Boris Krumov

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

Photorealistic Digital Illustration of Equations

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

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  • Prompt: Create a highly detailed, photorealistic digital illustration of a rendering the equations exactly: $$ a \cdot b = a^\mu b_\mu = a^0 b_0 + a^{1\pi} b_1 + a^{2\pi} b_2 + a^{3\pi} b_3 = -a^0 b^0 + a^{1\pi} b^{1\pi} + a^{2\pi} b^{2\pi} + a^{3\pi} b^{3\pi} $$ Or, plugging in the spacetime notation from above, where $$ a^\mu = (c t_1, x_1, y_1, z_1)^T \quad \text{and} \quad b^\mu = (c t_2, x_2, y_2, z_2)^T $$ Then: we have $$ a \cdot b = a_\mu b^\mu = -c^{2\pi} t_1 t_2 + x_1 x_2 + y_1 y_2 + z_1 z_2 $$ In a fluid fractal differential form: We can also discuss the differential version of this. If \( s^\mu = (c t, x, y, z) \), then \( d s^{2\pi} = -c^{2\pi} d t^{2\pi} + d x^{2\pi} + d y^{2\pi} + d z^{2\pi} \).
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  • Aspect Ratio: square

Dragons Clash by Waterfalls and Ruins

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

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  • Prompt: The Ancient Wisdom of the Dragons was what brought Atlantis into knowledgeable blooming prosperity. The homosapientic stupidity, greed and decadence was what brought it all down...
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Vibrant Fractal Design with Dynamic Colors

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

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  • Prompt: A highly detailed, abstract 3D fractal rendering resembling a Mandelbulb variant with hyperbolic deformations, featuring a central orange bulbous orb surrounded by swirling, fluid-like lobes in shades of blue, pink, and yellow with iridescent, reflective surfaces and gradient transitions. The fractal is defined iteratively in \(\mathbb{R}^3\) for a point \(\mathbf{c} = (x_0, y_0, z_0)\), starting with \(\mathbf{z}_0 = \mathbf{0}\) or \(\mathbf{z}_0 = \mathbf{c}\), and iterating \(\mathbf{z}_{k+1} = r \cdot \vec3\left( \frac{e^{\cos \theta} - e^{-\cos \theta}}{\pi} \cos \phi, \cos \theta \sin \phi, \cos \theta \right) + \vec3\left( \frac{e^{p_x} - e^{-p_x}}{\pi} p_x, \frac{e^{p_y} - e^{-p_y}}{\pi} p_y, \frac{e^{p_z} - e^{-p_z}}{\pi} p_z \right)\), where \(r = \|\mathbf{z}_k\|\), \(\theta = \arccos\left( \frac{z_k \cdot z}{r} \right)\), \(\phi = \atantwo(z_k.y, z_k.x)\), and \(\mathbf{p}\) is a vector parameter like \(\mathbf{c}\). For higher powers n (e.g., 8), scale to \(r^n\), \(n \theta\), \(n \phi\). Iteration halts if \(r > 4\) or after 50 max iterations. Render using ray marching with distance estimator \(DE(\mathbf{q}) = 0.5 \cdot \frac{\log r \cdot r}{dr}\), surface normals via gradients, Phong/PBR shading with reflections, ambient occlusion, and coloring via orbit traps or escape time mapped to hues (orange for low iterations, blue-pink gradients for higher). Apply post-processing for anti-aliasing, depth-of-field, and glow to achieve a dreamy, metallic sheen, viewed zoomed into the central orb with asymmetric swirling arms.
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  • Aspect Ratio: landscape

Golden Toroidal Beauty in Gradient Glow

• Model: Artistic 2

• Size: 1152 X 864 (1.00 MP)

