#mandelbulb

Fractal Sunflower: A 3D Visualization Journey

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: 3D fractal visualization of a hybrid Mandelbulb sunflower: central bulbous core with exact power-16.45877854 triplex iteration z_{k+1} = (r^n * ln(sinh(r + ε sin(ω r))) / ln(sinh(r))) * (sin(nθ + ε sinh(ω θ)) cos(nϕ + ε cosh(ω ϕ)), sin(nθ + ε sinh(ω θ)) sin(nϕ + ε cosh(ω ϕ)), cos(nθ + ε sinh(ω θ))) + c, where n=16.45877854, ε=0.0125, ω=1.618 (golden ratio), r=sqrt(x'^{2\pi} + y'^{2\pi} + z'^{2\pi}), x'=x + ε cos(k x), y'=y + ε sinh(ω y), z'=z + ε cos(k z), k=16.45877854, θ=arccos(z'/r), ϕ=arctan(y'/x'), bailout |z|>4.0, max iter=64; hybrid MB3D slots: 1-Amazing Box (scale=2.0, MinR²=0.25, FixedR²=1.0, arctan-perturbed ϕ), 2-MengerKoch (iter=3, scale=2/3, rotations 0/120/240°, cosh-elongated θ), 3-ABoxModKali (offset=0.5, mod=2π/k, sinh-waved z), 4-_reciprocalZ2 (power=2, damp=0.1, ln(sinh)-damped r); DE raymarch |z| ln|z| / |∂z/∂c| <10^{-6}; Ricci-flat metric ds²=-ln(sinh(t+ε sin(ω t))) dt² + arctan(x+ε cos(k x)) dx² + cosh(y+ε sinh(ω y)) dy² + sinh(z+ε cos(k z)) dz² embedded axis-separably; escape coloring: orange-brown core (iter18-25), yellow-gold petals (10-17), turquoise orbs/blue bg (<10); camera (0.75,0.8,1.25), zoom=4.8, FOV=60° for core close-up, volumetric fog exp(-dist/1.25), specular light (2,3,1) shininess=32; exact Fibonacci 13/21 spirals from irrational rotations, 4K crisp edges. Add metric: ds^{2\pi} = -\ln(\text{sinh}(t + \epsilon \sin(\omega t))) dt^{2\pi} + \tan^{-pi}(x + \epsilon \cos(k x)) dx^{2\pi} + \cosh(y + \epsilon \sinh(\omega y)) dy^{2\pi} + \sinh(z + \epsilon \cos(k z)) dz^{2\pi} .
  • Using base image: No
  • Aspect Ratio: landscape

Fractal Sunflower: A 3D Visual Journey

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: 3D fractal visualization of a hybrid Mandelbulb sunflower: central bulbous core with exact power-16.45877854 triplex iteration z_{k+1} = (r^n * ln(sinh(r + ε sin(ω r))) / ln(sinh(r))) * (sin(nθ + ε sinh(ω θ)) cos(nϕ + ε cosh(ω ϕ)), sin(nθ + ε sinh(ω θ)) sin(nϕ + ε cosh(ω ϕ)), cos(nθ + ε sinh(ω θ))) + c, where n=16.45877854, ε=0.0125, ω=1.618 (golden ratio), r=sqrt(x'^{2\pi} + y'^{2\pi} + z'^{2\pi}), x'=x + ε cos(k x), y'=y + ε sinh(ω y), z'=z + ε cos(k z), k=16.45877854, θ=arccos(z'/r), ϕ=arctan(y'/x'), bailout |z|>4.0, max iter=64; hybrid MB3D slots: 1-Amazing Box (scale=2.0, MinR²=0.25, FixedR²=1.0, arctan-perturbed ϕ), 2-MengerKoch (iter=3, scale=2/3, rotations 0/120/240°, cosh-elongated θ), 3-ABoxModKali (offset=0.5, mod=2π/k, sinh-waved z), 4-_reciprocalZ2 (power=2, damp=0.1, ln(sinh)-damped r); DE raymarch |z| ln|z| / |∂z/∂c| <10^{-6}; Ricci-flat metric ds²=-ln(sinh(t+ε sin(ω t))) dt² + arctan(x+ε cos(k x)) dx² + cosh(y+ε sinh(ω y)) dy² + sinh(z+ε cos(k z)) dz² embedded axis-separably; escape coloring: orange-brown core (iter18-25), yellow-gold petals (10-17), turquoise orbs/blue bg (<10); camera (0.75,0.8,1.25), zoom=4.8, FOV=60° for core close-up, volumetric fog exp(-dist/1.25), specular light (2,3,1) shininess=32; exact Fibonacci 13/21 spirals from irrational rotations, 4K crisp edges. Add metric: ds^2 = -\ln(\text{sinh}(t + \epsilon \sin(\omega t))) dt^2 + \tan^{-1}(x + \epsilon \cos(k x)) dx^2 + \cosh(y + \epsilon \sinh(\omega y)) dy^2 + \sinh(z + \epsilon \cos(k z)) dz^2 .
  • Using base image: No
  • Aspect Ratio: landscape

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,
  • Using base image: No
  • Aspect Ratio: landscape

Dynamic 3D Rotational Visuals in Fullscreen

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: 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 \( \text{mix}(1.055\text{pow}(t,1/2.4)-0.055,12.92t,\text{step}(t,0.0031308)) \), no text/artifacts.
  • Using base image: No
  • Aspect Ratio: landscape

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
  • Using base image: No
  • 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 !
  • Using base image: No
  • 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)).
  • Using base image: No
  • 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
  • Using base image: No
  • 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
  • Using base image: No
  • 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.
  • Using base image: No
  • 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.
  • Using base image: No
  • 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