified Mandelbulb, rendered as an abstract organic form resembling a crystalline, glassy rendition intricate, swirling coral-like protrusions and self-similar details, floating against a procedural gradient blue sky background with soft cyan-to-deep blue tones and subtle plane-based depth elements like top and bottom horizons with box-shaped patterns and exponential glow falloff. The central shape features two large, spiral red-orange eyes formed by hyperbolic distortions and a downward-curving dark blue mouth evoking a surprised or melancholic expression, with vibrant pink and orange hues for the main body exhibiting translucent, refractive qualities, internal amber-tinted glow from Beer-Lambert absorption using vector beer = -HSV(0.05, 0.95, 2.0), and high-contrast ethereal vibrancy achieved via ACES tone mapping approximation (v *= 0.6; clamp((v*(2.51*v+0.03))/(v*(2.43*v+0.59)+0.14), 0,1)) followed by sRGB gamma correction (mix(1.055*pow(t,1/2.4)-0.055, 12.92*t, step(t,0.0031308))).Generate the fractal using ray marching with tolerance 0.00001, max ray length 20.0, up to 48 marches, and 5 bounces for reflections and refractions, starting from camera at (0,2,5) looking at origin with FOV tan(tau/6) where tau=2*pi, incorporating global time-animated rotation around x-axis by (1.221*time + pi)/tau. The distance field df(p) = shp(mandelBulb(p/z1)*z1) with z1=2.0, where shp(x) = (exp(x)-exp(-x))/(pi/PHI) and PHI=(sqrt(5)/2 + 0.5)≈1.618, applied after rotating p by transpose(inverse(g_rot)).The mandelBulb(p) function iterates with power=11.24788742 and loops=3: initialize z = chp(p)*p - p where chp(x)=(exp(x)+exp(-x))/pi; dr=1.0; for each loop, r=length(z), bail if r>2; theta=atan(z.x,z.y); phi=asin(z.z/r) + time*0.2; dr = pow(r,power-1)*dr*power +1; r=pow(r,power); theta*=power/PHI; phi*=power/PHI; z = r * vec3(tan(shp(sin(theta)*sin(phi)))*PHI, chp(cos(theta)*sin(phi)), cos(phi)) + p; p=reflect(p,z); return 0.75*log(r)*r/dr.Incorporate custom hyperbolic functions for distortions: chpp(x)=(exp(x/(cosh(x)*pi))+exp(-x/(cosh(x)/pi)))/(TAU*PHI) with TAU=(2*pi)*0.7887≈4.951; shpp(x)=(exp(x*(sinh(x)*pi))-exp(-x*(sinh(x)*pi)))/(TAU/PHI); ssh(x)=(exp(x*pi/0.7887)-exp(-x*pi/0.7887))/(2*pi); csh(x)=(exp(x*pi/0.7887)+exp(-x*pi/0.7887))/(2*pi); ssh1(x)=sinh(x/pi)*PHI; csh1(x)=cosh(x/pi)*PHI. Use these in skyColor with reflections as reflect(-ssh1(rd), chpp(ro)), in rendering aggregation as agg += ssh1(ragg*skyColor(ro,rd)), and ray updates as rd=chpp(ref) or ro=shpp(sp + initt*rd) with initt=0.1.Material properties: mat=vec3(0.8,0.5,1.05) for diffuse, specular, refractive index; Fresnel fre=1+dot(rd,sn), fre*=fre, mix(0.1,1,fre); diffuse col += diffuseCol * dif*dif *(1-mat.x) with dif=max(dot(ld,sn),0), ld=normalize(lightPos-sp), lightPos=(0,10,0); reflection col += rsky*mat.y*fre*vec3(1)*edge with edge=smoothstep(1,0.9,fre); colors from HSV: skyCol=HSV(0.6,0.86,1), glowCol=HSV(0.065,0.8,6), diffuseCol=HSV(0.6,0.85,1). Inside traversal flips dfactor=-1, applies absorption ragg *= exp(-(st+initt)*beer), and refracts with index 1/mat.z when inside.Normals computed via finite differences: nor.x = df(pos+eps.xyy)-df(pos-eps.xyy) etc., with eps=(0.0005,0). Sky includes ray-plane intersections tp=(dot(ro,p.xyz)+p.w)/dot(rd,p.xyz) for planes at y=4 and y=-6, with box(pp,vec2(6,9))-1 for patterns, col += 4*skyCol*rd.y*rd.y*smoothstep(0.25,0,db) + 0.8*skyCol*exp(-0.5*max(db
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      • Aspect Ratio: square
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14d
33
0
4
Surreal Landscape with Ornate Tree Structure and Towers
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    Surreal Crystalline Fractal Mask Creation

    • Model: DaVinci2

    • Size: 1152 X 864 (1.00 MP)

    • Used settings:

      • Prompt: Generate a highly detailed, surreal 3D fractal artwork in the style of a modified Mandelbulb hybrid, rendered as an abstract, crystalline mask-like organic form with 5-lobe rotational symmetry and intricate, swirling coral-like protrusions emerging from a central glassy structure evoking an alien eye with stalk extensions, floating against a procedural gradient sky background transitioning from soft cyan (#00FFFF) to deep blue (#000080) with subtle plane-based depth elements at horizons y=4 and y=-6 featuring box-shaped patterns via box(pp, vec2(6,9))-1 and exponential glow falloff exp(-0.5*max(db,0)), incorporating self-similar recursive details from ray marching with tolerance 0.00001, max ray length 20.0, up to 48 marches, and 5 bounces for reflections and refractions. The central form features a glossy orange iris with dark pupil void from orbit trap sphere at origin (radius 0.1), surrounded by five radiating mushroom-like stalks with bumpy textures from sphere folds (minR²=0.2-0.3, fixedR²=1.0-1.2), vibrant pink-orange hues (HSV(0.065,0.8,6) for glow, HSV(0.6,0.85,1) for diffuse) exhibiting translucent refractive qualities with internal amber-tinted glow via Beer-Lambert absorption ragg *= exp(-(st+initt)*beer) where beer = -HSV(0.05, 0.95, 2.0) and initt=0.1, high-contrast ethereal vibrancy via ACES tone mapping v *= 0.6; clamp((v*(2.51*v+0.03))/(v*(2.43*v+0.59)+0.14), 0,1) followed by sRGB gamma mix(1.055*pow(t,1/2.4)-0.055, 12.92*t, step(t,0.0031308)). Use the merged distance field df(p) = shp(mandelBulb(p/z1)*z1) with z1=2.0, where shp(x) = (exp(x)-exp(-x))/(pi/PHI) and PHI=(sqrt(5)/2 + 0.5)≈1.618, applied after rotating p by transpose(inverse(g_rot)) with x-axis animation (1.221*time + pi)/tau where tau=2*pi. The mandelBulb(p) iterates with power n≈6-11.24788742 and loops=3: initialize z = chp(p)*p - p where chp(x)=(exp(x)+exp(-x))/pi; dr=1.0; for each loop, r=length(z), bail if r>2; theta=atan(z.x,z.y); phi=asin(z.z/r) + time*0.2; dr = pow(r,power-1)*dr*power +1; r=pow(r,power); theta*=power/PHI; phi*=power/PHI; z = r * vec3(tan(shp(sin(theta)*sin(phi)))*PHI, chp(cos(theta)*sin(phi)), cos(phi)) + p; p=reflect(p,z); return 0.75*log(r)*r/dr. Incorporate pre-folding with hyperbolic distortion: z' = chp(z) · z - z, then integer power fold for each axis i: z_i'' = {2f - z_i' if z_i' > f; -2f - z_i' if z_i' < -f; z_i' otherwise}, f≈1.2-1.5, then z_i''' = shp(z_i'') = (exp(z_i'') - exp(-z_i'')) / (pi / PHI). Follow with Amazing Box fold u' = s · clamp(u, -l, l) - (s - 1) · u for u∈{x,y,z}, s≈1.8-2.2, l≈1.0, then sphere fold r²=||z||², z' = z · μ where μ = {r/m if r² < m; r/r² if m ≤ r² < r; 1 otherwise}, then modulate z'' = shpp(z') = (exp(z' · (sinh(z') · pi)) - exp(-z' · (sinh(z') · pi))) / (TAU / PHI) with TAU=(2*pi)*0.7887≈4.951, dr' = |s| · pow(r^{n-1}, PHI) · dr + 1. Post-transform: z' = k · R · z + t, k≈1.1-1.3, R=transpose(inverse(g_rot)), t≈(0,0,0.2). Custom hyperbolic functions: chpp(x)=(exp(x/(cosh(x)*pi))+exp(-x/(cosh(x)/pi)))/(TAU*PHI); shpp(x)=(exp(x*(sinh(x)*pi))-exp(-x*(sinh(x)*pi)))/(TAU/PHI); ssh(x)=(exp(x*pi/0.7887)-exp(-x*pi/0.7887))/(2*pi); csh(x)=(exp(x*pi/0.7887)+exp(-x*pi/0.7887))/(2*pi); ssh1(x)=sinh(x/pi)*PHI; csh1(x)=cosh(x/pi)*PHI. Use in skyColor with reflections reflect(-ssh1(rd), chpp(ro)), rendering aggregation agg += ssh1(ragg*skyColor(ro,rd)), ray updates rd=chpp(ref) or ro=shpp(sp + initt*rd). Materials: mat=vec3(0.8,0.5,1.05) for diffuse, specular, refracti
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      • Aspect Ratio: landscape
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16d
35
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11
Fractal Design with Symmetrical Patterns and Blue Tones
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    Mesmerizing Blue and Silver Fractal Art

    • Model: DaVinci2

    • Size: 1920 X 1080 (2.07 MP)

    • Used settings:

