Inferring Iterated Function Systems Approximately from Fractal Images

Abstract

As an important mathematical concept, fractals commonly appear in nature and inspire the design of many artistic works. Although we can generate various fractal images easily based on different iterated function systems (IFSs), inferring an IFS from a given fractal image is still a challenging inverse problem for both scientific research and artistic design. In this study, we explore the potential of deep learning techniques for this problem, learning a multi-head auto-encoding model to infer typical IFSs (including Julia set and L-system) from fractal images. In principle, the proposed model encodes fractal images in a latent space and decodes their corresponding IFSs based on the latent representations. For the fractal images generated by heterogeneous IFSs, we let them share the same encoder and apply two decoders to infer the sequential and non-sequential parameters of their IFSs, respectively. By introducing one more decoder to reconstruct fractal images, we can leverage large-scale unlabeled fractal images to learn the model in a semi-supervised way, which suppresses the risk of over-fitting. Comprehensive experiments demonstrate that our method provides a promising solution to infer IFSs approximately from fractal images. Code and supplementary file are available at \url{https://github.com/HaotianLiu123/Inferring-IFSs-From-Fractal-Images}.