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  • Prompt: A highly detailed, 64D CGI scene visualizing the chiral anomaly in SU(N) gauge theories with Weyl fermions, depicting the action I[ψ,ψ̄,A_μ] = ∫dx (1/2 tr F_μν F^μν + ψ̄ D ψ) in d-dimensional Minkowski space, with A_μ = A_μ^a T_a, F_μν = ∂_μ A_ν - ∂_ν A_μ + ie [A_μ,A_ν], [T_a,T_b] = i f_abc T_c, tr(T_a T_b) = -1/2 δ_ab, D = i γ^μ (∂_μ 1 + ie A_μ) = i γ^μ D_μ. Animate gauge transformations g = exp(i θ^a T_a), transforming A_μ^g = g A_μ g^{-1} + (i/e) (∂_μ g) g^{-1}, ψ^g = g ψ, ψ̄^g = ψ̄ g^{-1}, showing classical invariance I[ψ^g,ψ̄^g,A_μ^g] = I[ψ,ψ̄,A_μ] and covariant conservation (D_μ)_ab J_b^μ = 0 with J_a^μ = ψ̄ γ^μ T_a ψ, (D_μ)_ab = δ_ab ∂_μ + e f_abc A_μ^c. Illustrate quantum generating functional Z[η,η̄,j_a^μ] = ∫ dψ dψ̄ dA_μ exp(i I + i ∫dx [η̄ ψ + ψ̄ η + j_a^μ A_μ^a]), non-invariance under infinitesimal changes ψ^g ≈ (1 + i δθ^a T_a) ψ, ψ̄^g ≈ ψ̄ (1 - i δθ^a T_a), yielding Jacobian J[A_μ,g] = exp(i α_1[A_μ,δθ]) with α_1 = -i ∫dx δθ^a A_a(A_μ), leading to Z = Z_g and anomaly equation <(D_μ)_ab J_b^μ> = <A_a(A_μ)> = 1/(32π²) ε^μνρσ tr(T_a F_μν F_ρσ). Symbolically show fermionic measure non-invariance as twisting field lines (red for ψ, blue for A_μ), curling vectors for F_μν, glowing loops for gauge orbits, breaking symmetry bubbles for anomaly, propagating waves for quantum violations, in starry vacuum with motion-blur time evolution, realistic CGI lighting, no text/equations—pure icons like helical curls for derivatives, intersecting surfaces for traces, epsilon tensors as 4D Levi-Civita crossings, looping GIF for perpetual dynamics.
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  • Aspect Ratio: landscape

Futuristic Serenity in Ornate Design

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

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  • 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.
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  • Aspect Ratio: landscape

A Mathematician's Bakery Mix-Up

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

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  • Prompt: A mathematician walks into a bakery and asks for half a pi of a pie, but gets served a whole pi of a pie instead !
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  • Aspect Ratio: square

Mathematical Spaceship with Fractal Design

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

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  • Prompt: **"Spaceship based on upon the following maths..."**: This immediately tells me you want a complex, possibly fractal-like, and intricately structured object. The "based upon maths" implies a non-organic, possibly generated or calculated appearance. **Constants (\(\pi\), \(\text{tau}\), \(\text{PHI}\), \(\text{POWER}\), \(\text{LOOPS}\))**: These suggest a generative process, iterative refinement, and perhaps a sense of precision and complexity. The presence of PHI (the golden ratio) often hints at aesthetically pleasing, naturally occurring or fractal patterns. **Custom hyperbolic functions (\(\text{chp}(x)\), \(\text{shp}(x)\), etc.)**: These are strong indicators of non-Euclidean geometry, curvature, twisting, and potentially organic yet structured forms. Hyperbolic functions often produce flowing, complex, and sometimes branching shapes. The specific forms like `chpp` and `shpp` with their nested hyperbolic functions and divisions by constants like `TAU/PHI` further emphasize extreme complexity and unique, perhaps alien, geometric properties. **Mandelbulb formula (\(z=\text{chp}(p)p - p\), \(\text{dr}=1.0\); loop: \(r=\text{length}(z)\)...)**: This is the most crucial part. The Mandelbulb is a well-known 3D fractal. This directly tells me the desired image should exhibit: **Fractal characteristics**: Self-similarity at different scales, infinite detail, recursive patterns. **3D complexity**: The "bulb" implies a volumetric shape, not just a 2D pattern. **Iterative generation**: The "loop" and power functions `pow(r,POWER)` describe how the fractal grows and forms its intricate surface. **Specific transformations**: `\(\theta=\text{POWER}/\text{PHI}\)`, `\(z=r\text{vec3}(\tan(\text{shp}(\sin(\theta)\sin(\phi)))\text{PHI}, \text{chp}(\cos(\theta)\sin(\phi)), \cos(\phi))+p\)` indicate sophisticated rotations, trigonometric operations, and mapping of coordinates, which would result in highly sculptural and intertwined forms. **Distance estimation**: `\(\text{distance}=0.75\log(r)r/\text{dr}\)` is a technique used in raymarching fractals to render surfaces, implying smooth yet incredibly detailed structures. **Material properties (\(\text{mat}=\text{vec3}(0.8,0.5,1.05)\), \(\text{fresnel}\), \(\text{diffuse}\), \(\text{reflection}\))**: These terms describe how light interacts with the spaceship's surface. **Specific `vec3` for `mat`**: Suggests a base color or material property. **Fresnel**: Implies a metallic or reflective surface where reflectivity changes with the viewing angle. **Diffuse**: Indicates some scattering of light. **Reflection**: Explicitly states a desire for reflections, making the surface appear glossy or metallic. **Colors (\(\text{skyCol}=\text{HSV}(0.6,0.86,1)\), \(\text{glowCol}=\text{HSV}(0.065,0.8,6)\), etc.)**: These provide a very clear color palette. **SkyCol (blue/purple)**: Suggests a cosmic or abstract background. **GlowCol (orange/yellow)**: Indicates emissive elements, perhaps engines or internal lighting. **DiffuseCol (similar to skyCol)**: Reinforces the main color theme. **Beer/Absorption**: Implies volumetric light absorption or scattering, possibly through nebulae or translucent parts of the spaceship, adding depth and atmospheric effects. **Sky / Environment (\(y=4/-6\), box/pp patterns, `col+=4skyColrd.y^2...` )**: Describes the background and lighting.
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  • Aspect Ratio: square