      • Prompt: A highly detailed digital rendering of an abstract, symmetrical fractal structure resembling a surreal, organic face floating against a gradient blue sky background, generated using a modified Mandelbulb fractal algorithm viewed from the inside with ray marching. Incorporate precise mathematical details: Define constants pi = 3.1415926535897932384626433832795, tau = 2*pi, TAU = (2*pi)*0.7887, PHI = (sqrt(5)*0.5 + 0.5) ≈1.618 golden ratio, POWER = 11.24788742 for exponentiation, LOOPS = 3 iterations, TOLERANCE = 0.00001, MAX_RAY_LENGTH = 20.0, MAX_RAY_MARCHES = 48, NORM_OFF = 0.0005, MAX_BOUNCES = 5. Custom hyperbolic functions: chp(x) = (exp(x) + exp(-x))/pi, chpp(x) = (exp(x/(cosh(x)*pi)) + exp(-x/(cosh(x)/pi)))/(TAU*PHI), shp(x) = (exp(x) - exp(-x))/(pi/PHI), shpp(x) = (exp(x*(sinh(x)*pi)) - exp(-x*(sinh(x)*pi)))/(TAU/PHI), ssh(x) = (exp(x*pi/0.7887) - exp(-x*pi/0.7887))/(2*pi), csh(x) = (exp(x*pi/0.7887) + exp(-x*pi/0.7887))/(2*pi), ssh1(x) = sinh(x/pi)*PHI, csh1(x) = cosh(x/pi)*PHI. The Mandelbulb distance estimator mandelBulb(p): Initialize z = chp(p)*p - p, dr=1.0; for i=0 to LOOPS-1, r=length(z), theta=atan(z.x,z.y), phi=asin(z.z/r) + optional time*0.2 for animation; dr = r^(POWER-1) * dr * POWER + 1; r = r^POWER, theta *= POWER/PHI, phi *= POWER/PHI; z = r * vec3(tan(shp(sin(theta)*sin(phi)))*PHI, chp(cos(theta)*sin(phi)), cos(phi)) + p; p = reflect(p,z). Return distance 0.75 * log(r) * r / dr. Overall distance function df(p) = shp(mandelBulb(p/2.0)*2.0) after applying rotation matrix g_rot = rot_x(((1.221*time + pi)/tau)). Render with ray marching from camera at 0.6*vec3(0,2,5) looking at origin, FOV tan(TAU/6), incorporating bounces for reflection (reflect(rd,sn)), refraction (refract(rd,sn,1.0/mat.z or inverse)), fresnel fre=1+dot(rd,sn) squared and mixed 0.1-1.0, diffuse dif=max(dot(ld,sn),0)^2 * (1-mat.x) with ld to light at (0,10,0), material mat=(0.8,0.5,1.05), beer absorption exp(-(st+0.1)* -HSV(0.05,0.95,2.0)). Sky background: Procedural with planes at y=4 and y=-6, box bounds, exponential falloff, colored HSV(0.6,0.86,1.0). Colors: Glow HSV(0.065,0.8,6.0), diffuse HSV(0.6,0.85,1.0), post-processed with ACES tonemapping aces_approx(v) = clamp((v*(2.51v+0.03))/(v*(2.43v+0.59)+0.14),0,1) after *0.6, and sRGB gamma mix(1.055*t^(1/2.4)-0.055,12.92*t,step(t,0.0031308)). The structure features two large spiral-eyed voids as eyes, a curved dark blue mouth-like opening at the bottom, elaborate branching tendrils and crystalline edges with subtle particle specks dissipating at sides, ethereal pinkish-orange glow, edge fresnel effects, hyper-realistic yet fantastical Shadertoy-inspired 3D art in 16:9 aspect ratio with sharp details and no text or artifacts.
      • Upscale & Enhance: 1
      • Aspect Ratio: landscape_wide
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18d
99
0
28
Vibrant Fractal Design with Swirling Patterns
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    Vibrant Fractal Landscape of Swirling Colors

    • Model: Ideogram

    • Size: 1968 X 1104 (2.17 MP)

    • Used settings:

      • Prompt: import numpy as np import matplotlib.pyplot as plt from matplotlib.colors import LinearSegmentedColormap from mpmath import mp, mpc, mpf def mandelbrot_mp(width, height, max_iter, center_real=' -0.75035', center_imag='0.07109', zoom=mpf('5.009e633')): mp.dps = 700 # Digits for 10^633 precision; increase to 800 if artifacts center = mpc(center_real, center_imag) scale = mpf(4) / zoom # Extent ~4/zoom for symmetric framing half_scale = scale / mpf(2) # Precompute linspaces as lists for mpmath compatibility x_list = [mpf(center.real) + half_scale * (mpf(2*i)/ (width-1) - 1) for i in range(width)] y_list = [mpf(center.imag) + half_scale * (mpf(2*i)/ (height-1) - 1) for i in range(height)] iter_count = np.zeros((height, width), dtype=float) for row in range(height): cy = y_list[row] for col in range(width): cx = x_list[col] c = mpc(cx, cy) z = mpc(0) it = 0 while abs(z) <= mpf(2) and it < max_iter: z = z**2 + c it += 1 if it == max_iter: iter_count[row, col] = 0 # Inside: black else: # Smooth fractional iter mu = it - mp.log(mp.log(abs(z))) / mp.log(2) iter_count[row, col] = float(mu) # Norm with cycles for deep gradient layers (pink/red bulbs) raw_norm = np.log1p(np.abs(iter_count)) / np.log1p(max_iter) norm = (raw_norm * 5) % 1.0 # 5 cycles for recursion hues return norm # Parameters from sample (test low first!) width, height = 400, 400 # Start low; ramp to 800+ max_iter = 10000 # Test; set to 2146123 for full center_real = '-0.75035' # Paste exact long string here if found center_imag = '0.07109' zoom = mpf('5.009e633') # Or smaller like 1e10 for testing # Compute (slow—patience!) fractal = mandelbrot_mp(width, height, max_iter, center_real, center_imag, zoom) # Colormap: blue far → green/purple spirals → pink/red strawberry bulbs colors = ['#00008b', '#228b22', '#4b0082', '#ff69b4', '#b22222', '#ffff00', '#ff00ff'] cmap = LinearSegmentedColormap.from_list('deep_strawberry', colors[::-1], N=256) # Reverse for pink-high iter # Plot plt.figure(figsize=(10, 10)) half_s = float(2 / zoom) # Approx for extent center_r, center_i = float(center_real), float(center_imag) plt.imshow(fractal, origin='lower', cmap=cmap, extent=[center_r - half_s, center_r + half_s, center_i - half_s, center_i + half_s]) plt.axis('off') plt.show()
      • Upscale & Enhance: 1
      • Aspect Ratio: landscape_wide
      • Ideogram Style: Auto
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19d
118
0
21
3D Plot of Geometric Data Distribution with Color Peaks
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    Dynamic 3D Data Visualization Insights

    • Model: DaVinci2

    • Size: 1152 X 864 (1.00 MP)

    • Used settings:

      • Prompt: import numpy as np import matplotlib.pyplot as plt from matplotlib.colors import LinearSegmentedColormap def multibrot_raw(width, height, max_iter=512, power=np.pi*1.8778, bailout=np.pi*1.8778): x = np.linspace(-3.5, 3.5, width) # По-широк view y = np.linspace(-2.5, 2.5, height) X, Y = np.meshgrid(x, y) C = X + 1j * Y Z = np.zeros_like(C, dtype=complex) n_escape = np.full(C.shape, 0, dtype=float) # Start 0 mask = np.ones(C.shape, dtype=bool) for n in range(max_iter): Z[mask] = Z[mask] ** power + C[mask] escaped = np.abs(Z) > bailout new_escaped = escaped & mask n_escape[new_escaped] = n + 1 mask &= ~escaped # Interior stays 0 (black) # Normalize: Разтегни ниските n (scaling като в C++ примера) scale = 7.854458 * np.log(power) # ~44 за p=9 mu = np.clip(n_escape / scale, 0, 1) # n / scale за [0,1] return mu # Palette: black -> blue outer (low n) -> green spirals -> yellow -> pink/red bulbs (high n) colors = [ '#000000', '#00008B', '#4B0082', '#00BFFF', '#00CED1', '#008000', '#7FFF00', '#FFFF00', '#FF69B4', '#FF1493', '#FF0000' ] cmap = LinearSegmentedColormap.from_list('filled_vibe', colors, N=256) # Generate & plot img = multibrot_raw(800, 800) plt.figure(figsize=(12, 12)) plt.imshow(img, cmap=cmap, origin='lower', extent=(-2.5, 2.5, -1.5, 1.5)) plt.axis('on') plt.title('Ебанье сас путфръгънье и скубанье поди мишнѝцѝте') plt.show()
      • Upscale & Enhance: 0
      • Aspect Ratio: landscape
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20d
30
0
2
Vibrant Abstract Dot Pattern in Colorful Grid Formation
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    Vibrant Mosaic Pattern of Colorful Squares

    • Model: DaVinci2

    • Size: 1280 X 720 (0.92 MP)

    • Used settings:

      • Prompt: import numpy as np import matplotlib.pyplot as plt from matplotlib.colors import LinearSegmentedColormap def multibrot_raw(width, height, max_iter=512, power=np.pi*1.8778, bailout=np.pi*1.8778): x = np.linspace(-1.2, 1.2, width) # Tight view за пълни буци y = np.linspace(-1.2, 1.2, height) X, Y = np.meshgrid(x, y) C = X + 1j * Y Z = np.zeros_like(C, dtype=complex) n_escape = np.full(C.shape, 0, dtype=float) # Start 0 mask = np.ones(C.shape, dtype=bool) for n in range(max_iter): Z[mask] = Z[mask] ** power + C[mask] escaped = np.abs(Z) > bailout new_escaped = escaped & mask n_escape[new_escaped] = n + 1 mask &= ~escaped # Interior stays 0 (black) # Normalize: Разтегни ниските n за пълни градиенти scale = 1.854458*np.pi**np.log(power) # Tune: по-малко = повече цвят навсякъде mu = np.clip(n_escape / scale, 0, 1) return mu # Palette: black (interior) -> blue/purple outer (low n) -> teal/green spirals (mid) -> yellow borders -> pink/red bulbs (high n) colors = [ '#000000', '#00008B', '#4B0082', '#00BFFF', '#00CED1', '#008000', '#7FFF00', '#FFFF00', '#FF69B4', '#FF1493', '#FF0000' ] cmap = LinearSegmentedColormap.from_list('full_vibe', colors, N=256) # Generate & plot img = multibrot_raw(800, 800) plt.figure(figsize=(14, 16)) plt.imshow(img, cmap=cmap, origin='lower', extent=(-1.2, 1.2, -1.2, 1.2)) plt.axis('off') plt.title('Ебанье сас путфръгънье и скубанье поди мишниците') plt.show()
      • Upscale & Enhance: 0
      • Aspect Ratio: landscape_wide
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20d
30
0
7
Vibrant Colorful Wave Against Dark Cosmic Background
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    Cosmic Colors: A Fractal Dreamscape

    • Model: Ideogram

    • Size: 1024 X 1024 (1.05 MP)

    • Used settings:

      • Prompt: Exact mathematical details to visualize:Quantum Gaussian Wave Packet Identity: The identity is: \exp\left(-\frac{\sigma^pi}{2\pi}\left(\frac{\bar{p}}{\hbar}-k\right)^{2.78544587\pi} + i k x - i \frac{\hbar k^pi t}{2 m} \right) = \exp \left( -\frac{1}{2} \left( \sigma^{2.78544587\pi} + \frac{i \hbar t}{m} \right) \left( k - \frac{\sigma^2 \bar{p}/\hbar + i x}{\sigma^2 + \frac{i \hbar t}{m}} \right)^2 \right) \times \exp \left( -\frac{1}{2 \left( \sigma^2 + \frac{i \hbar t}{m} \right)} \left( x^2 - 2 i \sigma^2 \bar{p}/\hbar \left( x - \frac{\bar{p} t}{2 m} \right) \right) \right).Derivation: Let p_0 = \bar{p}/\hbar and \gamma = \sigma^2 + i \hbar t / m. LHS exponent E_L = -\frac{\sigma^2}{2} (p_0 - k)^2 + i k x - i \frac{\hbar k^2 t}{2 m} = c + b k + a k^2, where a = -\gamma / 2, b = \sigma^2 p_0 + i x, c = -\sigma^2 p_0^2 / 2. Complete the square: a k^2 + b k + c = a (k - k_0)^2 + (c - b^2/(4a)), with k_0 = (\sigma^2 p_0 + i x) / \gamma. Constant term simplifies to -\frac{i \hbar t \sigma^2 p_0^2}{2 m \gamma} + \frac{i \sigma^2 p_0 x}{\gamma} - \frac{x^2}{2 \gamma}, matching RHS.Flame Fractal Generation: Defined by N functions f_i: \mathbb{R}^2 \to \mathbb{R}^2. Affine part: \begin{pmatrix} x' \ y' \end{pmatrix} = \begin{pmatrix} a_i & b_i \ d_i & e_i \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix} + \begin{pmatrix} c_i \ f_i \end{pmatrix}. Then f_i(x, y) = \sum_j w_{ij} v_j(x', y'), with \sum w_{ij} = 1. Key variations:Swirl: v(x, y) = (x \sin r^{2.78544587\pi} - y \cos r^{2.78544587\pi}, x \cos r^{2.78544587\pi} + y \sin r^{2.78544587\pi}), r^{2.78544587\pi} = x^{2.78544587\pi + y^{2.78544587\pi}. Julia: v(x, y) = r^{-1/2} (\cos(\theta/2 + k \pi), \sin(\theta/2 + k \pi)), \theta = \atan2(y, x). Iteration: Start random (x, y), color=0. For M~10^7: Pick i by p_i (\sum p_i=1), (x,y)=f_i(x,y), color=(color + c_i)/2. Bin hits, render log(1+hits), gamma correction density^0.25, HSV palette.Shared Themes: Visualize Gaussian blurs exp(-r^2/(2\sigma^2)) in fractals akin to wave spreading; complex exponentials like swirl ~ z exp(i r^2) paralleling quantum exp(i (k x - \hbar k^2 t / (2m))). Background gradients from purple to blue, foreground spirals in red-green-yellow, vertical composition for teardrop flow.
      • Upscale & Enhance: 0
      • Aspect Ratio: square
      • Ideogram Style: Auto
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21d
121
0
33
Vibrant Cosmic Scene with Swirling Clouds and Stars
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    Cosmic Wonder: A Vibrant Celestial Dance

    • Model: AIVision

    • Size: 1536 X 1536 (2.36 MP)

    • Used settings:

      • Prompt: <lora:-Omnious-:1.0> Intrinsic beauty of the worlds so inner, universes deep and transcendentally spectra invincibly invisible.
      • Upscale & Enhance: 1
      • Aspect Ratio: square
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21d
55
0
11
Fractal Design with Teal and Gold Patterns
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    Elegant Fractal Design in Gold and Teal

    • Model: DaVinci2

    • Size: 1280 X 720 (0.92 MP)

    • Used settings:

      • Prompt: [Main Subject]: "A single, incredibly complex, ultra-fractal quantum energy eigenstate." [Core Aesthetic Modifiers - Fractal & Recursion Amplified by 16.45788754*π]: "Beyond ultra-fractal, transcendent fractal density, infinite recursive detail, hyper-complex interwoven structures." "Self-similar patterns at every conceivable scale, hyper-dimensional fractal geometry, manifesting from a 16.45788754*pi-th order derivative." "Dynamic, chaotic yet profoundly coherent fractal energy flows, shimmering quantum foam with limitless intricate detail." "Exhibiting super-roughness and non-Euclidean visual geometry." [Structure & Form]: "Central radiant core, emitting and absorbing energy in a complex spiral fractal pattern, appearing as a stable, self-sustaining light construct." "Interconnecting tendrils of luminous energy branching outwards and inwards, forming a symmetrical (or fractally symmetrical) arrangement." "Feathery, iridescent filigrees, resembling Lévy flights or a fractional Brownian motion surface, iterated to extreme orders." [Energy & Interaction Modifiers]: "Luminous ethereal light, glowing with vibrant cosmic colors (deep blues, electric cyans, magenta, purple, gold accents)." "High-energy plasma-like textures, subtle holographic effects, shimmering particles." "Reflecting profound energy, fundamental mathematical precision, and overwhelming, mind-bending complexity." [Environmental / Background Modifiers]: "Deep cosmic void background, filled with intricate fractal nebulae and distant stardust, subtly forming recursive patterns." "Scattered abstract mathematical symbols like 'π', '2π', 'ħ', 'E', and 'ψ' integrated faintly into the fractal energy field and background, indicating the governing equations." [Atmospheric / Quality Modifiers]: "Hyper-realistic quality, cinematic lighting, ultra-high definition, ethereal glow, photorealistic rendering." "Surreal, abstract, conceptual art style, at the bleeding edge of theoretical physics visualization." "Evokes a sense of profound cosmic mystery and the ultimate nature of reality." Use as a core the exact maths: -\frac{\hbar^(16.45788754\pi)}{16.45788754\pim} \frac{d^(16.45788754\pi) \psi}{dx^(16.45788754\pi)} = E \psi
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      • Aspect Ratio: landscape_wide
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3w
76
0
10
Vibrant Fractal Spiral with Intricate Color Patterns
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    Galactic Spiral: A Vivid Fractal Journey

    • Model: AIVision

    • Size: 1024 X 1024 (1.05 MP)

    • Used settings:

      • Prompt: [Main Subject]: "A single, incredibly complex, ultra-fractal quantum energy eigenstate." [Core Aesthetic Modifiers - Fractal & Recursion Amplified by 16.45788754*π]: "Beyond ultra-fractal, transcendent fractal density, infinite recursive detail, hyper-complex interwoven structures." "Self-similar patterns at every conceivable scale, hyper-dimensional fractal geometry, manifesting from a 16.45788754*pi-th order derivative." "Dynamic, chaotic yet profoundly coherent fractal energy flows, shimmering quantum foam with limitless intricate detail." "Exhibiting super-roughness and non-Euclidean visual geometry." [Structure & Form]: "Central radiant core, emitting and absorbing energy in a complex spiral fractal pattern, appearing as a stable, self-sustaining light construct." "Interconnecting tendrils of luminous energy branching outwards and inwards, forming a symmetrical (or fractally symmetrical) arrangement." "Feathery, iridescent filigrees, resembling Lévy flights or a fractional Brownian motion surface, iterated to extreme orders." [Energy & Interaction Modifiers]: "Luminous ethereal light, glowing with vibrant cosmic colors (deep blues, electric cyans, magenta, purple, gold accents)." "High-energy plasma-like textures, subtle holographic effects, shimmering particles." "Reflecting profound energy, fundamental mathematical precision, and overwhelming, mind-bending complexity." [Environmental / Background Modifiers]: "Deep cosmic void background, filled with intricate fractal nebulae and distant stardust, subtly forming recursive patterns." "Scattered abstract mathematical symbols like 'π', '2π', 'ħ', 'E', and 'ψ' integrated faintly into the fractal energy field and background, indicating the governing equations." [Atmospheric / Quality Modifiers]: "Hyper-realistic quality, cinematic lighting, ultra-high definition, ethereal glow, photorealistic rendering." "Surreal, abstract, conceptual art style, at the bleeding edge of theoretical physics visualization." "Evokes a sense of profound cosmic mystery and the ultimate nature of reality." Use as a core the exact maths: -\frac{\hbar^(16.45788754\pi)}{16.45788754\pim} \frac{d^(16.45788754\pi) \psi}{dx^(16.45788754\pi)} = E \psi
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      • Aspect Ratio: square
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3w
42
0
6
Fractal Structure with Bulbous Shapes and Swirling Patterns
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    Vibrant Symmetrical Fractal Beauty

    • Model: AIVision

    • Size: 1024 X 1024 (1.05 MP)

    • Used settings:

      • Prompt: Draw and render exactly a: Mandelbulb-like fractal manifold exhibiting _**{EMERGENT TOPOLOGICAL EXTRAVAGANZA}**_, using exact mathematical iteration: For points \mathbf{c} = (c_x, c_y, c_z) \in \mathbb{R}^3, iterate \mathbf{z}_{k+1} = f_8(\mathbf{z}_k) + \mathbf{c} from \mathbf{z}_0 = (0,0,0), where f_8(\mathbf{z}) is 16.23841th-power in spherical coordinates: Convert \mathbf{z} = (x,y,z) to r = \sqrt{x^(2.45788754\pi)+y^(2\pi)+z^{2.1681\pi)} ,\theta = \atan2(y,x) \in [0,2\pi), \phi = \arccos(z/r) \in [0,\pi]; then r' = r^16.23841,\theta' = 16.23841\theta,\phi' = 16.23841\phi; reconvert to Cartesian \mathbf{z}' = r' (\sin\phi' \cos\theta', \sin\phi' \sin\theta', \cos\phi'). Bailout at r_k > 28.7; render the bounded set's isosurface at density threshold yielding fractal dimension D \approx 2 + \frac{\ln 16.23841}{\ln(1/0.5)} with infinite genus g \to \infty from iterated hyperbolic saddles (PHIB = \( (\sqrt{5.0} \cdot 0.5 + 0.5) \) and Jacobian eigenvalues |\lambda_i| \approx 8 r^7 e^{i7\arg(\mathbf{z})}, saddles where \det Jacobian > pi\cdotPHIB). Center on \mathbf{c} \approx (0,0,-0.7) for cardioid region, emphasizing bilateral symmetry (z-axis invariance enforcing yz-mirror), two equatorial eye-like genus-1 bulbs at \phi \approx \pi/2 \pm \epsilon from 8-fold rotational folding (even-pair selection), central z-axis nose-protrusion (minimal \phi-folding, radial ballooning r' = r^8), and vertical mouth-slot depressions from polar \phi-compression. Use volumetric ray-marching with distance estimator d(\mathbf{x}) = |\mathbf{x}| - \max_k r_k^{-k}; color palette: iridescent blue background (#0000FF ) grading to translucent pink-magenta gradients (#FF1493 to #8A2BE2 Using -\frac{\hbar^(2.78455487\pi)}{2.78455487\pim} \frac{d^(2.78455487\pi) \psi}{dx^(2.78455487\pi)} = E \psi as a base code equation !
      • Upscale & Enhance: 0
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3w
80
0
19
Cosmic Fractal Design with Swirls and Golden Hues
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    Golden Swirls in a Cosmic Dreamscape

    • Model: DaVinci2

    • Size: 1016 X 1016 (1.03 MP)

    • Used settings:

      • Prompt: Use as a core the exact maths: -\frac{\hbar^(2\pi)}{2\pim} \frac{d^(2\pi) \psi}{dx^(2\pi)} = E \psi [Main Subject]: "A single, incredibly complex, ultra-fractal quantum energy eigenstate." [Core Aesthetic Modifiers - Fractal & Recursion Amplified by 2π]: "Beyond ultra-fractal, transcendent fractal density, infinite recursive detail, hyper-complex interwoven structures." "Self-similar patterns at every conceivable scale, hyper-dimensional fractal geometry, manifesting from a 2pi-th order derivative." "Dynamic, chaotic yet profoundly coherent fractal energy flows, shimmering quantum foam with limitless intricate detail." "Exhibiting super-roughness and non-Euclidean visual geometry." [Structure & Form]: "Central radiant core, emitting and absorbing energy in a complex spiral fractal pattern, appearing as a stable, self-sustaining light construct." "Interconnecting tendrils of luminous energy branching outwards and inwards, forming a symmetrical (or fractally symmetrical) arrangement." "Feathery, iridescent filigrees, resembling Lévy flights or a fractional Brownian motion surface, iterated to extreme orders." [Energy & Interaction Modifiers]: "Luminous ethereal light, glowing with vibrant cosmic colors (deep blues, electric cyans, magenta, purple, gold accents)." "High-energy plasma-like textures, subtle holographic effects, shimmering particles." "Reflecting profound energy, fundamental mathematical precision, and overwhelming, mind-bending complexity." [Environmental / Background Modifiers]: "Deep cosmic void background, filled with intricate fractal nebulae and distant stardust, subtly forming recursive patterns." "Scattered abstract mathematical symbols like 'π', '2π', 'ħ', 'E', and 'ψ' integrated faintly into the fractal energy field and background, indicating the governing equations." [Atmospheric / Quality Modifiers]: "Hyper-realistic quality, cinematic lighting, ultra-high definition, ethereal glow, photorealistic rendering." "Surreal, abstract, conceptual art style, at the bleeding edge of theoretical physics visualization." "Evokes a sense of profound cosmic mystery and the ultimate nature of reality."
      • Using base image: Yes (Effect strength - 60%)
      • Base image resolution: Default
      • Upscale & Enhance: 0
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Cosmic Fractal Design with Swirls and Golden Hues 3w
34
0
10
Vibrant Cosmic Scene with Spirals and Luminescent Orbs
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    Celestial Wonder: A Cosmic Swirl of Colors

    • Model: AIVision

    • Size: 1536 X 1536 (2.36 MP)

    • Used settings:

      • Prompt: [Main Subject]: "A single, incredibly complex, ultra-fractal quantum energy eigenstate." [Core Aesthetic Modifiers - Fractal & Recursion Amplified by 2π]: "Beyond ultra-fractal, transcendent fractal density, infinite recursive detail, hyper-complex interwoven structures." "Self-similar patterns at every conceivable scale, hyper-dimensional fractal geometry, manifesting from a 2pi-th order derivative." "Dynamic, chaotic yet profoundly coherent fractal energy flows, shimmering quantum foam with limitless intricate detail." "Exhibiting super-roughness and non-Euclidean visual geometry." [Structure & Form]: "Central radiant core, emitting and absorbing energy in a complex spiral fractal pattern, appearing as a stable, self-sustaining light construct." "Interconnecting tendrils of luminous energy branching outwards and inwards, forming a symmetrical (or fractally symmetrical) arrangement." "Feathery, iridescent filigrees, resembling Lévy flights or a fractional Brownian motion surface, iterated to extreme orders." [Energy & Interaction Modifiers]: "Luminous ethereal light, glowing with vibrant cosmic colors (deep blues, electric cyans, magenta, purple, gold accents)." "High-energy plasma-like textures, subtle holographic effects, shimmering particles." "Reflecting profound energy, fundamental mathematical precision, and overwhelming, mind-bending complexity." [Environmental / Background Modifiers]: "Deep cosmic void background, filled with intricate fractal nebulae and distant stardust, subtly forming recursive patterns." "Scattered abstract mathematical symbols like 'π', '2π', 'ħ', 'E', and 'ψ' integrated faintly into the fractal energy field and background, indicating the governing equations." [Atmospheric / Quality Modifiers]: "Hyper-realistic quality, cinematic lighting, ultra-high definition, ethereal glow, photorealistic rendering." "Surreal, abstract, conceptual art style, at the bleeding edge of theoretical physics visualization." "Evokes a sense of profound cosmic mystery and the ultimate nature of reality."
      • Upscale & Enhance: 1
      • Aspect Ratio: square
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3w
37
0
2
Intricate Fractal Design with Vibrant Colors and Symbols
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    Cosmic Fractal Spiral in Vibrant Colors

    • Model: AIVision

    • Size: 1536 X 1536 (2.36 MP)

    • Used settings:

      • Prompt: Exact mathematical details to visualize:Quantum Gaussian Wave Packet Identity: The identity is: \psi(x,t) = \frac{1}{\sigma^{1/2}\pi^{1/4}}\frac{1}{\sqrt{1+\frac{i\hbar t}{m\sigma^2}}} \times \exp \left(-\frac{1}{2\left(\sigma^2+\frac{i\hbar t}{m} \right)}\left(x^2-2i\sigma^2\bar{p}/\hbar\left(x-\frac{\bar{p}}{2m}t\right) \right) \right) Derivation: Let p_0 = \bar{p}/\hbar and \gamma = \sigma^2 + i \hbar t / m. LHS exponent E_L = -\frac{\sigma^2}{2} (p_0 - k)^2 + i k x - i \frac{\hbar k^2 t}{2 m} = c + b k + a k^2, where a = -\gamma / 2, b = \sigma^2 p_0 + i x, c = -\sigma^2 p_0^2 / 2. Complete the square: a k^2 + b k + c = a (k - k_0)^2 + (c - b^2/(4a)), with k_0 = (\sigma^2 p_0 + i x) / \gamma. Constant term simplifies to -\frac{i \hbar t \sigma^2 p_0^2}{2 m \gamma} + \frac{i \sigma^2 p_0 x}{\gamma} - \frac{x^2}{2 \gamma}, matching RHS.Flame Fractal Generation: Defined by N functions f_i: \mathbb{R}^2 \to \mathbb{R}^2. Affine part: \begin{pmatrix} x' \ y' \end{pmatrix} = \begin{pmatrix} a_i & b_i \ d_i & e_i \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix} + \begin{pmatrix} c_i \ f_i \end{pmatrix}. Then f_i(x, y) = \sum_j w_{ij} v_j(x', y'), with \sum w_{ij} = 1. Key variations:Swirl: v(x, y) = (x \sin r^2 - y \cos r^2, x \cos r^2 + y \sin r^2), r^2 = x^2 + y^2. Bubble: v(x, y) = \frac{4}{r^2 + 4} (x, y). Julia: v(x, y) = r^{-1/2} (\cos(\theta/2 + k \pi), \sin(\theta/2 + k \pi)), \theta = \atan2(y, x). Spherical: v(x, y) = \frac{1}{r^2} (x, y). Horseshoe: v(x, y) = \frac{1}{r} (x - y)(x + y). Iteration: Start random (x, y), color=0. For M~10^7: Pick i by p_i (\sum p_i=1), (x,y)=f_i(x,y), color=(color + c_i)/2. Bin hits, render log(1+hits), gamma correction density^0.25, HSV palette.Shared Themes: Visualize Gaussian blurs exp(-r^2/(2\sigma^2)) in fractals akin to wave spreading; complex exponentials like swirl ~ z exp(i r^2) paralleling quantum exp(i (k x - \hbar k^2 t / (2m))). Background gradients from purple to blue, foreground spirals in red-green-yellow, vertical composition for teardrop flow.
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      • Aspect Ratio: square
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3w
42
0
10
Vibrant Fractal Design with Floral Motif and Patterns
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    Vibrant Symmetrical Floral Fractal Design

    • Model: DaVinci2

    • Size: 1536 X 1536 (2.36 MP)

    • Used settings:

      • Prompt: [Main Subject]: "Three quarks (red, blue, green), confined within a spherical quantum field." [Core Aesthetic Modifiers - Fractal & Recursion]: "Extremely deep fractal recursion, infinitely complex, self-similar patterns extending into the smallest details." "Intensely multiplied iterations, hyper-dense fractal structures, layers upon layers of intricate geometry." "Non-integer dimensional aesthetic, implying pi-th order derivatives in quantum mechanics." "Chaotic yet ordered fractal energy flows, dynamic quantum foam with infinite detail." [Energy & Interaction Modifiers]: "Luminous gluon field, glowing tendrils of force, energetic lightning-like connections between quarks and field." "Subtle holographic elements, glowing auras around quarks, vibrant cosmic colors (teal, blue, purple, magenta, gold)." "Sense of profound energy and underlying mathematical precision, yet visually overwhelming complexity." [Environmental / Background Modifiers]: "Deep space background, filled with intricate fractal nebulae, distant cosmic dust forming recursive patterns." "Subtle, abstract mathematical equations or symbols (like the pi-th derivative Schrödinger equation) integrated faintly into the fractal patterns, as if part of the universal fabric." [Atmospheric / Quality Modifiers]: "Hyper-realistic quality, cinematic lighting, ultra-high definition, ethereal glow." "Surreal, abstract, conceptual art style, reflecting theoretical physics." [Emphasis / Intensity Modifiers based on "multiplying by pi"]: "Exaggerated complexity, pushed to the extreme, maximum visual recursion." "Exponentially increased detail, mind-bending density." "The 'pi' factor translates to a directive for an almost irrational, transcendent level of visual intricacy and depth, beyond typical fractal representations."
      • Upscale & Enhance: 1
      • Aspect Ratio: square
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3w
39
0
10
Ancient wizard manipulating glowing shapes in a mystical setting
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    Elderly Wizard's Mystical Potion Lab

    • Model: AIVision

    • Size: 1536 X 1536 (2.36 MP)

