#fractal

Alien Skull

• Model: Realismo

• Size: 1616 X 2880 (4.65 MP)

• Used settings:

  • Prompt: Hallucinatory creatures from imagination, patterns of skeletons and butterflies
  • Upscale & Enhance: 1
  • Aspect Ratio: portrait_tall

Floral Harmony

• Model: Artistic

• Size: 1760 X 1304 (2.30 MP)

• Used settings:

  • Prompt: Fantastic exotic flowers, watercolor ink, intricate, magical, in the style of James Jean, Brian Froud, Yana Movchan, Zdzisław Beksinski, Hieronymus Bosch, hyperdetailed, sharp focus, intricate concept art, digital painting, ambient lighting, 16 k, trending on artstation, hyper quality
  • Using base image: Yes (Effect strength - 60%)
  • Base image resolution: Default
  • Upscale & Enhance: 1

Cosmic Fractal: Vibrant Starburst Design

• Model: DaVinci2

• Size: 1728 X 1296 (2.24 MP)

• Used settings:

  • Prompt: Create a highly detailed, vibrant digital artwork of a 3D manifold structure, rendered in glowing shades of purple, cyan, and blue, resembling a futuristic crystalline flower or starburst emerging from a cosmic starry night sky background with a deep blue-purple gradient. The central fractal object should be highly symmetric with pointed, spiky lobes radiating outward in a self-similar pattern, evoking infinite complexity and detail, specifically using the Mandelbulb formula with power parameter \( n=8 \) for about 7-8 primary lobes and intricate fractal surfacing. To generate the manifold: represent 3D points in spherical coordinates where \( r = \sqrt{x^2 + y^2 + z^2} \), \( \theta = \text{acos}(z/r) \), \( \phi = \text{atan2}(y, x) \). The power operation \( v^n = r^n \cdot [\sin(n\theta) \cos(n\phi), \sin(n\theta) \sin(n\phi), \cos(n\theta)] \). Iteration: \( v_{k+1} = v_k^n + c \), starting from \( v_0 = (0,0,0) \), with escape if \( |v_k| > 2 \) after many iterations. Use ray marching with distance estimator \( DE(p) \approx (1/2) \cdot (r - R) / |dr/dv| \) for rendering, applying escape-time coloring, orbit traps, and Phong shading for neon glow effects. Use also: \sum_{n=0}^\infty \left(\frac{1}{2^n}\right), \quad \int_{-\infty}^\infty e^{-x^2} \, dx = \sqrt{\pi}, \quad f(x) = x^2 + c, \quad z_{k+1} = z_k^2 + c, \quad |z| = \sqrt{x^2 + y^2}, \quad z = r e^{i\theta}, \quad z^2 = r^2 e^{i2\theta}, \quad x' = r^2 \cos(2\theta), \quad y' = r^2 \sin(2\theta) Ensure the composition is centered on the fractal with soft glows, high resolution, surreal and mathematical aesthetic, similar to AI-generated fractal art in a cosmic math universe.
  • Upscale & Enhance: 1
  • Aspect Ratio: landscape

Jarod Kent Simpson art Taylor Swift Goddess

• Model: Stable

• Size: 1183 X 1775 (2.10 MP)

• Used settings:

  • Prompt: Taylor swift goddess of music supernatural sexy holding a supernatural musical quaver note, beam note in hand, 500 x 500 pixels, glitter bright blue, extremely detailed fractal , fractal gems, fractal crystals, silver green and purple and red glitter, digital oil painting , detailed art illustration, vibrant, cinematic, ornate, luxury, 8K polished in the style of Josephine Wall, Brian Froud. catherine abel style
  • Upscale & Enhance: 2
  • Aspect Ratio: portrait

