#mandelbulb

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

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 !
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

Advanced MandelBulb Rendering Techniques

• Model: AIVision

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: 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,0)), and similar for circular ds=length(pp)-0.5, clamped and shaped with shp(clamp(col,0,10)).
  • Upscale & Enhance: 0
  • Aspect Ratio: square

Fractal Nightmares in an Alien Starship

• Model: Photonic

• Size: 1152 X 896 (1.03 MP)

• Used settings:

  • Prompt: inside an alien starship, fractal design, mandelbulb gothic, strange, disturbing, uncanny, mandelbrot surrealism, science fiction, horror, surrealism
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

Fractal Nightmares: Inside an Alien Starship

• Model: DaVinci2

• Size: 1152 X 896 (1.03 MP)

• Used settings:

  • Prompt: inside an alien starship, fractal design, mandelbulb gothic, strange, disturbing, uncanny, mandelbrot surrealism, science fiction, horror, surrealism
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

Enchanted Garden: 3D Fractal Floral Fantasy

• Model: AIVision

• Size: 2981 X 1677 (5.00 MP)

• Used settings:

  • Prompt: Ethereal purple flowers and delicate leaves elegantly arranged in a transparent vase, set against a vibrant azure backdrop. The intricate 3D fractal artwork captures the essence of a whimsical garden, with each petal and leaf meticulously crafted. The 3D illustration showcases a fusion of realism and fantasy, immersing viewers in a world of digital artistry. The detailed digital 3D art piece exudes beauty and sophistication, with a stunning render that brings the floral composition to life. This artwork is a trending sensation on Behance, captivating audiences with its innovative approach to 3D art. The mandelbulb design adds a touch of complexity and enchantment to the overall aesthetic, creating a visual masterpiece that mesmerizes the senses. The use of Octane Render enhances the intricate details and textures, elevating the artwork to new heights of visual splendor. Explore the mesmerizing world of 3D fractals and mandelbulbs in this stunning artistic creation.
  • Upscale & Enhance: 5
  • Aspect Ratio: landscape

Prehistoric Eden: A Neon Maqarnas Dream.

• Model: AIVision

• Size: 2236 X 2236 (5.00 MP)

• Used settings:

  • Prompt: Adam and Eve concealed in lush, prehistoricore surroundings, neon glow-in-dark body-painted with Maqarnas designs, blending into a mesmerizing fractal landscape. The scene features intricate Mandelbulb formations, intricate Fibonacci patterns, and complex tesselation. Utilize vibrant colors and contrasting hues inspired by Girih tiling, reminiscent of the Harlem Renaissance era. The image should exude a surreal, psychedelic vibe with a touch of cosmic essence. Employ volumetric lighting to enhance the details and create a hypnotic, highly detailed composition. Set against a backdrop of a Hudson River School-inspired landscape, infuse elements of lyrical abstraction for a dreamlike quality. Ensure the resolution is 8k for maximum clarity and detail. This masterpiece should be a fusion of art styles, from Arabesque to School of Illusion, resonating with the spirit of Nouveau art. The final image should be rendered using Mandelbulber3d and Horde3D, with a touch of Unreal Engine 5 magic, embodying the essence of infinity. The artwork should be as captivating as the works of Greg Rutkowski and Thomas Kinkade, suitable for DeviantArt and trending on ArtStation.
  • Upscale & Enhance: 5
  • Aspect Ratio: square

Mandelbulb Fractal Meets AI

• Model: Artistic 2

• Size: 1168 X 880 (1.03 MP)

• Used settings:

  • Prompt: Op art, trippy fractal
  • Using base image: Yes (Effect strength - 60%)
  • Base image resolution: Default
  • Upscale & Enhance: 0

Evolving Mandelbulb 01

• Model: CinemagicAI

• Size: 1732 X 1155 (2.00 MP)

• Used settings:

  • Quality: Normal
  • Face enhance: No
  • Aspect ratio: landscape
  • Motion control: No

Locomotive

• Model: Artistic

• Size: 896 X 704 (0.63 MP)

• Used settings:

  • Prompt: Sign of magic, Dark rainy morning in a fantastic old township, dirty, untidy, riverside, litter, steam, one picture, wicked perspective, timeless momentum, eerie and oppressive oil painting by Alexander Jansson, 88grzes, Orley Ypon, Yves Tanguy, Ismail Inceoglu, Huang Guangjian and Dan Witz, detailed painting, mandelbulb, Huang Guangjian, strong coloration, night, soft lighting, subsurface scattering, realistic, heavy shadow, masterpiece, best quality, ultra realistic, 8k, golden ratio, Intricate, High Detail, film scenery,
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

sexy alien fractal vines, leaves & flower fantasy

• Model: Fusion*

• Size: 864 X 672 (0.58 MP)

• Used settings:

  • Prompt: A 3D render of a sexy alien flower with fractal stamen and fractal vines and leaves
  • Using base image: Yes (Effect strength - 55%)
  • Base image resolution: Default
  • Upscale & Enhance: 0

underwater fractal fungi jellyfish peacock jungle

• Model: Artistic

• Size: 875 X 1199 (1.05 MP)

• Used settings:

  • Prompt: An underwater floral fractal forest growing fungi mycelium roots into a tall Manldebulb 3D psytharella aquatica fungi jungle and Nomura Jellyfish lights floating
  • Using base image: Yes (Effect strength - 44%)
  • Base image resolution: Default
  • Upscale & Enhance: 1