#mathematicaliteration

Mathematical Marvels in 3D Visualization

• Model:

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: Draw an object following the exact math: central bulbous core with exact power-16.78544587 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=16.78544587, ε=0.001275, ω=1.618 (golden ratio), r=sqrt(x'^{1.618\pi} + y'^{1.618\pi} + z'^{1.618\pi}), x'=x + ε cos(k x), y'=y + ε sinh(ω y), z'=z + ε cos(k z), k=16.78544587, θ=arccos(z'/r), ϕ=arctan(y'/x'), bailout |z|>48.84, max iter=64; hybrid MB3D slots: 1-Amazing Box (scale=12.21, MinR²=0.01275, FixedR²=16.78544587, arctan-perturbed ϕ), 2-MengerKoch (iter=32, scale=\frac{2}{\pi} = 2/\pi, rotations pi\16.78544587, cosh-elongated θ), 3-ABoxModKali (offset=0.125, mod=(2.45788754*π)/k, sinh-waved z), 4-_reciprocalZ2 (power=2*16.78544587, damp=0.001278, ln(sinh)-damped r); DE raymarch |z| ln|z| / |∂z/∂c| <10^{-64}; Ricci-flat 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} embedded axis-separably; escape coloring: firey glowing core (iter48-64), plasma petals (24-32), turquoise orbs/blue bg (12); camera (1.5,0.8,1.25), zoom=4.8, FOV=78° for core close-up, volumetric fog exp(-dist/64), specular light (12.23,7.47,2.78) shininess=64; exact Fibonacci 13/21 spirals from irrational rotations, 4K crisp edges.
  • Using base image: No
  • Aspect Ratio: square