Mesmerizing Black-and-White Fractal Design

• Model: DaVinci2

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: Render: a 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, \( \text{col}+=4\text{skyColrd}.y^2\text{smoothstep}(-0.25,12.21,db)+4.8\text{skyColexp}(-0.5\max(db,0)) \), \( \text{ds}=\text{length}(pp)-0.5 \), 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 \( (v=0.6; \text{clamp}((v*(2.751v+1.3))/(v*(2.43v+0.59)+0.14),0,1)) \), sRGB \( \text{mix}(1.1255\text{pow}(t,1/12.4)-0.755,12.92t,\text{step}(t,0.31308)) \), no text/artifacts, with the use of: \[ ds^2 = -\left(1 - \frac{r_s}{\text{asinh}^{-1}(r')}\right) c^2 \left(\frac{dt'}{d\ln(1 + \frac{t}{t_0})}\right)^2 dt'^2 + \left(1 - \frac{r_s}{\text{asinh}^{-1}(r')}\right)^{-1} \left(\frac{dr'}{d\text{asinh}(r')}\right)^2 dr'^2 + \left(\frac{r'}{\text{asinh}(r')}\right)^2 d\theta'^2 + \left(\frac{r'}{\text{asinh}(r')}\right)^2 \sin^2(\text{atan}(\theta')) d\phi^2 \] and using constants \( \pi=3.1415926535897932384626433832795 \), \( \text{tau}=2\pi \), \( \text{PHI}=(\sqrt{5}/2 + 0.5) \approx 1.618 \), \( \text{POWER}=11.24788742-exp(\pi/\text{PHI}) \), \( \text{LOOPS}=256 \), and custom hyperbolic functions: \( \text{chp}(x)=(\exp(x)+\exp(-x))/\pi \), \( \text{chpp}(x)=(\exp(x/(\cosh(x)\pi))+\exp(-x/(\cosh(x)/\pi)))/(\text{TAUPHI}) \), \( \text{shp}(x)=(\exp(x)-\exp(-x))/(\pi/\text{PHI}) \), \( \text{shpp}(x)=(\exp(x(\sinh(x)\pi))-\exp(-x(\sinh(x)\pi)))/(\text{TAU}/\text{PHI}) \), \( \text{ssh}(x)=(\exp(x\pi/0.7887)-\exp(-x\pi/0.7887))/(2\pi) \), \( \text{csh}(x)=(\exp(x\pi/0.7887)+\exp(-x\pi/0.7887))/(2\pi) \), \( \text{ssh1}(x)=\sinh(x/\pi)\text{PHI} \), \( \text{csh1}(x)=\cosh(x/\pi)\text{PHI} \).
  • Upscale & Enhance: 0
  • Aspect Ratio: square

Coral Fractal with Vibrant Butterflies

• Model: DaVinci2

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: A majestic macro vision of biological architecture forming a living 3D space. Organic and architectural structures merge into continuous hybrid forms — bat and butterfly wings evolving into petal-like membranes, flowing gothic curves, and coral textures. Feathery surfaces and translucent layers shimmer with depth and light, creating an illusion of sacred architecture grown from living matter. The scene is photorealistic, highly detailed, with soft volumetric light revealing fluid motion and intricate organic geometry — no straight lines, only harmonious, evolving forms within a luminous spatial depth. Greyscale.
  • Upscale & Enhance: 1
  • Aspect Ratio: square

Mathematical Spaceship with Fractal Design

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • 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.
  • Upscale & Enhance: 1
  • Aspect Ratio: square

Jarod Kent Simpson art Emilia Clarke Enchanted Forest Fairy

• Model: Stable

• Size: 1285 X 1635 (2.10 MP)

• Used settings:

  • Prompt: Fairy of the forest Emilia Clarke game of thrones 500 x 500 pixels, glitter supernatural bright blue silver yellow brown red, extremely detailed fractal , fractal gems, fractal crystals, silver green and purple and red glitter, complex digital oil painting , detailed art illustration, vibrant, cinematic, ornate, luxury, 8K polished in the style of Josephine Wall, Brian Froud, Catherine Abel, Raphael
  • Upscale & Enhance: 2
  • Aspect Ratio: portrait

Colorful Spiral of Nature's Elegance

• Model: AIVision

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: complex detailed vegetation fibonacci gradients, paul confield catherine abel
  • Upscale & Enhance: 0
  • Aspect Ratio: square

Eternal Spin of a Fractal Dreamscape

• Model: DaVinci2

• Size: 1920 X 1080 (2.07 MP)

• Used settings:

