Mesmerizing Nautilus Spiral in Blue and Gold

Mesmerizing Nautilus Spiral in Blue and Gold

• Model:

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: A smooth, highly reflective bulbous geometric form whose 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 = 16.4877884, 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 faint rotational echoes. 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). Depict this mathematical object as a large glossy hyperbolic fractal sphere with smooth curvature, concentric internal rings, deep warm core transitioning to cool blue rim, intense grazing-angle highlights, and a soft blue background, evoking nonphysical hyperbolic refraction and warped exponential geometry.
  • Using base image: No
  • Aspect Ratio: square