Markov Chain Algorithms for Programmable Active Matter
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We consider stochastic solutions to problems arising from programmable active matter based on emergent phenomena. We view active matter as a collection of simple computational elements (or particles) with limited memory that self-organize to solve system-wide problems of movement, configuration, and coordination. First, we present a solution to the compression problem, which aims to have the particle system gather as tightly together as possible through a distributed, local, and asynchronous algorithms. We assume the geometric amoebot model and show that we can achieve compression whenever we start with a particle system that is simply connected. We also present a stochastic solution to the separation problem, in which heterogenous (colored) particles interact initially without bias, but separate into homogeneous clusters in the presence of new environmental conditions. Based on joint work with Sarah Cannon, Joshua Daymude, Cem Gokmen and Andrea Richa.
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