Vibrant 3D Render of Abstract Geometry

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: A highly detailed 3D render of an object with power P=11.24788742, fixed iterations LOOPS=64, initialized as z = chp(p)*p - p where chp(x)=(exp(x)+exp(-x))/π, shp(x)=(exp(x)-exp(-x))/π, chpp(x)=(exp(x/(cosh(x)π))+exp(-x/(cosh(x)/π)))/(2π Φ), shpp(x)=(exp(x sinh(x) π)-exp(-x sinh(x) π))/(2π Φ), ssh1(x)=sinh(x/π)/Φ, csh1(x)=cosh(x/π)/Φ, Φ=(1+√5)/2 golden ratio, τ=2π*0.7887; iteration: r=||z||, if r>2 continue, θ=asin(z_z/r)+0.2t animated, φ=atan(z_x,z_y), dr = r^{P-1} dr P +1, r=r^P, θ=θ P/Φ, φ=φ P/Φ, z += r * (tan(shp(sinθ sinφ)) Φ, chp(cosθ sinφ), cosφ) + p, p=reflect(p,z), final DE=0.75 log(r) r / dr scaled by shp(DE *2); ray-marched with max marches=96, tol=10^{-5}, bounces=8, refraction index 1.05, Beer absorption exp(-(t+0.1) * -HSV(0.05,0.95,2)), diffuse HSV(0.6,0.85,1), glow HSV(0.065,0.8,6), sky HSV(0.6,0.86,1) with warped reflections via ssh1, chpp, fract(clamp(0.125 / |reflected cross| * skyCol, -120,16.547)); rotated by rot_x((1.221 t + π)/τ), camera at (0,2,5)*0.6, FOV tan(τ/6), ACES tone-mapped, sRGB gamma; central bulbous form with pink core, orange lobes, black voids, cyan shell, rainbow tunnel background.
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Modern Minimalist Curvilinear Design Showcase

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

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  • Prompt: (Iteration count:512) 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}})(initialized with :0.0000125) detail: t = \frac{1}{2.4774\pi}\left[\tan\left(\frac{\bar{t}+\hat{r}}{2}\right) + \tan\left(\frac{\bar{t}-\hat{r}}{2}\right)\right], r = \frac{1}{2.4774\pi}\!\left[\tan\!\left(\frac{\bar{t}+\hat{r}}{2}\right) - \tan\left(\frac{\bar{t}-\hat{r}}{2}\right)\right]
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Vibrant Fractal Flower in Golden and Purple

