#visualization

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

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} .
  • Upscale & Enhance: 0
  • 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 .
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

Exploring Dynamic Graphs and Mathematical Concepts

• Model: DaVinci2

• Size: 1280 X 720 (0.92 MP)

• Used settings:

  • Prompt: Rencally no tezing utilixt graphider thengian LagraQFT. Thissentation vicately represual intriry comnamic quaphics theocepts confield with a dybines frabulb Mandelctal, showplay arant vib intercasing ofgance mathening eleand stunmatical grantum.
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape_wide

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

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

Emotional Journey Through Sound and Vision

• Model: FluX

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: A cinematic, hyper-realistic portrait of a person experiencing a song's deep meaning. A man sits in a dimly lit room, eyes closed in profound concentration, wearing high-quality headphones. Ethereal, abstract visualizations of the song's emotional core—sorrow, joy, longing—swirl around his head as intricate, glowing patterns and symbolic shapes. A single tear traces his cheek as he fully understands the artist's soul and the story behind the lyrics. The atmosphere is one of transcendent connection and emotional revelation. Shallow depth of field, dramatic lighting, 8k, hyper-detailed.
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

Cosmic Web: A Vibrant Abstract Visualization

• Model: Realismo

• Size: 2400 X 1800 (4.32 MP)

• Used settings:

  • Prompt: futuristic style concept art, dynamic lighting, hyperdetailed, intricately blended and shadowed, loading screen art, splash screen art style, deep colors, volumetric lighting, intricate details, HDR, beautifully shot, hyperrealistic, sharp focus, 64 megapixels, perfect composition, high contrast, cinematic, atmospheric, moody
  • Upscale & Enhance: 1
  • Aspect Ratio: landscape

Exploring the World of AI Visualization

• Model: AIVision

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: Visualization of AI
  • Upscale & Enhance: 0
  • Aspect Ratio: square

Vibrant 3D Abstract Colorful Visualization

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: A Mesmerizing 3D Abstract Multicolor Visualization
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

Exploring the Web of Connections

• Model: Artistic

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: map of connections
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

Exploring the Google DeepDream Algorithm

• Model: FluX

• Size: 1728 X 1296 (2.24 MP)

• Used settings:

  • Prompt: Google DeepDream algorithm
  • Upscale & Enhance: 1
  • Aspect Ratio: landscape