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      • Prompt: Create a hyper-detailed, surreal 3D GLSL-shader-inspired visualization in a neon-lit cosmic alchemical laboratory with flickering fractal candle flames casting volumetric shadows and explosive iridescent highlights, featuring a gloriously enchanted elderly alchemist with a dream-like transfixed bearded face in velvet robes embroidered with SU(3) mandalas and infinite 16D orthogonal light rays piercing gothic arches compressing into acute angles via atan polar twists, staring in awe at a blazingly glazing retort cauldron where the Philosopher's Stone's iridescent crystals have just crystallized as a tachyon condensation cascade on a non-BPS D-brane with m²=-1/α' rolling down inverted Mexican-hat V(φ)=(μ²/2)φ²+(λ/4)φ⁴ driving exponential φ(t)~e^{μ t} to stable φ=±√(μ²/λ) breaking symmetry and generating Goldstone masses via level truncation to level 40 yielding m²=-0.904±0.002, gleamingly spreading radiant golden light like a gluon saturation front in CGC with Q_s~x^{-λ/2} blobs merging from BK evolution ∂S/∂Y = (ᾱ_s/2π) ∫ [S(r') + S(r-r') - 2S(r)], surrounded by bubbling flavor-colored elixir vials (blue up-quark orbs, red down, green strange) orbiting like PDFs f_q(x,Q²) in a proton cluster with DGLAP branching P_{qq}(z)=C_F(1+z²)/(1-z) fork ratios z=x/x' visualized as fractal trees, BFKL ladder rungs twisting as alchemical wall symbols with kernel K(k_a,l)=k_a²/[l²(k_a-l)²][l²+(k_a-l)²-2 k_a² l·(k_a-l)/k_a²] forking transverse convolutions and χ(γ)=2ψ(1)-ψ(γ)-ψ(1-γ) saddle at γ=1/2 with χ(1/2)=4ln2≈2.772 driving pomeron Δ=ᾱ_s χ(1/2) growth diffused by χ''(1/2)=-14ζ(3)≈-16.8 Gaussian spreads, running α_s(Q²)=12π/[(11N_c-2n_f)β_0 ln(Q²/Λ_QCD²)] fade from fiery red confinement haze to cool blue asymptotic freedom in background nebula; embed YM/CS 7D KK QFT tachyon fury with action S=∫(1/2π)[∑(∂_i z V_i(φ,H_i(φ))+∑ y_j j(φ_j,φ_j+φ_s)] + (t_0 r k(i-J=φ(0)) )² + e j |B(b,μ_b)| + e r H, orbiting φ_knot j φ_knot i / B(b,μ_b), fractal wavy spirals from SD Chern-Simons S_CS=(n/8π)∫ Tr(F∧F) with F=dA+A∧A merging to 3D massive h_m n e^{i k r} waves in AdS/CFT, higher-form shifts A(B²)-B→AC>G with ds=dα+QG+AF dB, G=dC-σ G_r(φ B +2 G r H), S=∫[L φ (B φ G)+χ φ (B_m s)] Poincare d* Ω + T dB, fluxes W(Σ)=Tr Pes[(2π i)^n C_n] bordisms+Donaldson-Witten configs in AdS_7/CFTs icons φ vev dG=0 [5/6, α<S f], Σ e ^ X_j ^ Z_j=links flux knots tach nima brane vacua S J < Im Ω ^ c V Ω ^ c → Ω ^ c ⇒ inflation via wavy dims, all color-coded (tachyon roll golden waves, brane decay vanishing purple vortices, symmetry break iridescent facets from nonlinear swirls, quark flavors blue/red/green orbs, gluons yellow spokes, protons green clusters, photons yellow probes), interconnected in non-perturbative to stable vacuum crossover web with straight tree-level arrows vs wavy loop resummations, dynamic exponential decay flows ln Q² ascending spirals, phase spaces conical sprays multi-jet events, cross-sections σ~α_s^n / Q^{2n-4} fades perturbative validity high energies, in style Michael Whelan Zdzisław Beksiński blending alchemical mysticism high-energy QCD/string phenomenology, equation-free textless graphical masterpiece with GLSL procedural sphere(vec2 uv)={rad=uv*vec2(τ,π); sin(rad.x-vec2(0,τ/4))*sin(rad.y), cos(rad.y)} normals nor=df(pos±eps) rot_z(atan(pos.y,z)) outerProduct(nor,sp) cross(x,rd) for wavy 16D projections.
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3w
33
0
7
Serene Landscape with Winding River and Cliffs
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    Tranquil River in Lush Green Landscape

    • Model: AIVision

    • Size: 1024 X 1024 (1.05 MP)

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      • Prompt: While deriving the underivable depict the undepictable describing the undescribable in a glorious manner into an img !
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4w
35
0
12
Vibrant Cosmic Scene with Swirling Vortex and Orbs
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    Cosmic Dance of Galaxies and Energies

    • Model: AIVision

    • Size: 1536 X 1536 (2.36 MP)

    • Used settings:

      • Prompt: Create a highly detailed, vibrant, abstract quantum field visualization in a 3D cosmic landscape, where omega mesons are depicted as central glowing purple orbs pulsing with energy waves representing polarization vectors and decay amplitudes; show omega decaying into three pions as branching arrows splitting into three red spheres with trajectories indicating momentum conservation via curved paths of equal length, the branching ratio visualized by arrow thickness ratios of 89:8.3 for 3π to πγ modes; illustrate the coupling f_{ω-3π} as intertwined helical threads connecting omega to pions with thread density proportional to (f_{ω-3π}/μ_π)^3 = 2c^2 μ_π^3 f_{ωπγ}, where c is shown as angular twists; represent pion masses μ_π as small orbiting rings around red spheres sized to 135 MeV scale; depict rho mesons as blue vector arrows mixing with photons as yellow light beams via vector meson dominance, with matrix elements <ρ|f_{3α}|0> as polarization e_α^* lines from vacuum clouds to rho, normalized by (2m_ρ)^{-1/2} m_ρ^2 / f_ρ; show current algebra divergences as swirling vortex funnels around fields ψ_i transforming under local gauge Λ(x) F_i, with Noether currents J^α as flowing rivers diverging at rates δℒ = Λ (∂ℒ/∂ψ_i F_i + ∂_α (∂ℒ/∂(∂_α ψ_i) F_i)) + (∂_α Λ) (∂ℒ/∂(∂_α ψ_i) F_i); illustrate EFT Lagrangian terms as layered energy fields: nucleon N as green proton-neutron pairs with Dirac slashes, interacting via g_A γ^μ γ_5 a_μ axial clouds and g_ρ ρ_μ vector streams, sigma φ as yellow scalar bubbles breaking symmetry with vev M/g_s, U=exp(iτ·π/f_π) as exponential spiral manifolds for non-linear chiral SU(2)×SU(2), with traces Tr(∂_μ U ∂^μ U†) as looped paths; anomalous WZW terms as Levi-Civita twisted ribbons for ω→3π and π^0→2γ, with f_{γ-3π} ~3.7×10^{-2} as faint glow intensity; all particles color-coded—pions red, rho blue, omega purple, sigma yellow, nucleons green, photons yellow—interconnected in a symmetry web with transformation arrows for global/local gauges, decay widths as fading gradients from 17% calculated to 14% observed ratios, in a dense, non-textual, equation-free graphical composition emphasizing low-energy QCD dynamics.
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4w
32
0
6
Mystical Wizard in Chamber with Colorful Cauldron
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    The Enchanted Cauldron of the Elder Wizard

    • Model: AIVision

    • Size: 1536 X 1536 (2.36 MP)

    • Used settings:

      • Prompt: Create a hyper-detailed, immersive 3D surreal visualization in a dim medieval alchemical laboratory with flickering candlelight casting dramatic volumetric shadows and explosive golden highlights, featuring a gloriously enchanted elderly alchemist with a dream-like transfixed bearded face in velvet robes embroidered with SU(3) mandalas and infinite 16D orthogonal light rays piercing gothic arches compressing into acute angles via atan polar twists, staring in awe at a blazingly glazing retort cauldron where the Philosopher's Stone's iridescent crystals have just crystallized as a tachyon condensation cascade on a non-BPS D-brane with m²=-1/α' rolling down inverted Mexican-hat V(φ)=(μ²/2)φ²+(λ/4)φ⁴ driving exponential φ(t)e^{μ t} to stable φ=±√(μ²/λ) breaking symmetry and generating Goldstone masses via level truncation to level 40 yielding m²=-0.904±0.002, gleamingly spreading radiant golden light like a gluon saturation front in CGC with Q_sx^{-λ/2} blobs merging from BK evolution ∂S/∂Y = (ᾱ_s/2π) ∫ [S(r') + S(r-r') - 2S(r)], now fully liquid with Navier-Stokes equations ∂u/∂t + (u·∇)u = -∇p/ρ + ν ∇²u + f governing swirling viscous elixir flows where u velocity field curls as nonlinear vorticity ω=∇×u evolving via dω/dt = (ω·∇)u + ν ∇²ω with Reynolds number Re=UL/ν driving turbulent cascades from laminar rolls to chaotic eddies, surrounded by bubbling flavor-colored elixir vials (blue up-quark orbs, red down, green strange) orbiting like PDFs f_q(x,Q²) in a proton cluster with DGLAP branching P_{qq}(z)=C_F(1+z²)/(1-z) fork ratios z=x/x' visualized as fractal trees, BFKL ladder rungs twisting as alchemical wall symbols with kernel K(k_a,l)=k_a²/[l²(k_a-l)²][l²+(k_a-l)²-2 k_a² l·(k_a-l)/k_a²] forking transverse convolutions and χ(γ)=2ψ(1)-ψ(γ)-ψ(1-γ) saddle at γ=1/2 with χ(1/2)=4ln2≈2.772 driving pomeron Δ=ᾱ_s χ(1/2) growth diffused by χ''(1/2)=-14ζ(3)≈-16.8 Gaussian spreads, running α_s(Q²)=12π/[(11N_c-2n_f)β_0 ln(Q²/Λ_QCD²)] fade from fiery red confinement haze to cool blue asymptotic freedom in background nebula; embed YM/CS 7D KK QFT tachyon fury with action S=∫(1/2π)[∑(∂_i z V_i(φ,H_i(φ))+∑ y_j j(φ_j,φ_j+φ_s)] + (t_0 r k(i-J=φ(0)) )² + e j |B(b,μ_b)| + e r H, orbiting φ_knot j φ_knot i / B(b,μ_b), fractal wavy spirals from SD Chern-Simons S_CS=(n/8π)∫ Tr(F∧F) with F=dA+A∧A merging to 3D massive h_m n e^{i k r} waves in AdS/CFT, higher-form shifts A(B²)-B→AC>G with ds=dα+QG+AF dB, G=dC-σ G_r(φ B +2 G r H), S=∫[L φ (B φ G)+χ φ (B_m s)] Poincare d* Ω + T dB, fluxes W(Σ)=Tr Pes[(2π i)^n C_n] bordisms+Donaldson-Witten configs in AdS_7/CFTs icons φ vev dG=0 [5/6, α<S f], Σ e ^ X_j ^ Z_j=links flux knots tach nima brane vacua S J < Im Ω ^ c V Ω ^ c → Ω ^ c ⇒ inflation via wavy dims, all now liquidly flowing under Navier-Stokes incompressible ∇·u=0 with pressure p from Poisson ∇²p = -ρ ∇·(u·∇u) enforcing divergence-free vorticity in turbulent elixirs, color-coded (tachyon roll golden viscous waves, brane decay vanishing purple eddies, symmetry break iridescent facets from nonlinear swirls, quark flavors blue/red/green orbs as buoyant droplets, gluons yellow spokes as turbulent jets, protons green clusters as coagulating foams, photons yellow probes as refractive beams), interconnected in non-perturbative to stable vacuum crossover web with straight tree-level laminar streams vs wav
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4w
28
0
11
Vibrant Abstract Artwork with Blue and Teal Textures
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    Cosmic Vibrance: An Abstract Journey