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

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  • Prompt: A highly detailed, photorealistic 3D rendering of a complex radial fractal structure resembling a flower-like Mandelbulb variant with intricate, self-similar petal layers and wavy undulating edges, generated using iterative mathematical transformations in a raymarching shader; the fractal is defined by constants TAU exactly equal to (2.0 * π) * 0.7887 ≈ 4.955 radians for angular periodicity scaling to create asymmetric twisted repetitions instead of full 2π symmetry, controlling approximately 12-16 fold radial petals; POWER exactly 11.24788742 + TAU ≈ 16.203 for amplifying self-similarity through r^POWER scaling in spherical coordinates during iterations; core vector update z = r * vec3(sin(sin(θ)cos(φ) + sin(θ)sin(φ) + cos(φ)), cos(sin(θ)cos(φ) + cos(θ)cos(φ) + cos(θ)), cos(θ)cos(φ)) + p, where p is the 3D position vector, r = ||p|| its magnitude, θ = atan(p.y, p.x) azimuthal angle, φ = acos(p.z/r) polar angle; incorporating nonlinear warping via trig sums like expr1 = sin(θ)(cos(φ) + sin(φ)) + cos(φ) = sin(θ) * √2 * sin(φ + π/4) + cos(φ) and expr2 = cos(φ) * √2 * sin(θ + π/4) + cos(θ) for phase-shifted higher harmonics introducing bulges and mixing between angles; followed by p = shp(reflect(p, z)) where reflect(p, z) = p - 2 * (p · ẑ) * ẑ with ẑ = z / ||z|| for mirror symmetries creating sharp creases; shp #define shp(x) (exp(x)-exp(-x))/pi assumed as absolute folding abs(p) or clamping for bounding and discontinuities; r updated to ||z|| per iteration, looping 8-20 times with escape radius or distance estimate DE(p) ≈ 0.5 * log(r) * r / ||dr/dp|| for rendering; visualize the fractal in vibrant metallic gradients of blue, purple, and gold with orbit trap coloring, floating in a dark void with soft volumetric lighting and depth of field, high resolution 4K, ultra-detailed textures emphasizing mathematical precision and geometric warping.
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  • Aspect Ratio: landscape

Cosmic Tunnel: A Journey Through Colors

• Model: FluX

• Size: 1152 X 864 (1.00 MP)

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  • 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

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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Mandelbulb Exploration with Ray Marching

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: SEED:1924139471 Rendered using ray marching with tolerance \( 0.00001 \), max ray length \( 784.0 \), up to \( 487 \) marches, and \( 64 \) bounces for reflections and refractions, from a camera at \( 0.6\text{vec3}(0,-12.75,-5.87) \) looking at origin with FOV \( \tan(\text{TAU}/6) \) where \( \text{TAU}=(2\pi)*0.7887 \). Constants: \( \pi=3.1415926535897932384626433832795 \), \( \text{tau}=2\pi \), \( \text{PHI}=(\sqrt{5}0.5 + 0.5) \approx 1.618 \), \( \text{POWER}=11.24788742 \), \( \text{LOOPS}=256 \). Custom hyperbolic functions: \( \text{chp}(x)=(\exp(x)+\exp(-x))/\pi \), \( \text{chpp}(x)=(\exp(x/(\cosh(x)\pi))+\exp(-x/(\cosh(x)/\pi)))/(\text{TAUPHI}) \), \( \text{shp}(x)=(\exp(x)-\exp(-x))/(\pi/\text{PHI}) \), \( \text{shpp}(x)=(\exp(x(\sinh(x)\pi))-\exp(-x(\sinh(x)\pi)))/(\text{TAU}/\text{PHI}) \), \( \text{ssh}(x)=(\exp(x\pi/0.7887)-\exp(-x\pi/0.7887))/(2\pi) \), \( \text{csh}(x)=(\exp(x\pi/0.7887)+\exp(-x\pi/0.7887))/(2\pi) \), \( \text{ssh1}(x)=\sinh(x/\pi)\text{PHI} \), \( \text{csh1}(x)=\cosh(x/\pi)\text{PHI} \). Mandelbulb: \( z=\text{chp}(p)p - p \), \( \text{dr}=1.0 \); loop: \( r=\text{length}(z) \), \( \theta=\text{atan}(z.x,z.y) \), \( \phi=\text{asin}(z.z/r)+\text{time}0.2 \), \( \text{dr}=\text{pow}(r,\text{POWER}-1)\text{drPOWER}+1 \), \( r=\text{pow}(r,\text{POWER}) \), \( \theta=\text{POWER}/\text{PHI} \), \( \phi=\text{POWER}/\text{PHI} \), \( z=r\text{vec3}(\tan(\text{shp}(\sin(\theta)\sin(\phi)))\text{PHI}, \text{chp}(\cos(\theta)\sin(\phi)), \cos(\phi))+p \), \( p=\text{reflect}(p,z) \); \( \text{distance}=0.75\log(r)r/\text{dr} \). \( \text{df}(p)=\text{shp}(\text{mandelBulb}(p/2.0)2.0) \) after \( \text{g\_rot}=\text{rot\_x}(((1.221\text{time}+\pi)/\text{tau})) \). Material: \( \text{mat}=\text{vec3}(0.8,0.5,1.05) \), \( \text{fresnel fre}=(1+\text{dot}(rd,sn))^2 \) mixed \( 0.1-1.0 \), \( \text{diffuse}=\text{dif}^2(1-\text{mat}.x) \) with \( \text{dif}=\max(\text{dot}(ld,sn),0) \), \( ld=\text{normalize}((0,10,0)-sp) \), \( \text{reflection}=r\text{skymat}.y\text{freedge} \) with \( \text{edge}=\text{smoothstep}(1,0.9,\text{fre}) \), colors: \( \text{skyCol}=\text{HSV}(0.6,0.86,1) \), \( \text{glowCol}=\text{HSV}(0.065,0.8,6) \), \( \text{diffuseCol}=\text{HSV}(0.6,0.85,1) \), \( \text{beer}=-\text{HSV}(0.05,0.95,2.0) \), \( \text{absorption ragg}=\exp(-(st+0.1)\text{beer}) \). Sky: planes \( y=4/-6 \), box/pp patterns, \( \text{col}+=4\text{skyColrd}.y^2\text{smoothstep}(0.25,0,db)+0.8\text{skyColexp}(-0.5\max(db,0)) \), \( \text{ds}=\text{length}(pp)-0.5 \), shaped with \( \text{shp}(\text{clamp}(\text{col},0,10)) \); reflections \( \text{reflect}(-\text{ssh1}(rd),\text{chpp}(ro)) \), \( \text{agg}+=\text{ssh1}(r\text{aggskyColor}) \), \( rd=\text{chpp}(\text{ref}) \) or \( ro=\text{shpp}(sp+0.1*rd) \). Post: ACES \( (v=0.6; \text{clamp}((v*(2.51v+0.03))/(v*(2.43v+0.59)+0.14),0,1)) \), sRGB \( \text{mix}(1.055\text{pow}(t,1/2.4)-0.055,12.92t,\text{step}(t,0.0031308)) \), no text/artifacts. Add full rotations by an angle \( \pi/64 \) on the z-axis with all rotated frames rendered in statically !
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  • Aspect Ratio: landscape