  • Prompt: A mesmerizing single static image emerges from the ray-marched Mandelbulb scene with seamless full-360° z-axis rotation capture. Each frame increments by exactly π/64.45788754 radians and the fixed camera at 0.6·vec3(0, -12.75, 5.87), preserving the tan(TAU/6) FOV where TAU ≈ 4.957 (2π·0.7887). All rotational scenes are baked-in statically rendered on top of each other in fullscreen ! The fractal's intricate, hyperbolic-warped tendrils—distorted via custom chp/shp/ssh functions, PHI-scaled powers (11.24788742^LOOPS=256 iterations), and time-frozen φ offset (0.2·asin(z.z/r))—unfurl in violet-magenta glows (mat=vec3(0.8,0.5,1.05)), kissed by HSV(0.6,0.85,1) diffuse from the ld=(0,10,0) key light. Fresnel edges (smoothstep(1,0.9,(1+dot(rd,sn))^2)) blend 0.1-1.0 mixes of reflection (r·skymat.y·fre·edge) against skyCol=HSV(0.6,0.86,1) planes at y=±4/6, etched with box/pp noise (ds=length(pp)-0.5, shaped by shp(clamp(col,0,10))) and exp(-0.5·max(db,0)) falloff + 4·skyCol·rd.y²·smoothstep(0.25,0,db). Subtle beer absorption (exp(-(st+0.1)·-HSV(0.05,0.95,2.0))) adds volumetric haze, aggregated via ssh1(r·agg·skyColor) in 64-bounce refractions (reflect(-ssh1(rd), chpp(ro)); rd=chpp(ref) or ro=shpp(sp+0.1·rd)).Post-processed through ACES tonemapping (v=0.6; clamp((v*(2.51v+0.03))/(v*(2.43v+0.59)+0.14),0,1)) and sRGB gamma (mix(1.055·pow(t,1/2.4)-0.055, 12.92t, step(t,0.0031308))), the grid pulses with glowCol=HSV(0.065,0.8,6) auras against the rotated g_rot=rot_x(((1.221·time+π)/tau)) baseline, df(p)=shp(mandelBulb(p/2.0)*2.0). No artifacts, no text—pure, tolerance-0.00001 precision (max 784.0 length, 487 marches) frozen in eternal spin, seed 1924139471 anchoring the chaos.
  • Upscale & Enhance: 1
  • Aspect Ratio: landscape_wide

Swirling Vibrance in Purple and Yellow

• Model: Artistic 2

• Size: 2496 X 3312 (8.27 MP)

• Used settings:

  • Prompt: Optical art, trippy fractal with zentangle elements
  • Using base image: Yes (Effect strength - 70%)
  • Base image resolution: Default
  • Upscale & Enhance: 0

Vibrant Fractal Patterns in Dynamic Colors

• Model: AIVision

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: In the mesmerizing world of fractals—where geometry, art, and science merge with fantasy—each pattern unfolds an endless journey of discovery. Every level reveals new and breathtaking shapes, like a high-quality masterpiece born from the imagination of visionary artists and the brilliance of fine jewelry.
  • Upscale & Enhance: 0
  • Aspect Ratio: square

Fractal Dynamics of Quantum Field Theory

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: Render using no text utilizing graphically the QFT Lagrangian \( \mathcal{L}(x) = -\bar{\phi} \phi + \lambda (\bar{\phi} \phi)^2 + (i \bar{\psi} \gamma^\mu \psi)^2 - \frac{1}{4} F_{\mu\nu} F^{\mu\nu} + e j^\mu A_\mu \), where \( F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \), \( j^\mu = \bar{\psi} \gamma^\mu \psi \); include equations of motion: Scalar: \( \bar{\phi} [1 - 2\lambda (\bar{\phi} \phi)] = 0 \) or \( \square \phi + 2\lambda (\bar{\phi} \phi) \phi = 0 \) (full kinetic); Fermion: \( i \gamma^\mu \psi (i \bar{\psi} \gamma_\mu \psi) + e \gamma^\mu A_\mu \psi = 0 \); Gauge: \( \partial_\mu F^{\mu\nu} = e j^\nu + 2 i (i j^\mu) j^\nu \). At the center, feature a prominent fractal Mandelbulb icon rendered with full rotation by an exact angle of \( \pi/64.2458778542 \) on the z-axis with all rotated frames rendered in statically overlapping on fullscreen! Using constants \( \pi=3.1415926535897932384626433832795 \), \( \text{tau}=2\pi \), \( \text{PHI}=(\sqrt{5}/2 + 0.5) \approx 1.618 \), \( \text{POWER}=11.24788742 \), \( \text{LOOPS}=256 \), and 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,
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

