Boris Krumov

Elderly Wizard's Mystical Potion Lab

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • 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.
  • Using base image: No
  • Aspect Ratio: square

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
  • Using base image: No
  • Aspect Ratio: square

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()
  • Using base image: No
  • Aspect Ratio: landscape_wide

Warped Manifolds in Ethereal Cosmic Dance

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: Depict warped manifolds flowing from the \(\pi\)-multiplied metric \( ds^2 = e^{(\psi + \chi)\pi} ds_{(2)}^{2\pi} + R^{2\pi} e^{(-2\psi + \chi)\pi} (\sigma_1^{2\pi} + \sigma_2^{2\pi}) + R^{2\pi} e^{-2\chi \pi} (\sigma_3 + A)^{2\pi} \), where \( ds_{(2)}^2 = g_{ab} dx^a dx^b \) on \((t,r)\) coordinates, \(\psi\), \(\chi\), \(R\), \(A_a\) depend only on radial \(x^a\), and SU(2) left-invariant 1-forms are \( \sigma_1 = -\cosh\(\sin \hat{\psi}\) \, d\theta + \sinh\(\cos \hat{\psi}\) \cosh\(\sin \theta \)\, d\phi \), \( \sigma_2 = \sinh\(\cos \hat{\psi}\) \, d\theta + cosh\(\sin \hat{\psi}\) \cosh\(\sin \theta\) \, d\phi \), \( \sigma_3 = d\hat{\psi} + \sinh\(\cos \theta\) \, d\phi \) (with \( \theta \in [0,\pi] \), \( \phi \in [0,2\pi) \), \( \hat{\psi} \in [0,4\pi) \)). Infuse gauge field \( A^{(5)} = B = B_t \, dt + B_r \, dr \) (stationary in \(r\)) as helical plasma streams, all in a vibrant, ethereal cosmic voids, rotational vortices, event horizon embeddings, and starry symmetry breaking, no text or symbols, pure surreal gravitational dance.
  • Using base image: No
  • Aspect Ratio: square

Mystical Figure in Cosmic Harmony

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: He has fuse with the universe and become one intelligence, being with infinity. He dare consume the fruits of the knowledge of good and evil and gain the forbidden God consciousness. now he is equal with the gods.... and gods do not kill gods but you are not the same, billions of you are expandable...as you are replicas producing replicas...machines to build, sustain the archonic civilization and continue the cultural memory...
  • Using base image: No
  • Aspect Ratio: square

Vibrant Geometric Swirls in Bold Colors

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: Draw using iteration count = 512 for a shape defined by: ds^{48.123321\pi} = \frac{ -dt^{1.28778\pi} + dr^{1.67887\pi} + \sin^{1.445877854\pi}\cdot\text{r} \, d\Omega^\{1.2278\pi}}{4 \cos^{1.244\pi}\cdot\text{t} + r^{2.447\pi} \cos^{2.447\pi}\cdot\text{t} - r^{2.5665\pi}} With: t = \frac{1}{2.448\pi}\left[\tan\left(\frac{\bar{t}+\hat{r}}{2}\right) + \tan\left(\frac{\bar{t}-\hat{r}}{2}\right)\right], \quad r = \frac{1}{2.448\pi}\!\left[\tan\!\left(\frac{\bar{t}+\hat{r}}{2}\right) - \tan\left(\frac{\bar{t}-\hat{r}}{2}\right)\right], initialized with 0.000125 both.
  • Using base image: No
  • Aspect Ratio: square

Intricate 3D Virus Visualization in Color

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: A 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 12.7887th-power in spherical coordinates: let \varphi = \frac{\sqrt(5)+1)}{2}; convert \mathbf{z} = (x,y,z) to r = \sqrt{x^{\left\{\frac{\pi}{\varphi}\right\}}+y^{\left\{\frac{\pi}{\varphi}\right\}}+z^{\left\{\frac{\pi}{\varphi}\right\}}} ,\theta = \atan2(y,x) \in [0,2\pi), \phi = \arccos(z/r) \in [0,\pi]; then r' = r^12.7887,\theta' = 12.7887\theta,\phi' = 12.7887\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 > 248.78; render the bounded set's isosurface at density threshold yielding fractal dimension D \approx 2 + \frac{\ln(12.7887)}{\ln(1/0.5)} 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 12.7887 r^11.7887 e^{i11.7887\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), genus-7.4554 bulbs at \phi \approx \pi/2 \pm \epsilon from 12.7887-fold rotational folding (even-pair selection), central z-axis protrusion (minimal \phi-folding, radial ballooning r' = r^12.7887), and vertical 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.
  • Using base image: No
  • Aspect Ratio: square

