# Differentiable Iterated Function Systems

arXiv: https://arxiv.org/abs/2203.01231 · HTML: https://mlsanity.com/paper/2203.01231/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 2 Mar 2022.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [Differentiable Drawing and Sketching](https://mlsanity.com/paper/2103.16194/) (2021)
- [An Expectation-Maximization Algorithm for the Fractal Inverse Problem](https://mlsanity.com/paper/1706.03149/) (2017)

## Abstract (arXiv)

This preliminary paper presents initial explorations in rendering Iterated Function System (IFS) fractals using a differentiable rendering pipeline. Differentiable rendering is a recent innovation at the intersection of computer graphics and machine learning. A fractal rendering pipeline composed of differentiable operations opens up many possibilities for generating fractals that meet particular criteria. In this paper I demonstrate this pipeline by generating IFS fractals with fixed points that resemble a given target image - a famous problem known as the inverse IFS problem. The main contributions of this work are as follows: 1) I demonstrate (and make code available) this rendering pipeline; 2) I discuss some of the nuances and pitfalls in gradient-descent-based optimization over fractal structures; 3) I discuss best practices to address some of these pitfalls; and finally 4) I discuss directions for further experiments to validate the technique.