Learnable Fractal Flames

2024-06-13

arXiv.org

AI Summary

This work addresses three key challenges in fractal art creation: difficulty in parameter tuning, lack of color supervision, and absence of style transfer capability. To this end, we propose the first differentiable fractal flame rendering framework. Methodologically, we fully differentiabilize the Iterated Function System (IFS), enabling end-to-end optimization of implicit fractal parameters; introduce a neural color mapping module to support supervised learning from color images, overcoming the monochromatic and non-differentiable limitations of conventional IFS; and design a multi-layer fractal fusion mechanism to model nonlinear generative functions and complex structural compositions. Experiments demonstrate stable convergence, real-time synthesis of high-fidelity colored fractal patterns, and successful artistic reconstruction of canonical artworks—such as *The Starry Night*—into fractal representations. The framework significantly enhances artists’ intuitive editing efficiency and fine-grained stylistic control over intricate fractal designs.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Cognitive Modeling & Cognitive Systems: Computational Creativity
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Fractal Pattern Generation
• Computer Learning
• Artistic Creation

Innovation

• Fractal Pattern Generation
• Colorful and Complex Combinations
• Artistic Aesthetics