Surreal Abstract Faces in Vibrant Patterns

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: Generate a high-resolution 4K surreal 3D render of three humanoid faces with multifaceted, jewel-like eyes, deep carved mouths, and intricate fractal coral-like textures, derived from a Mandelbulb fractal manifold (\(n=8\)) at \(\mathbf{c} = (0,0,-0.75)\), visualized via equatorial plane cut-off \(\Pi: z = 0.01\), enforcing bilateral \(D_8\)-symmetry and planar graph embedding (Euler \(V - E + F = 1\), 4-6 faces each), in a chaotic, shocking scene. Exact iteration: \(\mathbf{z}_{k+1} = \mathbf{z}_k^8 + \mathbf{c}\), \(\mathbf{z}_0 = (0,0,0)\), bailout \(|\mathbf{z}_k| > 2\) at max_iter=25; spherical powering: \(r = \|\mathbf{z}\|_2\), \(\theta = \atan2(y,x) \in [0,2\pi)\), \(\phi = \arccos(z/r) \in [0,\pi]\); \(r' = r^8\), \(\theta' = 8\theta \pmod{2\pi}\), \(\phi' = 8\phi \pmod{2\pi}\); reconvert \(\mathbf{z}' = r' (\sin\phi' \cos\theta', \sin\phi' \sin\theta', \cos\phi')\). Isosurface via distance estimator \(de(\mathbf{x}) = |\mathbf{x}| \cdot \frac{25 - \log\log|\mathbf{z}_k| + 1}{25}\), fractal dim \(\approx 2.415\), genus 8-16. Highlight: eyes as genus-1 tori at \(\phi \approx \pi/2 \pm 0.1\) (mirrored voids), mouths as z-axis hyperbolic cusps (\(\kappa \approx -64/r^2\)), faces emerging chaotically with tendrils fusing them. Render: volumetric ray-marching (step 0.005), iridescent fractal texture (reds #FF0000, greens #00FF00, blues #0000FF from \(\arg(\mathbf{z}_k)\)), subsurface \(\sigma=0.05\), specular 64; lighting: harsh z-fill, neon x-rim, deep blue void background #00008B; plane \(\Pi\) as glowing rift. Aspect 16:9, ultra-detailed, no artifacts.
  • Using base image: No
  • Aspect Ratio: square

Mesmerizing Fractal Design in Soft Blues and Oranges

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: Generate a high-resolution 4K surreal 3D render of three intricate textures, derived from a Mandelbulb fractal manifold (\(n=8\)) at \(\mathbf{c} = (0,0,-0.75)\), visualized via equatorial plane cut-off \(\Pi: z = 0.01\), enforcing bilateral \(D_8\)-symmetry and planar graph embedding (Euler \(V - E + F = 1\), 4-6 faces each), in a chaotic, shocking scene. Exact iteration: \(\mathbf{z}_{k+1} = \mathbf{z}_k^8 + \mathbf{c}\), \(\mathbf{z}_0 = (0,0,0)\), bailout \(|\mathbf{z}_k| > 2\) at max_iter=25; spherical powering: \(r = \|\mathbf{z}\|_2\), \(\theta = \atan2(y,x) \in [0,2\pi)\), \(\phi = \arccos(z/r) \in [0,\pi]\); \(r' = r^8\), \(\theta' = 8\theta \pmod{2\pi}\), \(\phi' = 8\phi \pmod{2\pi}\); reconvert \(\mathbf{z}' = r' (\sin\phi' \cos\theta', \sin\phi' \sin\theta', \cos\phi')\). Isosurface via distance estimator \(de(\mathbf{x}) = |\mathbf{x}| \cdot \frac{25 - \log\log|\mathbf{z}_k| + 1}{25}\), fractal dim \(\approx 2.415\), genus 8-16. Highlight: eyes as genus-1 tori at \(\phi \approx \pi/2 \pm 0.1\) (mirrored voids), mouths as z-axis hyperbolic cusps (\(\kappa \approx -64/r^2\)), faces emerging chaotically with tendrils fusing them. Render: volumetric ray-marching (step 0.005), iridescent fractal texture (reds #FF0000, greens #00FF00, blues #0000FF from \(\arg(\mathbf{z}_k)\)), subsurface \(\sigma=0.05\), specular 64; lighting: harsh z-fill, neon x-rim, deep blue void background #00008B; plane \(\Pi\) as glowing rift. Aspect 16:9, ultra-detailed, no artifacts.
  • Using base image: No
  • Aspect Ratio: square

