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Beautiful spatial patterns can be formed in a cellular automaton known as Abelian Sandpile Model (ASM), by dropping large N number of particles at a single site and then redistributing them according to ASM toppling rules. The patterns are usually composed of large number of macroscopic regions with sharp boundaries, all of which grow at the same rate with N, keeping the overall shape unchanged. This proportionate growth makes the patterns important in the context of biology where such ability to adapt to size variations is common in growing animals. The patterns are also a good example of analytically tractable complex structures generated using simple local rules. I will present exact characterization of few asymptotic (N→∞) patterns on two dimensional lattices, which involve some intriguing connection to the mathematics of discrete analytic functions. I will also discuss robustness of the patterns against different types of noise.

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Dr. Tridib Sadhu, Weizmann Institute of Science, Rehovot
Seminarraum Theoretische Physik
Contact: not specified