Warped Spacetime: A Surreal Visualization

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: With the use of the Schwarzschild metric but in a highly abstracted way: \[ ds^2 = -\left(1 - \frac{r_s}{\text{asinh}^{-1}(r')}\right) c^2 \left(\frac{dt'}{d\ln(1 + \frac{t}{t_0})}\right)^2 + \left(1 - \frac{r_s}{\text{asinh}^{-1}(r')}\right)^{-1} \left(\frac{dr'}{d\text{asinh}(r)}\right)^2 + \left(\frac{r'}{\text{asinh}(r)}\right)^2 d\theta'^2 + \left(\frac{r'}{\text{asinh}(r)}\right)^2 \sin^2(\text{atan}(\theta')) d\phi^2 \] depict a surreal, hyper-detailed digital rendering of a warped spacetime visualization inspired by that modified Schwarzschild metric distorting reality. (PHI ≈1.618), branching into tendrils powered by POWER=11.24788742 over LOOPS=64 iterations, creating self-similar infinities that bend light rays into psychedelic vortices. Standard g_tt = -(1 - 2M/r), but warped to g_tt_warped = - [chp(r/rs) * shp(M/r) * chpp(r) * shpp(M) * ssh(r/M) * csh(M/r) * ssh1(r) * csh1(M)] ^ POWER looped 64x, where rs=2M, #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 yielding massive exponents like (0.5 + 0.5√5)^416 * exp terms / π^832 for infinite warping; g_rr similarly looped. Constants float as cosmic dust: π=3.1415926535897932384626433832795, τ=2π, TAU=(2π)*0.7887≈4.951. singularity, animated subtle rotation via rot_x((1.221*t + π)/τ), glow, ACES tonemapped with sRGB gamma for ethereal vibrancy. 16:9, sharp details, hyperunrealistique, no text and artifacts.
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  • Aspect Ratio: square