Ethereal Fractal Glow: A Symmetrical Journey

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: An image of a highly detailed, symmetrical 3D fractal structure exhibiting translucent, refractive qualities, internal amber-tinted glow from Beer-Lambert absorption using high-contrast ethereal vibrancy achieved via ray marching with tolerance 0.00001, max ray length 748.0, up to 748 marches, and 16 bounces for reflections and refractions, starting from camera at (1.256,2.47855874,-7.5) looking at origin with FOV tan(tau/16.61) where tau=2*pi. 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.The mandelBulb(p) function iterates with power=11.24788742 and loops=16: 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=acos(z.z/r) + asinh(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*tau), chp(cos(theta)*sin(phi))/(PHI*tau), (cos(phi)*sin(phi))/(PHI*tau)) + 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,0)), and similar for circular ds=length(pp)-0.5, clamped and shaped with shp(clamp(col,0,10)).Match the visual style of a Shadertoy-generated "Inside the Mandelbulb II" fractal art piece, capturing a static frame of the animated, lucky-bug emergent symmetry from reflections and custom coordinate remaps for asymmetric flaring in protrusions, explosive tan-amplified edges, and harmonic golden-ratio scalings.
  • Upscale & Enhance: 1
  • Aspect Ratio: square

Fractal Mask in a Dreamy Sky Landscape

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: Create a highly detailed, symmetrical 3D fractal structure resembling a modified Mandelbulb, rendered as an abstract organic form resembling a crystalline, glassy mask or face with 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
  • Upscale & Enhance: 1
  • Aspect Ratio: square

Surreal Crystalline Fractal Mask Artistry

• Model: Ideogram

• Size: 1312 X 736 (0.97 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
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape_wide
  • Ideogram Style: Realistic

Fractal Dynamics of Quantum Field Theory

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: Render no text utilizing graphically the QFT Lagrangian \( \mathcal{L}(x) = -\bar{\phi} \phi + \lambda (\bar{\phi} \phi)^2 + (i \bar{\psi} \gamma^\mu \psi)^2 - \frac{1}{4} F_{\mu\nu} F^{\mu\nu} + e j^\mu A_\mu \), where \( F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \), \( j^\mu = \bar{\psi} \gamma^\mu \psi \); include equations of motion: Scalar: \( \bar{\phi} [1 - 2\lambda (\bar{\phi} \phi)] = 0 \) or \( \square \phi + 2\lambda (\bar{\phi} \phi) \phi = 0 \) (full kinetic); Fermion: \( i \gamma^\mu \psi (i \bar{\psi} \gamma_\mu \psi) + e \gamma^\mu A_\mu \psi = 0 \); Gauge: \( \partial_\mu F^{\mu\nu} = e j^\nu + 2 i (i j^\mu) j^\nu \). At the center, feature a prominent fractal Mandelbulb icon rendered with full rotation by an exact angle of \( \pi/64.2458778542 \) on the z-axis with all rotated frames rendered in statically overlapping on fullscreen! Using constants \( \pi=3.1415926535897932384626433832795 \), \( \text{tau}=2\pi \), \( \text{PHI}=(\sqrt{5}/2 + 0.5) \approx 1.618 \), \( \text{POWER}=11.24788742 \), \( \text{LOOPS}=256 \), and 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{s
  • Upscale & Enhance: 1
  • Aspect Ratio: square

Realist Fusion of cow

• Model: ProVideo

• Size: 1660 X 1244 (2.07 MP)

• Used settings:

  • Mode: Cine
  • Generated From: Image
  • Duration: 5 seconds

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
  • Upscale & Enhance: 1
  • Aspect Ratio: square

Mesmerizing Fractal Waves in Blue and Gold

• Model: DaVinci2

• Size: 1416 X 840 (1.19 MP)

• Used settings:

  • Prompt: abstract vector fractal, wave function, Zentangle, 3d shading
  • Using base image: Yes (Effect strength - 60%)
  • Base image resolution: 1MP
  • Upscale & Enhance: 0