fractals

fractals always fascinated me. their existence kind of defies the very concept of existence: how can you put infinitely much stuff in a single thing ?

apart from some random documentaries, i wasn't really introduced to fractals before a math problem i encountered while participating in a math activity organized by my high school in collaboration with the french association math-en-jeans.

in this problem, a paper-folding procedure was given:

1. take strip of paper
2. fold it upon itself by putting the right side on the left side, thus forming a smaller strip
3. repeat step 2. n times
4. put all folds at 90° angles the way they were folded

this allows making a geometrical figure that can fit on a grid, the question the problem asked was: what is the size of the smallest grid the figure can fit on ?

here are some of the figures obtained:

you can clearly see where this is going but imagine my past self working on a crappy python turtle script and discovering the fractal shape it made when n was high.

pure joy.

i got really interested in fractal rendering when i started fiddling with a python script – which is present by default on the numworks calculator – that draws the mandelbrot set.

i wanted to modify this script to make a tiny fractal explorer app and this is what i did: i first edited it directly on the calculator but the resulting script was really slow so i made a custom native app in c++ to be embedded in the numworks' software (see this repository).

as a 320x240 screen was not enough, i started working on a tiny fractal renderer software written in rust.

the work i've done on this software is detailed in the dedicated page but i really liked learning about some of the numerous technical aspects of rendering.