Distance-based iterated function systems on surfaces

Published in ACM SIGGRAPH Posters, 2026

Abstract

Iterated Function Systems (IFSs) are a classical tool for procedural fractal generation, but their formulation is strongly bind to the underlying coordinate system, and thus limited to flat Euclidean domains. We introduce an alternative formulation for an entire family of IFSs, exclusively based on the notion of distances and geodesic paths, that allows defining systems directly on Riemannian domains, enabling the procedural generation of fractal patterns that are aware of the underlying geometry.

BibTeX

@inproceedings{maggioli2026distance,
author = {Maggioli, Filippo and De Luca, Valerio and Generosi, Andrea and Galteri, Leonardo and Gallo, Luigi},
title = {Distance-based iterated function systems on surfaces},
year = {2026},
isbn = {9798400725487},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3799825.3818722},
doi = {10.1145/3799825.3818722},
booktitle = {Proceedings of the Special Interest Group on Computer Graphics and Interactive Techniques Conference Posters},
articleno = {6},
numpages = {3},
series = {SIGGRAPH Posters '26}
}