The Nietzschebrot

Revealing the anti-buddhabrot's structure with orbit traps

BEHOLD

4096 max iterations with a r=0.1 ball at ðe origin as ðe trap

ðese “Nietzschebrots” are rendered like a basic anti-buddhabrot(so a density map of where points inside ðe Mandelbrot set pass θru when iterated), but wiθ ðe contribution of orbits weighted by ðeir minimum distance to a certain orbit trap, producing far more interesting results.

ðe name perfectly illustrates ðe clarity of ðese renders, wiθ ðe anti-Buddha being of course, Nietzsche,

ðe confused “anti-buddhabrot” in false color for reference

Grand Unification

ðere are a few ways to color ðese, starting wiθ ðe most arbitrary approach, combining your Nietzschebrot render wiθ a basic anti-buddhabrot to make an artistic depiction ðat hopefully also shows off ðe structure better ðen a greyscale image.

heart & r=1 circle traps

Of course ðe classic nebulabrot coloring, using a different (max)iteration count for each color channel, also works

r/g/b = 3000/300/30 max, wiθ diagonal orbit traps

Or you could give each rgb channel its own orbit trap(or none)

Here shown on ðe 3d (x,y,z)^4/(1 + x^3, y^3, z^3) + c fractal(using ðe standard White mandelbulb power formula(& extrapolated division) for 3d pseudo-complex algebra), as ðis technique can be used to render any* oðer (similarly defined) fractal

🔴 = full anti-buddhabrot

🟢 = sphere trap

🔵 = heart trap

(wiθ enhanced contrast)

Afterword

more research is needed(aka, part 2 coming soon™ confirmed???)