This script was written with my friend Théo André for the math forum organized in Rognac in 2025 by Maths pour tous, and was largely inspired by my other friend Félix Castillon.
This script uses the principle of iterated function systems (IFS) : the process consists in applying a finite set of transformation to a basic shape (for this page, a big disk), and see a fractal appearing clearer and clearer with each iteration. In every case on this page, the transformations are affine and fairly simple, the complexity of the fractals arises from the action of iterating. By thinking really hard about it, it is possible to draw more or less whatever you like by choosing specific transformations : the Barnsley leaf is an example of that.
Use the arrow keys or the forward/back buttons to go forwards or backwards in iterations, the mouse to move and the mouse wheel to zoom. Don't ask for too many iterations, as it might crash your browser. In particular, don't ask for a bunch of iterations at once !
This script uses the principle of iterated function systems (IFS) : the process consists in applying a finite set of transformation to a basic shape (for this page, a big disk), and see a fractal appearing clearer and clearer with each iteration. In every case on this page, the transformations are affine and fairly simple, the complexity of the fractals arises from the action of iterating. By thinking really hard about it, it is possible to draw more or less whatever you like by choosing specific transformations : the Barnsley leaf is an example of that.
Use the arrow keys or the forward/back buttons to go forwards or backwards in iterations, the mouse to move and the mouse wheel to zoom. Don't ask for too many iterations, as it might crash your browser. In particular, don't ask for a bunch of iterations at once !