Differentiable Iterated Function Systems

• URL: http://arxiv.org/abs/2203.01231v2
• Date: Mon, 10 Jun 2024 15:49:45 GMT
• Title: Differentiable Iterated Function Systems
• Authors: Cory Braker Scott,
• Abstract summary: This paper presents initial explorations in rendering Iterated Function System (IFS) fractals using a differentiable rendering pipeline. I demonstrate this pipeline by generating IFS fractals with fixed points that resemble a given target image.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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