This is an extension / fork of a previous project.

The Mandelbrot is defined as points $c$ for which the iteration of $z_{n+1} = z_{n}^2 + c$ does escape towards infinity.

When complex numbers are multiplied, they appear to rotate on the complex plane. Tracing the trajectories can lead to cool shapes - spirals and stars.

How many points do these spirals/stars have based off of their starting location?

When investigating algorithms to identify periods of orbits in the Mandelbrot I came up with an algorithm that can quantify apparent "shapes". Check out the inter-active app here.

The result of the algorithm is this, displaying the various regions that will produce various shapes:

General overview:

bin         - compiled binaries, object files, and dependency files
gui         - typescript and sass gui code
gui-dist    - html code and compiled js
screenshots - trajectory screenshots used on the web page and README
src         - C++ render code

Kickstart:

npm i
make
./bin/mandelbrot.exe
webpack
cp -rv render.png screenshots gui-dist