A Comparative Analysis of Detecting Symmetries in Toroidal Topology

Abstract

In late 1940's and with the introduction of cellular automata, various types of problems in computer science and other multidisciplinary fields have started utilising this new technique. The generative capabilities of cellular automata have been used for simulating various natural, physical and chemical phenomena. Aside from these applications, the lattice grid of cellular automata has been providing a byproduct interface to generate graphical patterns for digital art creation. One notable aspect of cellular automata is symmetry, detecting of which is often a difficult task and computationally expensive. This paper uses a swarm intelligence algorithmStochastic Diffusion Search -to extend and generalise previous works and detect partial symmetries in cellular automata generated patterns. The newly proposed technique tailored to address the spatially-independent symmetry problem is also capable of identifying the absolute point of symmetry (where symmetry holds from all perspectives) in a given pattern. Therefore, along with partially symmetric areas, the centre of symmetry is highlighted through the convergence of the agents of the swarm intelligence algorithm. Additionally this paper proposes the use of entropy and information gain measure as a complementary tool in order to offer insight into the structure of the input cellular automata generated images. It is shown that using these technique provides a comprehensive picture about both the strucMohammad Ali Javaheri Javid Department of Computing, Goldsmiths, University of London London SE14 6NW, United Kingdom e-mail: m.javaheri@gold.ac.uk ture of the images as well as the presence of any complete or spatially-independent symmetries. These technique are potentially applicable in the domain of aesthetic evaluation where symmetry is one of the measures.