Contents:

1. Explore Möbius transformations
2. Use random Möbius transformations to make an IFS fractal
3. Draw the limit set of a group of Möbius transformations

1. Explore Möbius transformations:

Live demo: https://timhutton.github.io/mobius-transforms/

2. Use random Möbius transformations to make an IFS fractal:

Live demo: https://timhutton.github.io/mobius-transforms/ifs.html

For higher resolution images, there's a GPU version here: https://observablehq.com/@timhutton/mobius-ifs

More images:

3. Draw the limit set of a group of Möbius transformations:

Live demo: https://timhutton.github.io/mobius-transforms/dfs_recipes.html

Example of SVG output: