Fraktoler Curious

A proof I wrote a few years ago about the rotational symmetry of Multibrot (aka Mandelbrot generalized)

2 years ago | [YT] | 1

Fraktoler Curious

Domain coloring of tetration base e (e^^z) made in Ultra Fractal 6:
First picture shows the complex plot of f(z) = e^^z, viewport z from 8 + 8i to -8 - 8i (Integer lattice included)
Second picture shows the plot of f(z) = e^^(e^^z) (Basically tetration iterated twice), with the same viewport but without the integer lattice.

Making fractals from this tetration function is very hard due to the slow computing speed, low precision and unstable behavior when iterating.

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2 years ago (edited) | [YT] | 0

Fraktoler Curious

Domain coloring of f(z) = Re(z)^Im(z) - Im(z)^Re(z)
This shows the solutions of the equation x^y = y^x (Black lines & points)
Darker: f(z) gets small, close to 0
Lighter: f(z) gets large, "close" to infinity
Hue: Argument of f(z) (red = positive real, cyan = negative real)

Second image is the same as first image except the integer lattice

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3 years ago (edited) | [YT] | 2