Vibrant Fractal Patterns in Intricate Design

Vibrant Fractal Patterns in Intricate Design

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

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  • Prompt: A shape is generated by a 3-D iterative map defined by the functions chp(x)=(e^x+e^{-x})/π, shp(x)=(e^x−e^{-x})/π, chpp(x)=[e^{x/(cosh(x)π)}+e^{-x/(cosh(x)/π)}]·Φ/τ, and shpp(x)=[e^{x(sinh(x)π)}−e^{-x(sinh(x)π)}]·Φ/τ and Φ=(sqrt(5)+1)/2. The surface arises from iterating z₀ = chp(p)p − p, then for each step computing r=‖z‖, θ=atan2(zₓ,zᵧ), φ=arcsin(z_z/r)+ωt, raising r to power P = 16.478874, scaling θ and φ by P/Φ, then updating z ← r^P·(p × 1/chpp(z)) + p and reflecting p across z. The final radial structure is defined by D(p)=shp(0.75·log(r)·r/dr), forming a smooth inflated hyperbolic-fractal sphere with wild rotational echoes on each normal vector. Light behaves through a dual ray map: outside reflection v−2(v·n)n, inside hyperbolic refraction H(v−2(v·n)n) with H(x)=shpp(x), and sky directions reflected across chpp(x) with 512 iterations for raytracing.
  • Upscale & Enhance: 1
  • Aspect Ratio: square