Learnable Fractal Flames

TL;DR

This paper introduces a differentiable rendering method for fractal flames that enables learning of fractal parameters from images, supporting color, non-linear functions, and multi-fractals, facilitating artistic control and complex artwork creation.

Contribution

It extends differentiable fractal rendering to include color, non-linear functions, and multi-fractals, allowing intuitive image-based control of fractal generation.

Findings

Enables learning fractal parameters from images using gradient descent.

Supports complex, colorful fractal artwork creation.

Provides a new tool for artists to control fractal design via reference images.

Abstract

This work presents a differentiable rendering approach that allows latent fractal flame parameters to be learned from image supervision using gradient descent optimization. The approach extends the state-of-the-art in differentiable iterated function system fractal rendering through support for color images, non-linear generator functions, and multi-fractal compositions. With this approach, artists can use reference images to quickly and intuitively control the creation of fractals. We describe the approach and conduct a series of experiments exploring its use, culminating in the creation of complex and colorful fractal artwork based on famous paintings.