Mathematical Visualizations

Fractals, cellular automata, and more!

Mandelbrot and Julia Sets Discrete Painleve Equations

dP1 qP1 qP4

Visualizing complex-valued functions Game of Life Langton's Ant

Discrete Painleve Equations

This is given by the recurrence equation

\[w_{n+1}w_{n-1}=\frac{1}{w_n}-\frac{1}{aq^nw_n^2}\]

with $a,q\in\mathbb C$ constants.

Number of iterates:

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$n$	$w_n$	Stereographic projection of $w_n$