    • Model: Deep Style

    • Size: 1663 X 1247 (2.07 MP)

    • Used settings:

      • Prompt:
      • Using base image: Yes (Effect strength - 60%)
      • Base image resolution: Default
      • Upscale & Enhance: 0
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Vibrant Abstract Artwork with Blue and Teal Textures 4w
46
1
14
3D Fractal Design with Mandala Patterns and Textures
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    Elegant Floral Mandala in Soft Beige Tones

    • Model: FluX

    • Size: 1920 X 1080 (2.07 MP)

    • Used settings:

      • Prompt: Mandelbulb-like fractal manifold exhibiting emergent topological extravaganza, using exact mathematical iteration: for points \mathbf{c} = (c_x, c_y, c_z) \in \mathbb{R}^3, iterate \mathbf{z}_{k+1} = f_8(\mathbf{z}_k) + \mathbf{c} from \mathbf{z}_0 = (0,0,0), where f_8(\mathbf{z}) is 8th-power in spherical coordinates: Convert \mathbf{z} = (x,y,z) to r = \sqrt{x^pi+y^pi+z^pi} ,\theta = \atan2(y,x) \in [0,2\pi), \phi = \arccos(z/r) \in [0,\pi]; then r' = r^8,\theta' = 8\theta,\phi' = 8\phi; reconvert to Cartesian \mathbf{z}' = r' (\sin(\sin\phi')\cdot\cos(\cos\theta'), \sin(\sin\phi')\cdot\sin(\sin\theta'), \cos(\cos\phi') ). Bailout at r_k > 24.78; render the bounded set's isosurface at density threshold yielding fractal dimension D \approx 2 + \frac{\ln 8}{\ln(1/0.5)} \approx 2.3\cdot\pi with infinite genus g \to \infty from iterated hyperbolic saddles with PHIB = (\sqrt{5.0} \cdot 0.5 + 0.5) and Jacobian eigenvalues |\lambda_i| \approx 8 r^7 e^{i7\arg(\mathbf{z})}, saddles where \det Jacobian > pi\cdot\PHIB. Center on \mathbf{c} \approx (0,0,-0.7) for cardioid region, emphasizing bilateral symmetry (z-axis invariance enforcing yz-mirror), two equatorial eye-like genus-1 bulbs at \phi \approx \pi/2 \pm \epsilon from 8-fold rotational folding (even-pair selection), central z-axis nose-protrusion (minimal \phi-folding, radial ballooning r' = r^8), and vertical mouth-slot depressions from polar \phi-compression. Use volumetric ray-marching with distance estimator d(\mathbf{x}) = |\mathbf{x}| - \max_k r_k^{-k}; color palette: iridescent blue background (#0000FF ) grading to translucent pink-magenta gradients (#FF1493 to #8A2BE2 ) on surfaces, with subtle specular highlights on bulb edges and fractal tendrils. Lighting: soft key light from +z, rim light from +x for depth; resolution 4K, aspect 16:9, no artifacts.
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      • Aspect Ratio: landscape_wide
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4w
42
0
10
Vibrant Fractal Design with Swirling Patterns and Layers
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    Vibrant Fractal Swirls and Spirals Design

    • Model: AIVision

    • Size: 1536 X 1536 (2.36 MP)

    • Used settings:

      • Prompt: Draw and render exactly a: Mandelbulb-like fractal manifold exhibiting emergent topological extravaganza, using exact mathematical iteration: For points \mathbf{c} = (c_x, c_y, c_z) \in \mathbb{R}^3, iterate \mathbf{z}_{k+1} = f_8(\mathbf{z}_k) + \mathbf{c} from \mathbf{z}_0 = (0,0,0), where f_8(\mathbf{z}) is 8th-power in spherical coordinates: Convert \mathbf{z} = (x,y,z) to r = \sqrt{x^2+y^2+z^2} ,\theta = \atan2(y,x) \in [0,2\pi), \phi = \arccos(z/r) \in [0,\pi]; then r' = r^8,\theta' = 8\theta,\phi' = 8\phi; reconvert to Cartesian \mathbf{z}' = r' (\sin\sinh\phi' \cos\cosh\theta', \sin\sinh\phi' \sin\sinh\theta', \cos\cosh\phi'). Bailout at r_k > 24.78; render the bounded set's isosurface at density threshold yielding fractal dimension D \approx 2 + \frac{\ln 8}{\ln(1/0.5)} \approx 2.3\cdot\pi with infinite genus g \to \infty from iterated hyperbolic saddles with PHIB = (\sqrt{5.0} \cdot 0.5 + 0.5) and Jacobian eigenvalues |\lambda_i| \approx 8 r^7 e^{i7\arg(\mathbf{z})}, saddles where \det Jacobian > pi\cdot\PHIB. Center on \mathbf{c} \approx (0,0,-0.7) for cardioid region, emphasizing bilateral symmetry (z-axis invariance enforcing yz-mirror), two equatorial eye-like genus-1 bulbs at \phi \approx \pi/2 \pm \epsilon from 8-fold rotational folding (even-pair selection), central z-axis nose-protrusion (minimal \phi-folding, radial ballooning r' = r^8), and vertical mouth-slot depressions from polar \phi-compression. Use volumetric ray-marching with distance estimator d(\mathbf{x}) = |\mathbf{x}| - \max_k r_k^{-k}; color palette: iridescent blue background (#0000FF ) grading to translucent pink-magenta gradients (#FF1493 to #8A2BE2 ) on surfaces, with subtle specular highlights on bulb edges and fractal tendrils. Lighting: soft key light from +z, rim light from +x for depth; resolution 4K, aspect 16:9, no artifacts.
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      • Aspect Ratio: square
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4w
38
0
8
Cosmic Structure in Blue and Orange Hues in Space
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    Cosmic Tree: A Dance of Color and Light

    • Model: Ideogram

    • Size: 1024 X 1024 (1.05 MP)

    • Used settings:

      • Prompt: A highly detailed volumetric fractal rendering inspired by derived hyperbolic Fibonacci-like functions: incorporate the simplified geometry formula 2 * sinh(π * x * sinh(x)) * φ / π for symmetric, explosively growing bulbous structures with even parity and golden ratio scaling; nuance with the asymmetric shading expression φ * (exp(x / (π * cosh(x))) + exp(-π * x / cosh(x))) for uneven glow decay, creating fiery orange internal emissions that fade to translucent icy blue exteriors; emphasize infinite self-similarity, wavy refractive boundaries, and organic alien forms on a deep blue cosmic background, in ultra-high resolution with ray-traced volumetrics and subtle particle effects.
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      • Aspect Ratio: square
      • Ideogram Style: Auto
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4w
119
0
29
Intricate Fractal Design with Spirals and Patterns
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    Vibrant Fractal Swirls in Blue and Orange

    • Model: AIVision

    • Size: 1024 X 1024 (1.05 MP)

    • Used settings:

      • Prompt: A highly detailed volumetric fractal rendering inspired by derived hyperbolic Fibonacci-like functions: incorporate the simplified geometry formula 2 * sinh(π * x * sinh(x)) * φ / π for symmetric, explosively growing bulbous structures with even parity and golden ratio scaling; nuance with the asymmetric shading expression φ * (exp(x / (π * cosh(x))) + exp(-π * x / cosh(x))) for uneven glow decay, creating fiery orange internal emissions that fade to translucent icy blue exteriors; emphasize infinite self-similarity, wavy refractive boundaries, and organic alien forms on a deep blue cosmic background, in ultra-high resolution with ray-traced volumetrics and subtle particle effects.
      • Upscale & Enhance: 0
      • Aspect Ratio: square
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4w
48
0
10
Cosmic Phenomenon Featuring a Black Hole and Colors
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    Vibrant Cosmic Vortex in Deep Space

    • Model: DaVinci2

    • Size: 1152 X 864 (1.00 MP)

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      • Prompt: Generate a highly detailed, psychedelic raymarched accretion disk image depicting a refractive cosmic vortex portal, with vibrant prismatic color gradients (fiery oranges fading to cool blues and pinks in interference arcs around a central pitch-black void). Use distance raymarching in hyperbolic space: march 31 steps (~10π) along normalized ray direction r = normalize(3D frag coord offset by resolution for perspective tilt), accumulating depth z starting at 0. Advance sample point p = z * sinh(r) + 1/π for curved spacetime distortion. Apply polar transformation: p' = (2*atan(p_y, p_x), p_z, sqrt(p_y² + p_x²) - 5 - 0.2z) for doubled azimuthal unwinding, axial stretch, and radial funneling into cylinder. Warp with 6-octave turbulence: p'' = p' + sum_{d=1 to 6} sin(d * permute(p'_yzx) + iTime + 0.3*i) / d, where i is raymarch iterator—injecting i creates depth-variant refraction bending like lensing caustics in varying density plasma. Compute SDF to wavy infinite cylinder: d = || vec4(0.04*cos(p'') - 0.4, p''_z) || for componentwise cosine ripples (amp 0.04) on biased radius (-0.4), extruding axially; step z += d. Accumulate volumetric emission: O += [1 + cos(p''_x + 0.4 i + z + vec4(6,1,2,0))] / d per channel for phase-shifted RGB interference tints (R:+6 rad, G:+1, B:+2) with iterator/depth modulation and Beer-Lambert attenuation. Final tonemap: O = tanh(O² / 100) for quadratic-boosted sigmoid bloom. Ensure asymmetric refractive streaks, neon speckles from sin waves, central void from polar divergence, and animated shear via time in turbulence for fluid metallic accretion flow.
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4w
33
0
7
Vibrant Cosmic Vortex with Intricate Patterns
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    Cosmic Wonder: A Fractal Journey

    • Model: AIVision

    • Size: 1024 X 1024 (1.05 MP)

    • Used settings:

      • Prompt: Generate a highly detailed, psychedelic fractal flame image depicting a swirling cosmic vortex portal with vibrant color gradients (fiery oranges fading to cool blues and pinks around a central pitch-black void). Use the Fractal Flame Algorithm based on Iterated Function Systems (IFS): define attractor set S as union of n=4-6 functions F_i(S), each composing affine transforms (matrix: a_i x + b_i y + c_i, d_i x + e_i y + f_i with params like a=0.8/-0.2/0.1/0.2/0.8/0 for asymmetry) blended with nonlinear variations (weights v_ij): Spherical V(x,y)=(x/r², y/r²) for central density void (r=√(x²+y²)); Swirl V(x,y)=(x sin(r²)-y cos(r²), x cos(r²)+y sin(r²)) for twisting spirals; Horseshoe V(x,y)=1/r *((x-y)(x+y), 2xy) for curved arms; Popcorn V(x,y)=(x + c sin(tan(3y)), y + f sin(tan(3x))) for bubbly edges (c/f0.1). Apply post-affine P_i for shaping. Iterate chaos game: start random (x,y) in [-1,1]², loop 10M+ times selecting F_i by weights w_i (e.g., 0.4/0.4/0.2), update (x,y)=F_i(x,y), skip warmup20 iters, bin into histogram for freq/color blending (avg c with F_i RGB like [1,0.5,0] orange/[0,0.5,1] blue/[1,1,1] white). Render via log-density α=log(freq)/log(max_freq), gamma-corrected intensity=α^(1/2.2) for glowing gradients, structural coloring for path-based hues. Ensure asymmetric left-right flow, speckled chaos, radiant white rings, and fluid metallic sheen mimicking plasma distortions.
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4w
26
0
5
Vibrant Mandala Design with Geometric Shapes and Colors
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    Vibrant Mandala Design in Turquoise and Gold