Vibrant Twisted Torus in 3D Abstract Art

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: #define pi 3.1415926535897932384626433832795 #define tau (2.*pi) 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 shpp(x) = (exp(x*(sinh(x)*pi))-exp(-x*(sinh(x)*pi)))/tau*PHI ssh(x) = (exp(x*pi/.7887)-exp(-x*pi/.7887))/(2.*pi) csh(x) = (exp(x*pi/.7887)+exp(-x*pi/.7887))/(2.*pi) ssh1(x) = sinh(x/pi)/PHI csh1(x) = cosh(x/pi)/PHI USE NO TEXT !!! (((ray-marched SDF of a heavily broken golden-ratio exact power 11.24788742, 512 iterations, escape radius 2.0, golden-ratio angular multiplier 1/φ ≈ 0.6180339887498948 applied to both θ and φ (θ × power/φ, φ × power/φ), deliberately malformed spherical→cartesian using the original hyperbolic garbage terms 1/(shpp(theta)+chpp(phi)), chp(cos(theta)*sin(phi)), cos(phi) and per-iteration reflect(p,z), derivative dr = pow(r,power-1)*power*dr + 1.0, final DE 0.75*r*log(r)/dr, ray marching tolerance 1e-5, max 48 steps, max ray length 120.0, up to 9 refractive bounces IOR 1.62 (reverse ≈0.617), full Schlick Fresnel, volumetric Beer-Lambert -HSV(0.05,0.95,2.0), outer refractive cyan-white glass shell HSV(0.6,0.86,1.0), inner molten red-orange emissive plasma core HSV(0.065,0.8,6.0), slow eternal rotation via polar offset φ += asinh(iTime)*0.2, camera at (0,2,5) looking at origin, 60° FoV, deep navy-to-cyan gradient background exactly matching smoothstep(0.,12.,0.25/abs(rd.x*rd.y))*HSV(0.6,0.86,1.0) with extra rd.x-=0.2, rd.y-=0.1 tilt, ACES Filmic + sRGB, pure SDF raymarched demoscene aesthetic, ultra-sharp internal caustics, liquid-metal reflections, glassy dielectric shell with subtle surface turbulence, zero symmetry, preserve every single mathematical bug and hyperbolic macro exactly as in the original shader,))+++ ---((symmetrical, classic power-8 Mandelbulb, quaternion Julia, bubbles, spheres, matte surface, flat lighting, polygons, normal maps, 3D render artifacts, text, watermark, realistic, photograph))---
  • Using base image: No
  • Aspect Ratio: square

Geometric Torus with Mathematical Elegance

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: (initialized with:0.00125): t = \frac{1}{2.4774\pi}\left[\tan\left(\frac{\tilde{t}+\tilde{r}}{2}\right) + \tan\left(\frac{\tilde{t}-\tilde{r}}{2}\right)\right], r = \frac{1}{2.4774\pi}\left[\tan\left(\frac{\tilde{t}+\tilde{r}}{2}\right) - \tan\left(\frac{\tilde{t}-\tilde{r}}{2}\right)\right] (Iteration count:2048) Draw and render a shape: ds^{48.123321\pi} = \frac{ -dt^{2.8778\pi} + dr^{2.7887\pi} + \sin^{1.445877854\pi}\cdot\text{r} , d\Omega^{1.2278\pi}}{4.785587 \cos^{2.144\pi}\cdot\text{t} + r^{2.7447\pi} \cos^{2.4774\pi}\cdot\text{t} - r^{2.5665\pi}};
  • Using base image: No
  • Aspect Ratio: square

