Computing Naturally in the Billiard Ball Model

Details Computing Naturally in the Billiard Ball Model Computing Naturally in the Billiard Ball Model

2009-09-20

arxiv.org/abs/0909.3631v1

Proceedings of the 8th International Conference on Unconventional Computation, UC09, Ponta Delgada, Portugal; Springer-Verlag:

Nonlinear Sciences

Cellular Automata and Lattice Gases

10 pages, 7 figures

Scientific paper

10.1007/978-3-642-03745-0_29

Fredkin's Billiard Ball Model (BBM) is considered one of the fundamental models of collision-based computing, and it is essentially based on elastic collisions of mobile billiard balls. Moreover, fixed mirrors or reflectors are brought into the model to deflect balls to complete the computation. However, the use of fixed mirrors is "physically unrealistic" and makes the BBM not perfectly momentum conserving from a physical point of view, and it imposes an external architecture onto the computing substrate which is not consistent with the concept of "architectureless" in collision-based computing. In our initial attempt to reduce mirrors in the BBM, we present a class of gates: the m-counting gate, and show that certain circuits can be realized with few mirrors using this gate. We envisage that our findings can be useful in future research of collision-based computing in novel chemical and optical computing substrates.

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