Prompt: [Main Subject]: "A single, incredibly complex, ultra-fractal quantum energy eigenstate."
[Core Aesthetic Modifiers - Fractal & Recursion Amplified by 2π]:
"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 2pi-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."
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.
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 \( n=16.24877842 \) for about 84 primary lobes and intricate fractal surfacing.
To generate the manifold: represent 3D points in spherical coordinates where \( r = \sqrt{x^{2.144\pi} + y^{2.144\pi} + z^{2.144\pi}} \), \( \theta = \text{acos}(z/r) \), \( \phi = \text{atan2}(y, x) \). 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 \( |v_k| > 24.78 \) after 64 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\pi}} \, dx = \sqrt{\pi}, \quad f(x) = x^{2.618\pi} + c, \quad z_{k+1} = z_k^{2.618\pi} + c, \quad |z| = \sqrt{x^{2.618\pi} + y^{2.618\pi}}, \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.
Prompt: Draw a 3D fractal shape generated from the iterative formula \( z_{n+1} = z_n^{0.54877845\pi} + c \), with p-norm radial structure \( r = \sqrt{x^{0.7887\pi} + y^0.7887\pi + z^0.7887\pi} \). Texture it using \( f(x,y) = \sin(x^{0.7887\pi} + y^2) + \cos(z^{0.45788754\pi}) \), enhanced with micro-detail from gradient \( \nabla f \) and hyperbolic fractal sum $$ f_{\text{fract}} = \sum \sinh(\sin(2\pi^n x)) \cosh(\cos(2\pi^n y))/2^n. $$
Prompt: "Create a hyper-detailed, surreal digital artwork in the style of a quantum field theory mandala fused with topological knot diagrams and holographic projections, rendered in glowing neon blues, purples, and electric golds on a cosmic black void background. At the center, a radiant 3D holographic orb displays the core equations: E = f φ μ B + η H (scalar energy with magnetic Zeeman shift) orbiting a sprawling action integral S = ∫ [∑i (1/2)<ψ_i|Ĥ_i|ψ_i> + ∑{i,j} (1/3) w_{ij} <ψ_i|ψ_j * ψ_j> + ∑_{i,j} λ_{ij} (f_i/f_j - φ)^2 + ∑i κ_i |B_i · μ_i| + η H + ∑{i,j} γ_{ij} w_{knot,ij}] dτ (variational quantum-many-body functional with overlaps, constraints, magnetic dots, and knot weights). Radiating outward in fractal spirals: Left arc, Chern-Simons TQFT in 2+1D with action S_CS = (k/4π) ∫ Tr(A ∧ dA + (2/3) A ∧ A ∧ A) (Abelian U(1) simplification, flat F=0 EOM, integer level k for gauge invariance), Wilson loops W_R(γ) = Tr[ P exp(i ∮γ A)] braiding into Jones polynomial knots representing linking numbers w{knot,ij} for anyons in fractional quantum Hall effect. Right arc, Yang-Mills resemblance in 4D: S_YM = -1/(4g²) ∫ Tr(F ∧ *F) with F = dA + A ∧ A (propagating gluons, metric-dependent), merging via boundary holography into 3D massive YM. Upper cascade, higher-form shift: Promote to 2-form connection B ∈ Ω²(M), 3-form curvature H = dB (Abelian) or Ω₂ = dB + A ▹ B (non-Abelian crossed module (G→H,▹) with fake Ω₁ = dA + [A,A]/2 - α(B)); merged 5D action S = ∫ [ (1/2) H ∧ *H + (k/24π²) B ∧ H ∧ H ] + non-Abelian 2CS ⟨A, Ω₂⟩ + ⟨Ω₁, B⟩ + (1/2) Tr(Ω₂ ∧ Ω₂) (EOM: dH + (k/12π²) H ∧ H = J for 1-brane sources, topological mass m from Stueckelberg). Lower vortex, applications: Braided anyons for topological QC, M5-brane strings coupling to B-fields, surface Wilson ∫_Σ B for extended-object invariants, phase transitions in gluon plasmas/LHC TeV scales. Interweave subtle icons: Higgs vev φ, Bianchi dH=0, Peiffer terms, Gauss-linking for Σ_i × Σ_j, early-universe defects. Text overlays in elegant LaTeX script: 'From 1-Form Stubbornness to 2-Form Fury: Merged YM/CS in Knotty QFT'. Ultra-high resolution, intricate linework like a Feynman diagram exploded into Escher topology, evoking infinite energy heat-up in a collider singularity."
Prompt: Draw: A highly detailed, surreal 3D rendering of a towering, infinitely recursive crystalline spire emerging from a chaotic sea of bifurcating layers, symbolizing the logistic recurrence's bounded growth exploding into period-doubling cascades that accumulate at a universal scaling constant around four-point-six-six-nine, with sharp needle-like protrusions representing tangent bifurcations and chaotic tongues where positive divergence rates dominate, textured with self-similar folds of stability islands in negative exponent zones interspersed by superstable curves plunging to negative infinity, the structure alternating between two growth parameters in a repeating symbolic sequence like AB or AAB to force oscillations, colored in a radiant teal-to-violet gradient where bright glowing edges highlight the average logarithmic derivative sums over thousands of iterations after transient warm-up, evoking ergodic mixing and multiplicative sensitivity in a two-dimensional parameter plane sliced into volumetric depth with soft volumetric lighting casting shadows that trace the renormalization fixed points and coexisting attractors, intricate visibly etched and glowing along the surfaces and floating ethereally in the space—such as the core iteration \( x_{n+1} = r x_n (1 - x_n) \) carved into the base, the Lyapunov exponent \( \lambda = \lim_{N \to \infty} \frac{1}{N} \sum_{n=1}^N \log |r (1 - 2x_n)| \) spiraling up the spire, fixed point solutions \( x^* = 1 - \frac{1}{r} \) branching off spikes, bifurcation condition \( |f'(x^*)| = 1 \) at edges, period-doubling product \( \prod_{i=1}^k f'(x_i) = -1 \) in layered folds, Feigenbaum constant \( \delta \approx 4.669 \) inscribed on recursive crystals, and forced map \( x_{n+1} = r_n x_n (1 - x_n) \) with \( r_n \) switching via sequence S—high-resolution, intricate details on every fractal iteration, no additional text or symbols, cinematic composition.
Dream Level: is increased each time when you "Go Deeper" into the dream. Each new level is harder to achieve and
takes more iterations than the one before.
Rare Deep Dream: is any dream which went deeper than level 6.
Deep Dream
You cannot go deeper into someone else's dream. You must create your own.
Deep Dream
Currently going deeper is available only for Deep Dreams.