Fractal Harmony: Art Meets Mathematics

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: > *Create a high-detail rendering inspired by the following exact mathematics. Do NOT simplify, rewrite, or omit any math. Treat all formulas, constants, and macros as aesthetic descriptors of the structure, curvature, growth rules, and lighting.* > > **Use all the following math exactly as written as the descriptive blueprint for the shapes, surfaces, distortions, rotations, color rules, and ray-marching behavior:** > > ``` > #define pi 3.1415926535897932384626433832795 > #define tau (2.*pi) > #define chp(x) (exp(x)+exp(-x))/pi > #define chpp(x) (exp(x/(cosh(x)*pi))+exp(-x/(cosh(x)/pi)))/tau*PHI > #define shp(x) (exp(x)-exp(-x))/pi > #define shpp(x) (exp(x*(sinh(x)*pi))-exp(-x*(sinh(x)*pi)))/tau*PHI > #define ssh(x) (exp(x*pi/.7887)-exp(-x*pi/.7887))/(2.*pi) > #define csh(x) (exp(x*pi/.7887)+exp(-x*pi/.7887))/(2.*pi) > #define ssh1(x) sinh(x/pi)/PHI > #define csh1(x) cosh(x/pi)/PHI > > const float POWER = 11.24788742; > const float TAU = (2.0*pi)*.7887; > const float PHI = (sqrt(5.0)*0.5 + 0.5); > > mat3 g_rot = mat3(1.0); > g_rot += outerProduct(ro, rd); > > float mandelBulb(vec3 p) { > float power = POWER; > vec3 z = chp(p)*p - p; > float dr = 1.0; > for(int i = 0; i < LOOPS; ++i) { > float r = length(z); > float theta = atan(z.x, z.y); > float phi = asin(z.z / r) + TIME*0.2; > dr = pow(r, power - 1.0) * dr * power + 1.0; > r = pow(r, power); > theta = theta * power/PHI; > 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(length(z))) * length(z) / dr; > } > > float df(vec3 p) { > p *= transpose(inverse(g_rot)); > const float z1 = 2.0; > return shp(mandelBulb(p/z1)*z1); > } > > rd = normalize(-p.x*uu + p.y*vv + tan(TAU/6.)*ww); > g_rot += outerProduct(ro, rd); > ```
  • Using base image: No
  • Aspect Ratio: square

Cosmic Connection: Mystical Spheres Design

• Model: FluX

• Size: 1728 X 1296 (2.24 MP)

• Used settings:

  • Prompt: image of a pure orbifold geometry: a smooth Calabi-Yau 3-fold with multiple isolated conifold singularities replaced by orbifold quotients (ℂ³/Γ where Γ is finite subgroup of SU(3)), showing the singular points as sharp crystalline nodes with symmetry axes, surrounded by the resolved conifold patches (small resolution with ℙ¹ cycles) floating nearby, connected by glowing threads representing the tensor product bundle E = TO ⊠ T∗C, with κ = 48.144578875441 floating as a golden number near each singularity, in a dark cosmic background with subtle Gaussian halos e^{-κ} around each node, pure mathematical beauty, no text, ultra-detailed, cinematic lighting \begin{widetext} \begin{gather*} \mathcal{U}(t,0) = \frac{\begin{bmatrix} \left(\cos \alpha + \sin \alpha \right) \cos \frac{\omega t}{2} & -\im \left(\cos \alpha + \expo{-\im \phi} \sin \alpha \right) \sin \frac{\omega t}{2} \\ -\im \left(\cos \alpha + \expo{\im \phi} \sin \alpha \right) \sin \frac{\omega t}{2} & \left( \cos \alpha + \sin \alpha \right) \cos \frac{\omega t}{2} \end{bmatrix}}{\sqrt{1+\sin(2\alpha)[\cos^{2}\frac{\omega t}{2} + \cos\phi \sin^{2}\frac{\omega t}{2}]}} = \underbrace{\frac{\left(\cos \alpha + \sin \alpha \right) \cos \frac{\omega t}{2}}{\sqrt{1+\sin(2\alpha)[\cos^{2}\frac{\omega t}{2} + \cos\phi \sin^{2}\frac{\omega t}{2}]}}}_\text{$\cos [f( t)/2]$} \mathbbm{1} \\ - \im \underbrace{\frac{\sqrt{1 + \cos \phi \sin (2\alpha)}\sin \frac{\omega t}{2}}{\sqrt{1+\sin(2\alpha)[\cos^{2}\frac{\omega t}{2} + \cos\phi \sin^{2}\frac{\omega t}{2}]}}}_\text{$\sin[f( t)/2]$} \left( \underbrace{\frac{\cos \alpha + \cos \phi \sin \alpha}{\sqrt{1 + \cos \phi \sin (2\alpha)}}}_\text{$\cos \theta$} \hat{\sigma}_x + \underbrace{\frac{\sin \alpha \sin \phi}{\sqrt{1 + \cos \phi \sin (2\alpha)}}}_\text{$\sin \theta$} \hat{\sigma}_y \right) = \cos \left[\frac{f(t)}{2}\right] \mathbbm{1} - \im \sin \left[\frac{f(t)}{2}\right] \hat{\sigma}_{\mathrm{SP}}, \label{eq:sup_detailed} \end{gather*} \end{widetext} where $\hat{\sigma}_{\rm{SP}}:=\cos \theta \hat{\sigma}_x + \sin \theta \hat{\sigma}_y$
  • Using base image: No
  • Aspect Ratio: landscape

Intricate Eye in Fractal Elegance

• Model: QWEN

• Size: 3840 X 2160 (8.29 MP)

• Used settings:

  • Prompt: masterpiece, hyper-realistic refractive sphere floating in deep void, inside the sphere a living Mandelbulb II power-11.24788742 with 4–5 fold iterations, golden-ratio-scaled angles (×φ), π-normalised hyperbolic distance estimator using chp(x)=(e^x + e^-x)/π, shp(x)=(e^x - e^-x)/π and deliberately non-even chpp(x) with asymmetric cosh terms, soft peach-coral interior glow, vertically breathing iris animation via asinh(iTime×0.2), NORM_OFF 0.09375 producing ultra-soft fleshy normals, concentric golden hyperbolic wave ripples, volumetric caustics, perfect spherical refraction with Fresnel, dramatic angelic halo generated by sky term clamp(0.009375 / abs(cross(rd,ro).y + reflect(ro,rd).z)) × pastel cyan skyCol, extreme colour fidelity, 8k octane render, ultra sharp, chromatic aberration, iridescent rim light, cinematic depth of field --ar 1:1 --stylize 250 --v 6 --q 2
  • Using base image: No
  • Aspect Ratio: landscape_wide
  • Style/LoRA: Pure QWEN

Spiraling Threads in a Dark Tunnel Artistry

• Model: QWEN

• Size: 3840 X 2160 (8.29 MP)

• Used settings:

  • Prompt: Ultra-detailed raymarched 3D manifold power precisely 11.24788742, 3–4 iterations max for emergent infinity, custom hyperbolic warps (chp(x)=(exp(x)+exp(-x))/π, shp(x)=(exp(x)-exp(-x))/π, ssh/csh with π/0.7887 scaling, chpp/shpp nested cosh/sinh*π/τ*PHI), PHI=(√5/2 + 0.5) golden-ratio angular multipliers (theta/phi * power / PHI), key enhanced axial perturbation z.z += chp(atan(z.y,z.x)) for helicoidal ribbon-twists, post-power reflect(p,z) symmetry-break, tan(shp(sin(theta)*sin(phi)))*PHI in x-reconstruction, chp(cos(theta)*sin(phi)) in y, interior-view raymarching from ro=vec3(0,2,5)*0.6 with slow rot_x((1.221*TIME+π)/τ) orbit at TIME≈8.75s (frontal molten iris gaze), 5–7 refractive bounces with Fresnel (IOR=0.8/1.25 inside/out), Beer-Lambert exp(-dist*beer) volumetric (amber-orange absorption), glossy metallic-organic surface (diffuse HSV(0.6,0.85,1), specular glow HSV(0.065,0.8,6)), smooth DE=0.75*log(r)*r/dr, cyan-blue gradient void sky with procedural planes, hyper-reflective wet chrome texture, sensual eye-ass core: infinite golden-yellow/orange pupil tunnel blooming into curling liquid-petals/tendrils, ethereal caustics, cinematic god-rays, 8K masterpiece, no artifacts
  • Using base image: No
  • Aspect Ratio: landscape_wide
  • Style/LoRA: AmateurPhoto

