I played with a similar approach a while ago. By changing the algorithm a bit it's possible to create various other beautiful images:

https://drive.google.com/drive/folders/1TSgLRdO0tKIFUb6Oj8yN...

Here's a link to my post (unfortunately, in Russian) describing the process: https://t.me/little_pieces/822?single

A quick translation:

1. We have a 2D space and a regular shape with N angles, where N is a parameter.

2. Choose a function f : R -> R (e.g. f(x) = x / 2 for Sierpinsky).

3. Choose a random "current" point

4. Choose a random angular point of the N-shape

5. Calculate the distance D between two points. Move the current point to the selected angle point by distance calculated as f(D).

6. Repeat steps 4-5, saving position of the current point on each step, until there is enough data to draw a density map

Another person from gen-club[0] (Russian telegram chat dedicated to generative art) made a 3D-version of it[1][2]:

[0] https://t.me/gen_c

[1] https://t.me/mathimages/156

[2] https://codepen.io/strangerintheq/full/ZEKXamr (zoom out at startup)