## Mandelbrot set sketch in Scratch

Despite my personal disbelieve in and dislike of the colored blocks dragging simulator 3, I nevertheless wanted to extract functionality other than the hardcoded cat mascot path tracing from the aforementioned software; one of the most efficient visual result to build effort ratio yields a simple plot of the Mandelbrot set, formally known as

$M:=\{z\in\mathbb{C}:|\lim_{n\to\infty}\mathrm{itr}^n(z)|<\infty\}$

where the iterator is defined as

$\mathrm{itr}^n(z) := \mathrm{itr}^{n-1}(z)^2+z, \\ \mathrm{itr}^0(z) := 0.$

The render resolution is kept at a recognizable minimum as not to overburden the machine tasked with creating it. Source: mandelbrot-set.sb3