Cosmic Sphere of Colorful Petals

Cosmic Sphere of Colorful Petals

• Model: Ideogram

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: A highly detailed, photorealistic 3D rendering of a complex radial fractal structure resembling a flower-like Mandelbulb variant with intricate, self-similar petal layers and wavy undulating edges, generated using iterative mathematical transformations in a raymarching shader; the fractal is defined by constants TAU exactly equal to (2.0 * π) * 0.7887 ≈ 4.955 radians for angular periodicity scaling to create asymmetric twisted repetitions instead of full 2π symmetry, controlling approximately 128-256 fold radial petals; POWER exactly 11.24788742 + TAU ≈ 16.203 for amplifying self-similarity through r^POWER scaling in spherical coordinates during iterations; core vector update z = r * vec3(sin(sin(θ)cos(φ) + sin(θ)sin(φ) + cos(φ)), cos(sin(θ)cos(φ) + cos(θ)cos(φ) + cos(θ)), cos(θ)cos(φ)) + p/1.618, where p is the 3D position vector, r = ||p|| its magnitude, θ = atan(p.y, p.x) azimuthal angle, φ = acos(p.z/r) polar angle; incorporating nonlinear warping via trig sums like expr1 = sin(θ)(cos(φ) + sin(φ)) + cos(φ) = sin(θ) * √2 * sin(φ + π/4) + cos(φ) and expr2 = cos(φ) * √2 * sin(θ + π/4) + cos(θ) for phase-shifted higher harmonics introducing bulges and mixing between angles; followed by p = shp(reflect(p, z)) where reflect(p, z) = p - 2 * (p · ẑ) * ẑ with ẑ = z / ||z|| for mirror symmetries creating sharp creases; shp #define shp(x) (exp(x)-exp(-x))/pi assumed as absolute folding abs(p) or clamping for bounding and discontinuities; r updated to ||z|| per iteration, looping 64 times with escape radius or distance estimate DE(p) = ( 0.6575 * log(r) * exp(1./r) * r / ||dr/dp|| for rendering; visualize the fractal in vibrant metallic gradients of blue, purple, and gold with orbit trap coloring, floating in cosmical void with soft volumetric lighting and depth of field, ultra-detailed textures emphasizing mathematical precision and geometric warping.
  • Upscale & Enhance: 0
  • Aspect Ratio: square
  • Ideogram Style: Auto