Abstract
Are there uniquely spherical cellular automata machines? Might there be computational processes that come about more naturally on spheres than they would in the plane? This chapter describes an exploration of geodesic grids as environments for cellular automata (CA) and specifically addresses the movements of Game of Life (GoL) gliders whose interactions are affected by the positive curvature of spheres. 2D CA are typically arranged on regular planar grids with periodic boundary conditions — equivalent to the topology of a torus. This chapter instead considers the dynamics of CA on spheres. The unavoidable discontinuities that arise from mapping a 2D grid onto the sphere are accepted as integral components of the environment. A novel XOR gate built on GoL is demonstrated, utilizing the double-crossing of glider paths following geodesic great circles.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berlekamp, E.R., Conway, J.H., Guy, R.K.: What Is Life? Winning Ways for Your Mathematical Plays, vol. 2: Games in Particular, Chap. 25. Academic Press, London (1982)
Grunbaum, B., Shephard, G.C.: Tilings and Patterns. Freeman, New York (1987) (balanced tilings explained in pp. 129–134)
Kiester, R.A., Sahr, K.: Planar and Spherical Hierarchical, Multi-resolution Cellular Automata. Computers, Environment and Urban Systems. Elsevier, Amsterdam (2008)
Langon, C.: Life at the Edge of Chaos. Artificial Life. Addison–Wesley, Reading (1992)
Margenstern, M.: Cellular Automata in Hyperbolic Spaces. Old City Publishing, Philadelphia, London, Paris (2007)
Rendell, P.: Turing universality of the Game of Life. In: Adamatzky, A. (ed.) Collision-Based Computing. Springer, Berlin (2002)
Rennard, J.P.: Implementation of logical functions in the Game of Life. In: Adamatzky, A. (ed.) Collision-Based Computing. Springer, Berlin (2002)
Yukita, S.: Dynamics of cellular automata on groups. IEICE Trans. Inf. Syst. E82-D (10), 1316–1323 (1999)
Yukita, S.: Cellular automata in non-euclidean spaces. In: Proceedings of the 7th WSEAS International Conference on Mathematical Methods and Computational Techniques in Electrical Engineering, pp. 200–207. World Scientific and Engineering Academy and Society, Stevens Point (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag London Limited
About this chapter
Cite this chapter
Ventrella, J. (2010). A Spherical XOR Gate Implemented in the Game of Life. In: Adamatzky, A. (eds) Game of Life Cellular Automata. Springer, London. https://doi.org/10.1007/978-1-84996-217-9_19
Download citation
DOI: https://doi.org/10.1007/978-1-84996-217-9_19
Publisher Name: Springer, London
Print ISBN: 978-1-84996-216-2
Online ISBN: 978-1-84996-217-9
eBook Packages: Computer ScienceComputer Science (R0)