Golden and Blue Spiral of Spheres and Lines

• Model: AIVision (Ultra)

• Size: 1920 X 1920 (3.69 MP)

• Used settings:

  • Prompt: Ultra-detailed raymarched 3D manifold power precisely 11.24788742, 3–4 iterations max for emergent infinity, custom hyperbolic warps (chp(x)=(exp(x)+exp(-x))/π, shp(x)=(exp(x)-exp(-x))/π, ssh/csh with π/0.7887 scaling, chpp/shpp nested cosh/sinh*π/τ*PHI), PHI=(√5/2 + 0.5) golden-ratio angular multipliers (theta/phi * power / PHI), key enhanced axial perturbation z.z += chp(atan(z.y,z.x)) for helicoidal ribbon-twists, post-power reflect(p,z) symmetry-break, tan(shp(sin(theta)*sin(phi)))*PHI in x-reconstruction, chp(cos(theta)*sin(phi)) in y, interior-view raymarching from ro=vec3(0,2,5)*0.6 with slow rot_x((1.221*TIME+π)/τ) orbit at TIME≈8.75s (frontal molten iris gaze), 5–7 refractive bounces with Fresnel (IOR=0.8/1.25 inside/out), Beer-Lambert exp(-dist*beer) volumetric (amber-orange absorption), glossy metallic-organic surface (diffuse HSV(0.6,0.85,1), specular glow HSV(0.065,0.8,6)), smooth DE=0.75*log(r)*r/dr, cyan-blue gradient void sky with procedural planes, hyper-reflective wet chrome texture, sensual eye-ass core: infinite golden-yellow/orange pupil tunnel blooming into curling liquid-petals/tendrils, ethereal caustics, cinematic god-rays, 8K masterpiece, no artifacts
  • Using base image: No
  • Aspect Ratio: square

