Differentiable Iterated Function Systems

TL;DR

This paper introduces a differentiable rendering pipeline for IFS fractals, enabling inverse fractal generation and optimization, with initial demonstrations and discussions on challenges and future directions.

Contribution

It presents the first differentiable rendering pipeline for IFS fractals, facilitating inverse fractal design and highlighting optimization challenges.

Findings

Demonstrated the pipeline with code availability

Identified pitfalls in gradient-based fractal optimization

Outlined best practices and future research directions

Abstract

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 \emph{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.