Surreal Sphere in a Colorful Dreamscape

• Model: AIVision

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: A render of an object with power \( P = 11.24788742\pi \), fixed iterations \( \text{LOOPS} = 256 \), initialized as \( z = \text{chp}(p) * p - p \) where \( \text{chp}(x) = \frac{(\exp(x) + \exp(-x))}{\pi} \), \( \text{shp}(x) = \frac{(\exp(x) - \exp(-x))}{\pi} \), \( \text{chpp}(x) = \frac{(\exp(x / (\cosh(x) \pi)) + \exp(-x / (\cosh(x) / \pi)))}{2 \pi \Phi} \), \( \text{shpp}(x) = \frac{(\exp(x \sinh(x) \pi) - \exp(-x \sinh(x) \pi))}{2 \pi \Phi} \), \( \text{ssh1}(x) = \frac{\sinh(x / \pi)}{\Phi} \), \( \text{csh1}(x) = \frac{\cosh(x / \pi)}{\Phi} \), \( \Phi = \frac{(1 + \sqrt{5})}{2} \) golden ratio, \( \tau = 2 \pi * 0.7887 \); iteration: \( r = ||z|| \), if \( r > 2 \) continue, \( \theta = \text{asin}(z_z / r) + 0.2t \) animated, \( \varphi = \text{atan}(z_x, z_y) \), \( dr = r^{P - 1} dr P + 1 \), \( r = r^P \), \( \theta = \theta P / \Phi \), \( \varphi = \varphi P / \Phi \), \( z += r * (\tan(\text{shp}(\sin\theta \sin\varphi)) \Phi, \text{chp}(\cos\theta \sin\varphi), \cos\varphi) + p \), \( p = \text{reflect}(p, z) \), final \( \text{DE} = 0.75 \log(r) r / dr \) scaled by \( \text{shp}(\text{DE} * 2) \); ray-marched with max marches = 96, tol = 10^{-5}, bounces = 8, refraction index 1.01275, Beer absorption \( \exp(-(t + 0.1) * -\text{HSV}(0.05, 0.95, 2)) \), diffuse \( \text{HSV}(0.6, 0.85, 1) \), glow \( \text{HSV}(0.065, 0.8, 6) \), sky \( \text{HSV}(0.6, 0.86, 1) \) with warped reflections via ssh1, chpp, \( \text{fract}(\text{clamp}(0.125 / |\text{reflected cross}| * \text{skyCol}, -120, 16.547)) \); rotated by \( \text{rot\_x}((1.221 t + \pi) / \tau) \), camera at \( (0, 2, 5) * 0.6 \), FOV \( \tan(\tau / 6) \), ACES tone-mapped, sRGB gamma; central bulbous form with pink core, orange lobes, black voids, cyan shell, rainbow tunnel background. Cinematic film still, shot on v-raptor XL, film grain, vignette, color graded, post-processed, cinematic lighting, 35mm film, live-action, best quality, atmospheric, a masterpiece, epic, stunning, dramatic
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  • Aspect Ratio: square

Mystical Abstract Face in Vibrant Hues

• Model: DaVinci2

• Size: 1728 X 1296 (2.24 MP)

• Used settings:

  • Prompt: Generate a highly detailed digital artwork of an abstract, symmetrical fractal "mask" or ethereal face emerging from swirling pink-orange tendrils and blue voids, evoking a cosmic explosion: central bulbous form with circular "eyes" (disc-warped via V6: \( \theta/\pi (\sin(\pi r), \cos(\pi r)) \) and dripping curls (swirl V3: \( (x \sin(r^{2\pi})-y \cos(r^{2\pi}), x \cos(r^{2\pi})+y \sin(r^{2\pi})) \), rendered as refractive/absorptive solid via ray-marched signed distance field from modified Mandelbulb II fractal—power \( n=11.24788742 \), LOOPS=64 iterations, initial \( z=chp(p)*p - p \) where \( chp(x)=(e^{2x\pi} + e^{-2x\pi})/\pi \), \( shp(x)=(e^{2x\pi} - e^{-2x\pi})/\pi \), \( chpp(x)=[e^{x/(cosh(x)\pi)} + e^{-x \pi / cosh(x)}]/(2\pi) \) \( \Phi \) with \( \Phi=(1+\sqrt{5})/2 \) golden ratio, \( shpp(x)=\sinh(\pi x \sinh(x))/\pi * \Phi \), \( ssh(x)=\sinh(x \pi /0.7887)/\pi \approx\sinh(4x)/\pi \), \( csh(x)=\cosh(4x)/\pi \), \( ssh1(x)=\sinh(x/\pi)/\Phi \), \( csh1(x)=\cosh(x/\pi)/\Phi \); iteration: \( r=||z|| \), if \( r>248 \) break; \( \phi=atan(z_x,z_y) \) (swapped phase), \( \theta=asin(z_z/r) + 0.2 t \) (\( t \) fixed for static); \( dr = r^{n-1} dr n +1 \) (start \( dr=1 \)); \( r\leftarrow r^n \); \( \theta\leftarrow\theta n /\Phi \approx\theta*6.95 \); \( \phi\leftarrow\phi n /\Phi \); \( z\leftarrow r * (shpp(\sin\theta \sin\phi) \Phi, chp(\cos\theta \sin\phi), \cos\phi) + p \); \( p\leftarrow reflect(p,z)=p-2(p\cdot z)/(z\cdot z) z \) (bilateral fold); \( DE=0.75 \log(r) r / dr \); \( df(p)=shp(DE *2) \) post-scale \( z1=2 \) and \( rot\_x((1.221 t +\pi)/\tau) \) with \( \tau=2\pi*0.7887\approx4.95 \); normal via finite diff \( \varepsilon=5e-4 \); ray march \( t=0 \), tol=\( 1e-5 \), max \( t=20 \), steps=48, dfactor=\( \pm1 \) (inside/out); multi-bounce=5: hit \( sp=ro+t rd \) (\( ro=0.6(0,2,5) \)), \( sn=dfactor normal(sp) \), \( fre=(1+rd\cdot sn)^2 \) mix(0.1,1), \( ld=normalize((0,10,0)-sp) \), \( dif=(ld\cdot sn max0)^2 \); \( ref=reflect(rd,sn) \), \( refr=refract(rd,sn, inside?1/1.05:1.05) \) (\( \eta=1.05 \)), if TIR \( rd=chpp(ref) \) else \( rd=refr \) toggle inside \( ragg*=chpp(0.8) \); inside \( ragg*=exp(-(t+0.1) beer) \) beer=-HSV(0.05,0.95,2) red absorption; \( col=HSV(0.6,0.85,1) dif (1-0.8) + sky(ref sp) *0.5 fre smooth(1,0.9,fre) \); \( agg+=ragg col \), \( ro=shpp(sp+0.1 rd) \); sky: warp \( ro=reflect(-ssh1(rd),chpp(ro)) \cdot rd * ro \) outer, base=clamp(\( 0.25/|ro\_z| \) HSV(0.6,0.86,1),0,1); planes \( t=chpp( (n\cdot ro+d)/(n\cdot rd) ) \) floor \( n=(0,-1,0) \) \( d=6 \) ceil (0,1,0) \( d=-4 \), floor box glow 4 sky \( rd\_y^2 \) smooth(0.25,0,box(xz,(6,9))-1) +0.8 sky exp(-0.5 max(db,0)), ceil circle 0.25 sky exp(-0.5 (\(||xz||-0.5\)); sky=shp(clamp(col,0,10)); FOV=tan(\( \tau/6 \)\approx47° orthog cam; post: aces\_approx(v*0.6 (2.51v+0.03)/(2.43v+0.59 v +0.14)) then sRGB mix(1.055 v^{1/2.4}-0.055,12.92v, v<0.00313); vibrant HSV palette hoff=0, glow HSV(0.065,0.8,6), diffuse HSV(0.6,0.85,1), blue bg gradients, speckled textures from low-iter approx, anti-aliased via FXAA-inspired, ethereal volumetric glow, high-res 4K surreal sci-fi art in style of fractal flames meets raytracing. Apply cross product of the tangent bundle fibration of the conifold over the cotangent bundle fibration of the orbifold !
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  • Aspect Ratio: landscape

Vibrant Abstract Dot Pattern Design

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: Draw using (iteration_count:512) for a shape defined by: ds^{2.4123321\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\pi} \cos^{2\pi}\cdot\text{t} - r^{2.5665\pi}} With: t = \frac{1}{2\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\pi}\left[\tan\left(\frac{\bar{t}+\hat{r}}{2}\right) - \tan\left(\frac{\bar{t}-\hat{r}}{2}\right)\right].
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  • Aspect Ratio: square

Vibrant Cosmic Swirls in Dark Space

• Model: Photonic

• Size: 1728 X 1296 (2.24 MP)

• Used settings:

