# An Expectation-Maximization Algorithm for the Fractal Inverse Problem

arXiv: https://arxiv.org/abs/1706.03149 · HTML: https://mlsanity.com/paper/1706.03149/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2017.

## Built on by (most cited first, 3 of 3)

- [Towards Worst-Case Guarantees with Scale-Aware Interpretability](https://mlsanity.com/paper/2602.05184/) (2026)
- [Differentiable Iterated Function Systems](https://mlsanity.com/paper/2203.01231/) (2022)
- [Critical Percolation as a Synthetic Data Model for Interpretability](https://mlsanity.com/paper/2606.20347/) (2026)

## Abstract (arXiv)

We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of transformations. The data is a point cloud in mathbb RH with arbitrary dimension H. Each IFS defines a probability distribution on mathbb RH, so that the fractal inverse problem can be cast as a problem of parameter estimation. We show that the algorithm reconstructs well-known fractals from data, with the model converging to high precision parameters. We also show the utility of the model as an approximation for datasources outside the IFS model class.