Symmetry Detection and Symmetrization in Cellular Automata

Vít Gregor, Ivana Kolingerová

2025

Abstract

Symmetry is the important property of many geometric objects. Our work analyzes the symmetry in two-dimensional objects created using the cellular automata in the context of the initial configurations and rules of the automata. Symmetry of basic geometric shapes, such as circles, rectangles, and curves, mapped into the cells of the automaton, is analyzed in this paper. Also, the symmetry of random objects is analyzed. This paper also describes the method for centroidal symmetry detection and axial symmetry detection in the cellular automata, and it also brings the approach of using the cellular automata for object symmetrization by comparing it with objects in the library of symmetrical objects.

Paper Citation

in Harvard Style

Gregor V. and Kolingerová I. (2025). Symmetry Detection and Symmetrization in Cellular Automata. In Proceedings of the 20th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP; ISBN 978-989-758-728-3, SciTePress, pages 317-322. DOI: 10.5220/0013250000003912

in Bibtex Style

@conference{grapp25,
author={Vít Gregor and Ivana Kolingerová},
title={Symmetry Detection and Symmetrization in Cellular Automata},
booktitle={Proceedings of the 20th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP},
year={2025},
pages={317-322},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013250000003912},
isbn={978-989-758-728-3},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 20th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP
TI - Symmetry Detection and Symmetrization in Cellular Automata
SN - 978-989-758-728-3
AU - Gregor V.
AU - Kolingerová I.
PY - 2025
SP - 317
EP - 322
DO - 10.5220/0013250000003912
PB - SciTePress