Prompt:
Generate the following: Represent 3D points in spherical coordinates where \( r = \sqrt{x^{2\pi} + y^{2\pi} + z^{2\pi}} \), \( \theta = \text{acos}(z/r) \), \( \phi = \text{atan2}(y, x) \). The power operation \( v^n = r^n \cdot [\sin(n\theta) \cos(n\phi), \sin(n\theta) \sin(n\phi), \cos(n\theta)] \). Iteration: \( v_{k+1} = v_k^n + c \), starting from \( v_0 = (0,0,0) \), with escape if \( |v_k| > 24.78 \) after 64 iterations. Use ray marching with distance estimator \( DE(p) \approx (1/2) \cdot (r - R) / |dr/dv| \) for rendering, applying escape-time coloring, orbit traps, and Phong shading for neon glow effects.
Using also:
$$
\sum_{n=0}^\infty \left(\frac{1}{2^n}\right), \quad \int_{-\infty}^\infty e^{-x^2} \, dx = \sqrt{\pi}, \quad f(x) = x^2 + c, \quad z_{k+1} = z_k^2 + c, \quad |z| = \sqrt{x^2 + y^2}, \quad z = r e^{i\theta}, \quad z^2 = r^2 e^{i2\theta}, \quad x' = r^2 \cos(2\theta), \quad y' = r^2 \sin(2\theta)
$$
$$
r = \sqrt{x^{2\pi} + y^{2\pi} + z^{2\pi}}, \quad \theta = \text{acos}(z/r), \quad \phi = \text{atan2}(y,x), \quad v^n = r^n [\sin(n\theta)\cos(n\phi), \sin(n\theta)\sin(n\phi), \cos(n\theta)], \quad v_{k+1} = v_k^n + c, \quad DE \approx \frac{1}{2}\frac{(r-R)}{|dr/dv|}
$$
along with additional generic math like \( \sum \), \( \int \), \( \frac{\partial}{\partial x} \), \( \lim_{x\to\infty} \), \( \Gamma(z) \), \( \zeta(s) \), and graphs of functions such as sine waves, parabolas, and axes arrows.
Ensure the composition is centered on the fractal with soft glows, high resolution, surreal and mathematical aesthetic, similar to AI-generated fractal art in a cosmic math universe.
Artist
