Jonathan. Frech’s WebBlog

Mandelbrot set sketch in Scratch (#217)

Jonathan Frech

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

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

where the iterator is defined as

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

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