#mathematicalobject

Vibrant 3D Render of Abstract Geometry

• Model:

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: A highly detailed 3D render of an object with power P=11.24788742, fixed iterations LOOPS=64, initialized as z = chp(p)*p - p where chp(x)=(exp(x)+exp(-x))/π, shp(x)=(exp(x)-exp(-x))/π, chpp(x)=(exp(x/(cosh(x)π))+exp(-x/(cosh(x)/π)))/(2π Φ), shpp(x)=(exp(x sinh(x) π)-exp(-x sinh(x) π))/(2π Φ), ssh1(x)=sinh(x/π)/Φ, csh1(x)=cosh(x/π)/Φ, Φ=(1+√5)/2 golden ratio, τ=2π*0.7887; iteration: r=||z||, if r>2 continue, θ=asin(z_z/r)+0.2t animated, φ=atan(z_x,z_y), dr = r^{P-1} dr P +1, r=r^P, θ=θ P/Φ, φ=φ P/Φ, z += r * (tan(shp(sinθ sinφ)) Φ, chp(cosθ sinφ), cosφ) + p, p=reflect(p,z), final DE=0.75 log(r) r / dr scaled by shp(DE *2); ray-marched with max marches=96, tol=10^{-5}, bounces=8, refraction index 1.05, Beer absorption exp(-(t+0.1) * -HSV(0.05,0.95,2)), diffuse HSV(0.6,0.85,1), glow HSV(0.065,0.8,6), sky HSV(0.6,0.86,1) with warped reflections via ssh1, chpp, fract(clamp(0.125 / |reflected cross| * skyCol, -120,16.547)); rotated by rot_x((1.221 t + π)/τ), camera at (0,2,5)*0.6, FOV tan(τ/6), ACES tone-mapped, sRGB gamma; central bulbous form with pink core, orange lobes, black voids, cyan shell, rainbow tunnel background.
  • Using base image: No
  • Aspect Ratio: square