GPU Accelerated Computation and Visualization of Hexagonal Cellular Automata St´ ephane Gobron 1 , Herv´ e Bonafos 2 , and Daniel Mestre 1 1 Institute of Mouvement Sciences, CNRS, Marseille, France {stephane.gobron, daniel.mestre}@univmed.fr, 2 herverv@aol.com Abstract We propose a graphics processor unit (GPU)-accelerated method for real-time com- puting and rendering cellular automata (CA) that is applied to hexagonal grids. Based on our previous work [9] –which introduced first and second dimensional cases– this paper presents a model for hexagonal grid algorithms. Proposed method is novel and it encodes and transmits large CA key-codes to the graphics card and consequently, this technique allows to visualize the CA information flow in real-time to easily identify emerging be- haviors even for large data sets. To show the efficiency of our model we first present a set of characteristic hexagonal behaviors, and then describe computational statistics for cen- tral processing unit (CPU) and GPU on a set of different hardware and operating system (OS) configurations. We show that our model is flexible and very efficient as it permits to compute CA close to a thousand times faster than classical CPU methods. Additionally, free access is provided to our downloadable software for hexagonal grid CA simulations. Keywords—Hexagonal cellular automaton, GPU-accelerated computation, Digi- tal imaging, Real-time rendering, Emerging behavior. 1 Introduction Fig. 1. [left] Example of hexagonal CA (2D h b CA) applied to the conference logo (101 steps); [right] Example of hexagonal structures found in nature: (a) stones found in the Giant’s Causeway, Ireland; (b) honeycomb; (c) eye of a fly; (d) hexagon spotted over Saturns surface; (e) snowflakes. This paper belongs to a series of papers concerning the computation and rendering real- time boolean multi-dimensional cellular automata (CA). Based on our previous approach proposing first dimension and second von Neumann dimension CA [9], the current work focuses on 2D hexagonal structures (2D h b CA). As shown by the literature described in next Subsection 1, CA is a powerful tool that can be used in a wide variety of domains. Unfortunately, in CA, emerging phenomena are often impossible to predict by theoretical approaches [20]. To help researchers compute complex phenomena –such as species competition and evolution [3]– faster, or identifying emerging behaviors almost instantaneously, we propose real-time graphical visualization