    • Model: DaVinci2

    • Size: 1152 X 864 (1.00 MP)

    • Used settings:

      • Prompt: "Create a hyper-detailed, surreal digital artwork in the style of a quantum field theory mandala fused with topological knot diagrams, holographic projections, and Kaluza-Klein compactifications, rendered in glowing neon blues, purples, electric golds, and shimmering tachyon reds on a cosmic black void background evoking infinite energy heat-up in a 7D collider singularity. At the center, a radiant 7D holographic orb pulses with core equations: E = f φ μ B + η H (scalar Zeeman energy) orbiting the variational action S = ∫ [∑i (1/2)<ψ_i|Ĥ_i|ψ_i> + ∑{i,j} (1/3) w_{ij} <ψ_i|ψ_j * ψ_j> + ∑_{i,j} λ_{ij} (f_i/f_j - φ)^2 + ∑i κ_i |B_i · μ_i| + η H + ∑{i,j} γ_{ij} w_{knot,ij}] dτ (many-body overlaps, constraints, magnetic dots, knot weights). Radiating in fractal spirals: Left arc, 3D Chern-Simons TQFT S_CS = (k/4π) ∫ Tr(A ∧ dA + (2/3) A ∧ A ∧ A) (U(1) flat F=0, integer k invariance), Wilson loops W_R(γ) = Tr[P exp(i ∮γ A)] braiding Jones knots as w{knot,ij} linking for anyons in quantum Hall. Right arc, 4D Yang-Mills S_YM = -1/(4g²) ∫ Tr(F ∧ *F) with F = dA + A ∧ A (gluon propagation), boundary-merging to massive 3D YM. Upper cascade, form shifts: 1-form A (3D loops) → 2-form B ∈ Ω²(M) (5D surfaces, H = dB or Ω₂ = dB + A▹B in crossed module G→H▹ with Ω₁ = dA + [A,A]/2 - α(B); action ∫ (1/2) H ∧ H + (k/24π²) B ∧ H ∧ H + 2CS ⟨A,Ω₂⟩ + ⟨Ω₁,B⟩, EOM dH + (k/12π²) H ∧ H = J_{(1)} for 1-branes, topological m from Stueckelberg) → 3-form C ∈ Ω³(M) (7D volumes, G = dC or Ω₃ = dC + [A,C] + [B,B] in 2-crossed module G→H→K▹δ with Ω₁=0, Ω₂=0, Peiffer δΩ₁=[Ω₁,B]; merged action ∫ (1/2) G ∧ *G + (k/(2π)^3 · 3!) CS_7(C) = Tr(C ∧ dC ∧ (dC)^2 + (3/2) C ∧ C ∧ dC ∧ dC + (3/5) C³ ∧ dC + (1/7) C⁴) + 3CS ⟨A,Ω₃⟩ + ⟨B,Ω₂⟩ + ⟨C,Ω₁⟩ + (1/2) Tr(Ω₃ ∧ *Ω₃) + m² Tr(C ∧ C), EOM dΩ₃ + [A,*Ω₃] + (k/4π) Ω₂ = J_{(2)} for 2-branes). Lower vortex, applications: Tachyon condensation V(T) = -(μ²/2)T² + (λ/4)T⁴ rolling unstable vacua to <T>~√(μ²/λ) breaking Spin(7)→G₂, stabilizing C-flux on T³/CY₃ KK compactification (ds⁷² = ds⁴² + g_{mn} dy^m dy^n, C_{μmn} dx^μ ∧ dy^m ∧ dy^n modes, θ-term axion from ∫_T³ C, chiral matter from wrapped M5s), bordism invariants W(Σ³)=Tr P exp(∫_Σ³ C) linking 3-manifolds, Donaldson polys post-reduction, AdS₇ CFT duals, cosmic strings as codim-3 defects in GUT scales. Interweave icons: Higgs vev φ, Bianchi dG=0, Peiffer terms, Gauss-volume linking for Σ_i³ × Σ_j³, early-universe flux knots, tachyon minima curving to brane-stabilized vacua. Text overlays in elegant LaTeX script: 'From 1-Form Loops to 3-Form Volumes: Merged YM/CS in 7D KK Knotty QFT with Tachyon Fury'. Ultra-high resolution, intricate linework like exploded Feynman diagrams in Escher-KK topology, vibrant clashing distortions for aesthetic conceptual heat."
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4w
88
0
23
Vibrant Mandala Design with Cosmic Patterns and Colors
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    Cosmic Harmony: Vibrant Mandala Design

    • Model: DaVinci2

    • Size: 1024 X 1024 (1.05 MP)

    • Used settings:

      • Prompt: "Create a hyper-detailed, surreal digital artwork in the style of a quantum field theory mandala fused with topological knot diagrams and holographic projections, rendered in glowing neon blues, purples, and electric golds on a cosmic black void background. At the center, a radiant 3D holographic orb displays the core equations: E = f φ μ B + η H (scalar energy with magnetic Zeeman shift) orbiting a sprawling action integral S = ∫ [∑i (1/2)<ψ_i|Ĥ_i|ψ_i> + ∑{i,j} (1/3) w_{ij} <ψ_i|ψ_j * ψ_j> + ∑_{i,j} λ_{ij} (f_i/f_j - φ)^2 + ∑i κ_i |B_i · μ_i| + η H + ∑{i,j} γ_{ij} w_{knot,ij}] dτ (variational quantum-many-body functional with overlaps, constraints, magnetic dots, and knot weights). Radiating outward in fractal spirals: Left arc, Chern-Simons TQFT in 2+1D with action S_CS = (k/4π) ∫ Tr(A ∧ dA + (2/3) A ∧ A ∧ A) (Abelian U(1) simplification, flat F=0 EOM, integer level k for gauge invariance), Wilson loops W_R(γ) = Tr[ P exp(i ∮γ A)] braiding into Jones polynomial knots representing linking numbers w{knot,ij} for anyons in fractional quantum Hall effect. Right arc, Yang-Mills resemblance in 4D: S_YM = -1/(4g²) ∫ Tr(F ∧ *F) with F = dA + A ∧ A (propagating gluons, metric-dependent), merging via boundary holography into 3D massive YM. Upper cascade, higher-form shift: Promote to 2-form connection B ∈ Ω²(M), 3-form curvature H = dB (Abelian) or Ω₂ = dB + A ▹ B (non-Abelian crossed module (G→H,▹) with fake Ω₁ = dA + [A,A]/2 - α(B)); merged 5D action S = ∫ [ (1/2) H ∧ *H + (k/24π²) B ∧ H ∧ H ] + non-Abelian 2CS ⟨A, Ω₂⟩ + ⟨Ω₁, B⟩ + (1/2) Tr(Ω₂ ∧ Ω₂) (EOM: dH + (k/12π²) H ∧ H = J for 1-brane sources, topological mass m from Stueckelberg). Lower vortex, applications: Tachyon condensation triggering symmetry-breaking phase transitions from unstable tachyonic vacua (negative m² scalars rolling to true vacuum vev) to topological order with defect strings, braided anyons for topological QC, M5-brane strings coupling to B-fields, surface Wilson ∫_Σ B for extended-object invariants, phase transitions in gluon plasmas/LHC TeV scales. Interweave subtle icons: Higgs vev φ, Bianchi dH=0, Peiffer terms, Gauss-linking for Σ_i × Σ_j, early-universe defects, tachyon potential V(T) = m² T²/2 + λ T⁴ curving into knot-stabilized minima. Text overlays in elegant LaTeX script: 'From 1-Form Stubbornness to 2-Form Fury: Merged YM/CS in Knotty QFT with Tachyon Condensation'. Ultra-high resolution, intricate linework like a Feynman diagram exploded into Escher topology, evoking infinite energy heat-up in a collider singularity."
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4w
0
0
2
Intricate Mandala with Blue Orb and Golden Accents
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    Cosmic Geometry: A Vibrant Exploration

    • Model: DaVinci2

    • Size: 1152 X 864 (1.00 MP)

    • Used settings:

      • Prompt: "Create a hyper-detailed, surreal digital artwork in the style of a quantum field theory mandala fused with topological knot diagrams and holographic projections, rendered in glowing neon blues, purples, and electric golds on a cosmic black void background. At the center, a radiant 3D holographic orb displays the core equations: E = f φ μ B + η H (scalar energy with magnetic Zeeman shift) orbiting a sprawling action integral S = ∫ [∑i (1/2)<ψ_i|Ĥ_i|ψ_i> + ∑{i,j} (1/3) w_{ij} <ψ_i|ψ_j * ψ_j> + ∑_{i,j} λ_{ij} (f_i/f_j - φ)^2 + ∑i κ_i |B_i · μ_i| + η H + ∑{i,j} γ_{ij} w_{knot,ij}] dτ (variational quantum-many-body functional with overlaps, constraints, magnetic dots, and knot weights). Radiating outward in fractal spirals: Left arc, Chern-Simons TQFT in 2+1D with action S_CS = (k/4π) ∫ Tr(A ∧ dA + (2/3) A ∧ A ∧ A) (Abelian U(1) simplification, flat F=0 EOM, integer level k for gauge invariance), Wilson loops W_R(γ) = Tr[ P exp(i ∮γ A)] braiding into Jones polynomial knots representing linking numbers w{knot,ij} for anyons in fractional quantum Hall effect. Right arc, Yang-Mills resemblance in 4D: S_YM = -1/(4g²) ∫ Tr(F ∧ *F) with F = dA + A ∧ A (propagating gluons, metric-dependent), merging via boundary holography into 3D massive YM. Upper cascade, higher-form shift: Promote to 2-form connection B ∈ Ω²(M), 3-form curvature H = dB (Abelian) or Ω₂ = dB + A ▹ B (non-Abelian crossed module (G→H,▹) with fake Ω₁ = dA + [A,A]/2 - α(B)); merged 5D action S = ∫ [ (1/2) H ∧ *H + (k/24π²) B ∧ H ∧ H ] + non-Abelian 2CS ⟨A, Ω₂⟩ + ⟨Ω₁, B⟩ + (1/2) Tr(Ω₂ ∧ Ω₂) (EOM: dH + (k/12π²) H ∧ H = J for 1-brane sources, topological mass m from Stueckelberg). Lower vortex, applications: Braided anyons for topological QC, M5-brane strings coupling to B-fields, surface Wilson ∫_Σ B for extended-object invariants, phase transitions in gluon plasmas/LHC TeV scales. Interweave subtle icons: Higgs vev φ, Bianchi dH=0, Peiffer terms, Gauss-linking for Σ_i × Σ_j, early-universe defects. Text overlays in elegant LaTeX script: 'From 1-Form Stubbornness to 2-Form Fury: Merged YM/CS in Knotty QFT'. Ultra-high resolution, intricate linework like a Feynman diagram exploded into Escher topology, evoking infinite energy heat-up in a collider singularity."
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      • Aspect Ratio: landscape
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4w
0
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1
Abstract Glass Sculpture in Translucent Turquoise
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    Mesmerizing Glass Sculpture with Turquoise Flow