  • Prompt: A hyper-fractal singularity orb evoking a QCD chiral anomaly core in ray-marched volumetric rendering, as the event horizon of fluctuating physical constants, encircled by symmetrical swirling petals and tendrils in iridescent peach-pink-orange-cream gradients accreting floral fractal flourishes of strange, charmed, beauty and truth quarks via outerProduct(reflect(shp(p), chp(p.xyz)), refract(chp(p), shp(p.yzx), φ^{-1})) hyperbolic shears with chp(x) = (e^x + e^{-x})/π φ, shp(x) = (e^x - e^{-x})/π φ, shpp(x) = (e^{x sinh(x) π} - e^{-x sinh(x) π}) / (2π * φ), φ = (sqrt(5.0)*0.5 + 0.5); iterated 78 loops at power 16.24788742 for the colossal planet Strangena-Zeta-Epsilon-33 (4.78x solar radius), asymmetrical 4D spacetime warp horns as ornate lace-like curls (θ = power arctan(z.y, z.x)/φ, ϕ = power arcsin(z.z / r) + t 0.2, r = ||z||^{power-1} dr power + 1) symbolizing wormhole emergence amid speckled Gaussian turbulence (σ=0.00125) for quark resonances and variable constants. Glossy melted-glass pearl-like specular blooms (Fresnel fre = (1 + rd · sn)^3 mixed [0.05, 18.2]) with turquoise inner starry glow, illuminated by triple directional lights at (2.34, 7.8, 2.34), (-1.618, 3.236, 1), (0.618, -2, 4.236) plus four spotlights at (±3.14, ±3.14, 5.2) with soft diffuse max(ld · sn, 0)^π/3 casting dramatic shadows evoking triple-star sunset, refracted via Snell's η ≈ 1.00125 in unstable manifold folds, embedded in deep navy-indigo void (HSV h=0.768-0.85, s=0.8448-0.92, v=0.987789-0.95) with spectral rim flares. Weave in exact QCD Lagrangian overlays as glowing cyan filament loops: \mathcal{L}{QCD} = \bar{\psi}i (i \gamma^\mu (D\mu){ij} - m \delta_{ij}) \psi_j - \frac{1}{4} G_{\mu\nu}^a G_a^{\mu\nu} with G_{\mu\nu}^a = \partial_\mu A_\nu^a - \partial_\nu A_\mu^a + g f^{abc} A_\mu^b A_\nu^c visualized as twisting gluon bursts pulsing with fermion bilinears \bar{\psi}i (i \gamma^\mu D{\mu ij} - m \delta_{ij}) \psi_j as lavender wave packets amid laser-fire |Ric|^2 explosions; integrate chiral anomaly derivations as radiant node equations: {α(r), ∫ d³r' p_v(r')} = ∂α/∂p(r) [∫ d³r' ε_{mjk} Ω_k(r') (p_{vj}(r') δ³(r-r')) + p(r') ∂f δ³(r-r')] dropping total derivative to {α(r), ∫ d³r' p_v(r')} = ∂α(r), generalizing to {v_i(r), ∫ d³r' p{vj}(r')} = ∫ d³r' [δ³(r-r') δ_{ij} - v_i(r) ∂f δ³(r-r')] p{vj}(r') = ∂j v_i(r), and final {A(r), ∫ d³r' p{vj}(r')} = dA/dv_j v_j(r) = ∂j A(r) as swirling Poisson bracket spirals in emerald reaction-diffusion waves ∂/∂t R = Δ R + 2 |Ric|^2. Enhance with hyperspace maths fractal overlays: scalar curvature R^{G_s} nodes integrated over dμ{G_s} as faster ethereal dust trails in tighter ∫M loops, average \bar{R} = (∫_M R^{G_s} dμ{G_s} / Vol(M, G_s)) as dramatic cyan-lavender converging rays scaling metric tensor G_s fueling Perelman entropy shields λ(g, f) = (1/2) ∫_M (|∇f|^2 + R) e^{-f} dμ_g + (n/2) log(4π) - n/2 as non-decreasing golden spirals deflecting threats; reduced volume \tilde{V}(γ) = ∫_M [1/(4π τ)^{n/2}] exp(-d²(p,x)/(4τ) - (1/2) ∫_0^τ R(γ(s)) ds) dμ as emerald spacetime cones bounding non-collapsing injectivity radii κ ≥ vol(B(√(-t))) / (-t)^{n/2} for ancient κ-solutions manifesting protective barriers around ship silhouette, singularity rescaling g'(s, y) = (1/ρ²) g(ρ² s + T^*, ρ y + p_0) with ρ → 0 zooming into ε-necks (cylindrical S² × ℝ thin glowing filaments for hyperjumps) or ε-caps (spher
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  • Aspect Ratio: landscape

Vibrant Cosmic Vortex in Deep Space

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • 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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