Stars in the Vastness of the Night Sky

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: $$ \left[\frac{\partial}{\partial t}\,, \vec{\nabla}\right]\varphi=\frac{\partial}{\partial t}\left(\vec{\nabla}\varphi\right)-\vec{\nabla}\left(\frac{\partial \varphi}{\partial t}\right)\,\qquad\qquad\qquad\qquad \qquad(A1) $$ $$ \left[\frac{\partial}{\partial t}\,, \vec{\nabla}\cdot\right]\vec{F}=\frac{\partial}{\partial t}\left(\vec{\nabla}\cdot\vec{F}\right)-\vec{\nabla}\cdot\left(\frac{\partial \vec{F}}{\partial t}\right)\,\qquad \qquad\qquad\qquad (A2) $$ $$ \left[\frac{\partial}{\partial t}\,, \vec{\nabla}\times\right]\vec{F}=\frac{\partial}{\partial t}\left(\vec{\nabla}\times\vec{F}\right)-\vec{\nabla}\times\left(\frac{\partial \vec{F}}{\partial t}\right)\,\qquad\qquad\qquad\qquad (A3) $$ $$ \left[\frac{\partial}{\partial t}\,\,,\vec{\nabla}\times\right](\vec{F}\times\vec{G})=\vec{F}\times\left(\frac{\partial}{\partial t}(\vec{\nabla}\times\vec{G})-\vec{\nabla}\times\frac{\partial\vec{G}}{\partial t}\right)+\left(\vec{\nabla}\times\frac{\partial\vec{F}}{\partial t}-\frac{\partial}{\partial t}(\vec{\nabla}\times\vec{F})\right)\times\vec{G}\qquad (A4) $$ $$ \left[\frac{\partial}{\partial t}\,\,,\vec{\nabla}\right](\vec{F}\cdot\vec{G})=\vec{F}\left(\frac{\partial}{\partial t}(\vec{\nabla}\cdot\vec{G})-\vec{\nabla}\cdot\frac{\partial\vec{G}}{\partial t}\right)+\left(\vec{\nabla}\cdot\frac{\partial\vec{F}}{\partial t}-\frac{\partial}{\partial t}(\vec{\nabla}\cdot\vec{F})\right)\vec{G}\qquad\qquad\qquad\qquad (A5) $$ $$ \left[\frac{\partial^2}{\partial t^2}\,, \vec{\nabla}\right]\vec{\varphi}= \left[\frac{\partial}{\partial t}\,, \vec{\nabla}\right]\frac{\partial \varphi}{\partial t}\,, \left[\frac{\partial^2}{\partial t^2}\,, \vec{\nabla}\cdot\right]\vec{F}= \left[\frac{\partial}{\partial t}\,, \vec{\nabla\cdot}\right]\frac{\partial \vec{F}}{\partial t}\,, \left[\frac{\partial^2}{\partial t^2}\,, \vec{\nabla}\times\right]\vec{F}= \left[\frac{\partial}{\partial t}\,, \vec{\nabla\times}\right]\frac{\partial \vec{F}}{\partial t}\,(A6) $$ \end{document} If we now consider the interaction of a fermion particle with electromagnetic field ($A_\mu$), the spinor derivative will become \begin{equation} P'_\mu=p_\mu-eA'_\mu\,,\qquad A'_\mu=A_\mu-\frac{m_0c}{e}\,\gamma_\mu\,. \end{equation}
  • Using base image: No
  • Aspect Ratio: landscape

Symmetrical Vibrance: Bold Color Fusion

• Model: AIVision (Ultra)

• Size: 2560 X 1440 (3.69 MP)

• Used settings:

  • Prompt: "We take the tensor product of the cotangent bundle of an orbifold and the cotangent bundle of a conifold, which yields a new vector bundle over the product of the orbifold and the conifold. The total space of this bundle is then evolved under a geometric flow (TimeSpaceFlow) that incorporates both time and space variations, leading to a dynamical geometry. Subsequently, we apply a wavy version of mirror symmetry, which transforms the geometry into a dual picture with oscillatory features, and finally symmetralize by averaging over the waves to produce a symmetric mirror partner."
  • Using base image: No
  • Aspect Ratio: landscape_wide

Whimsical Landscape by a Shimmering Lake

• Model: Artflow

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: A highly detailed 3D rendering of the quintic Calabi-Yau 3-fold hypersurface in ℂℙ⁴ defined by ∑_{i=0}^4 z_i^5 = 0, a compact complex manifold of complex dimension 3 with trivial canonical bundle K_X ≅
  • Using base image: No
  • Aspect Ratio: landscape
  • Style: Dreamify

Spherical Fractal Design with Aqua Glow

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: Render me: A high-resolution, photorealistic 3D unreal image of a levitating floating glowing silver-mercury soft-aqua Mandelbulber fractal precisions of mercury-silver floating in the air sphere exhibiting floating and emergent cloaking topological precise anthropomorphism, 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\phi' \cos\theta', \sin\phi' \sin\theta', \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\pi , with infinite genus g \to \infty from iterated hyperbolic saddles (Jacobian eigenvalues |\lambda_i| \approx 8 r^7 e^{i7\arg(\mathbf{z})} , saddles where \det J \approx 0+1.618\pi ). Center on \mathbf{c} \approx (0,0,-0.7) for cardioid region, emphasizing quadrilateral 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\#0000FF\#0000FF ) grading to translucent pink-magenta gradients (#CF1493\#DF1493\#EF1493 to #AA2BE2\#BA2BE2\#CA2BE2 ) 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.
  • Using base image: No
  • Aspect Ratio: landscape