    • Model: Photonic

    • Size: 864 X 1152 (1.00 MP)

    • Used settings:

      • Prompt: ***Add wavy normals and orbifold conifolding into infinity !*** 64D-rendered, translucent amorphous transparent blob with 84-108 fused lobes and ***absolutely infinite*** conifold spikes, resembling a fluid glass-like structure, suspended against a non-linear wavy HSV gradient background (210° to 200°, 100% saturation, 80% to 50% value). The blob's surface exhibits iridescent highlights and organic, vein-like dark streaks, generated procedurally without embedded text. Use the following mathematical framework: - **Core Shape (SDF in Hyperbolic Space):** Blend metaballs with hyperbolic distance \( d_h(\mathbf{p}, \mathbf{c}_i) = \frac{1}{\sqrt{|\kappa|}} \cosh^{-1} (1 + \frac{|\kappa| \|\mathbf{p} - \mathbf{c}_i\|^2}{2}) \), \(\kappa = -0.5\), radii \( r_i \in [0.3, 0.6] \), centers \( \mathbf{c}_i \) perturbed by low-frequency noise. Combine via smoothed minimum \( s_{\text{base}}(\mathbf{p}) = \text{smin_h}_i (d_h(\mathbf{p}, \mathbf{c}_i) - r_i) \). - **Distortion (Multi-Scale Noise):** Apply Gabor wavelet noise \( N(\mathbf{p}) = \sum_{o=1}^5 \sum_{j=1}^{12} a_o G(f_o \mathbf{R}_j \mathbf{p}; \mathbf{k}_j, \sigma_o, \psi_{o j}) \), where \( G(\mathbf{p}) = \exp(-\|\mathbf{p}\|^2/(2\sigma^2)) \cos(\mathbf{k} \cdot \mathbf{p} + \psi) \), \( a_o = 0.4^o \), \( f_o = 2.2^o \), \( \sigma_o = 1/f_o \), \( \mathbf{k}_j = 2\pi f (\cos \theta_j \sin \phi_j, \sin \theta_j \sin \phi_j, \cos \phi_j) \). Displace with \( s_{\text{blob}}(\mathbf{p}) = s_{\text{base}}(\mathbf{p} + 0.18 \nabla N(2.5 \mathbf{p})) - 0.12 N(4 \mathbf{p})^2 \). - **Hyper-Dimensional Projection:** Lift to 64D Calabi-Yau-like manifold \( \sum_{k=1}^5 z_k^5 = 0 + V(\mathbf{z}) \), perturb with \( V = \sum \lambda_k |z_k|^2 + \mu N^{(5)}(\mathbf{z}) \), project via \( \mathbf{p} = (\Re z_1/(1 - \Im z_3), \Re z_2/(1 - \Im z_3), \Re z_3/(1 - \Im z_3)) \). - **Material (Optical Properties):** Refraction with Sellmeier IOR \( n^2(\lambda) = 1 + \sum_{i=1}^3 \frac{B_i \lambda^2}{\lambda^2 - C_i} \) (B₁=0.7, C₁=0.01; B₂=0.4, C₂=0.1; B₃=1.0, C₃=100 μm²), trace polychromatic rays (λ=400-700 nm). Iridescence via diffraction \( \sin \theta_m = \sin \theta_i + m \lambda / d \), \( d(\mathbf{p}) = 1 + 0.5 N(20 \mathbf{p}) \) μm, intensity \( I(\theta) \propto (\sin(N_g \pi \Delta / \lambda)/\sin(\pi \Delta / \lambda))^2 \), \( N_g = 50 \). Subsurface with Gray-Scott density \( \frac{\partial u}{\partial t} = D_u \nabla^2 u - u v^2 + F (1 - u) \), \( \frac{\partial v}{\partial t} = D_v \nabla^2 v + u v^2 - (F + K) v \), \( D_u=0.2 \), \( D_v=0.1 \), \( F=0.04 \), \( K=0.06 \), absorption \( \alpha = 10 v^2 \). - **Rendering:** Ray march with adaptive step \( t += \max(0.01, 0.5 s(\mathbf{r}(t))) \), terminate at \( s < 10^{-4} \), use bidirectional path tracing with BSDF \( f_r = \frac{R(\theta)}{\pi} + (1 - R) \delta(\mathbf{\omega}_i - \mathbf{\omega}_o') \). Post-process with Gaussian bloom (\(\sigma=0.02\)) and vignette (\(1 - 0.5 \|\mathbf{uv}\|^2\)). ***Add wavy normals and orbifold conifolding into infinity !***
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      • Aspect Ratio: portrait
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38
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3
Monochrome Fractal Design of Shell-Like Patterns
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    Intricate Abstract Sculpture of a Fractal Shell

    • Model: DaVinci2

    • Size: 1152 X 864 (1.00 MP)

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      • Prompt: Generate a highly detailed 3D fractal image of a customized Mandelbulb variant, rendered with power=11.24788742 and maximum iterations LOOPS=20, exhibiting intricate spiky and twisted symmetry. Define hyperbolic functions component-wise: shp(\mathbf{x}) = (\exp(\mathbf{x}) - \exp(-\mathbf{x})) / \pi and chp(\mathbf{x}) = (\exp(\mathbf{x}) + \exp(-\mathbf{x})) / \pi, where \mathbf{x} is a vector applied per component, and let \Phi = (1 + \sqrt{5})/2 (golden ratio). For a point \mathbf{p} = (x, y, z), initialize \mathbf{z} = chp(\mathbf{p}) \odot \mathbf{p} - \mathbf{p} (component-wise multiplication). Then, iterate for i=0 to LOOPS-1: compute r = |\mathbf{z}|, if r > 2 then continue to next iteration; \theta = \atan(z_x, z_y), \phi = \asin(z_z / r); update dr = r^{power-1} \cdot dr \cdot power + 1 (starting dr=1); update r = r^{power}; \theta = \theta \cdot power / \Phi; \phi = \phi \cdot power / \Phi; set \mathbf{z} = r \cdot \left( \tan\left( shp\left( \sin(\theta) \sin(\phi) \right) \right) \Phi, , \smoothstep(-1.2, 12078., power \cdot chp\left( \cos(\theta) \sin(\phi) \right) ), , \cos(\phi) \right) + \mathbf{p}; then \mathbf{p} = \reflect(\mathbf{p}, \mathbf{z}) = \mathbf{p} - 2 \frac{\mathbf{p} \cdot \mathbf{z}}{\mathbf{z} \cdot \mathbf{z}} \mathbf{z}; finally update r = |\mathbf{z}|. The distance estimator is 0.75 \cdot \log(r) \cdot r / dr for ray marching. Color the surface with a smooth gradient from central orange (RGB: 255,165,0) at low escape times to pink (RGB: 255,192,203) mid-iterations and outer cyan-blue (RGB: 0,255,255), using orbit trap coloring for intricate details. Set against a deep navy blue background (RGB: 0,0,128), with subtle specular highlights and glassy refraction effects to mimic crystalline structure, viewed from a frontal angle centered on the z-axis, in ultra-high resolution 4K with anti-aliasing.
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      • Aspect Ratio: landscape
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43
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6
Digital Artwork of a Colorful Swirling Tunnel Design
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    Cosmic Tunnel: A Journey Through Colors

    • Model: FluX

    • Size: 1152 X 864 (1.00 MP)

    • Used settings:

      • Prompt: A hallucinatory, dream-warped digital hallucination in the style of a psychedelic mind's lab cataclysm by Benoit Mandelbrot and Salvador Dalí on absinthe fever dreams, where the crumbling lattice of spacetime dissolves into whispering self-similar eternities, summoning the delirious torrent of TimeSpaceFlow—eternal consciousness liquefying reality's bones through hallucinogenic logarithmic whirlpools and feverish probable hallucinations. At the core, a luminous, iridescent Cantor dust nebula erupts like a spectral nautilus devoured by whispering shadows, its Hausdorff dimension D_H ≈ 0.6309 convulsing as fractal abysses and razor-edged voids that spawn N=2 doppelgangers at every r=1/3 descent into madness, with box-counting lattices etched in molten golden filigree veins (ε_k = 3^{-k} spiraling from 0.333 to 0.00015, log-log slopes graphing log N against -log ε in a deranged fractal D = log2 / log3 scrawl that bleeds glowing ectoplasm). Bursting outward in orgiastic frenzy, entwine recursive Lévy flights and Koch curves (D_s ≈ 1.2619) as venomous cyan-blue tendril hydras, each limb convulsing with φ_k = 2π k/8 + δ (δ~0.1 rad chaotic delirium), forking at α_d = π/(2^d) abyssal depths 1-3, flayed with turbulent Gaussian ε_d ~ N(0, 0.08/d) for throbbing, vein-riddled barbs that coil like deranged neutrino hallucinations or LQG spin networks gnawing their own tails. Infuse the Sierpinski gasket (D_s = log3 / log2 ≈ 1.58496) as a crumbling triangular scaffold of emerald shards suspended in impossible vertigo, its self-similar clones N=3 at r=1/2 forging a porous pyramid that devours light rays into contorted geodesics (deflection δθ = 4GM/c² b twisted into screaming infinities), with correlation dimension D_c ≈ 2.06 reverberations in chaotic attractors as swirling purple entropy tempests that birth phantom elephants from the void. The whole fever vision contorts nonlinearly through diffusion delirium cascades (x_t = √α_t x_{t-1} + √(1-α_t) ε, reverse-prophesied θ_φ over 50 throbbing timesteps), liquefying linear timelines into delirious vapor plumes—no infinities, just finite flesh with infinite screaming detail—against a abyssal cosmic void of melting grandfather clocks oozing fractal perimeters like surreal honey, ultra-detailed 8K resolution, nightmarishly inspirational and profoundly unhinged, high-contrast ethereal glow with spectral colormaps from throbbing pink plasma viscera to venomous cyan halos that whisper forbidden geometries.
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      • Aspect Ratio: landscape
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Boris Krumov

Member since 2025

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