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Sierpinski Gasket in a Reaction-Diffusion System
Phys. Rev. Lett. 81, 1726 – Published 24 August, 1998
DOI: https://doi.org/10.1103/PhysRevLett.81.1726
Abstract
We shall show by computer simulations that a Bonhoeffer van der Pol type reaction-diffusion system in one dimension reveals a curious spatiotemporal pattern in the motion of interacting pulses. For suitably chosen nonlinearity and parameters, the trajectory of pulses exhibits a self-similar regular pattern like a Sierpinski gasket in the space-time coordinate. This is caused by self-replication of a pulse and annihilation and/or preservation of propagating pulses upon collision. The formation of the Sierpinski gasket can be understood by mapping the time evolution of pulses to an equivalent cellular automaton.
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