Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 15: Pattern Formation

DY 15.2: Talk

Tuesday, April 2, 2019, 10:15–10:30, H3

Controlling discrete pattern formation with local signals — •Stephan Kremser, Tiago Ramalho, Hao Wu, and Ulrich Gerland — Technical University of Munich

Programmability is a fruitful concept to explore the extent to which a dynamical system can be steered by external inputs or internal feedback signals. Here, we propose a minimal system for studying the programmability of discrete patterning, based on one-dimensional cellular automata, which process discrete local signals to update their internal state according to logical rules. The organization signals are given by individual cells that are located either within the system or at its boundary. This framework is sufficiently general to encompass a broad class of model systems, yet simple enough to permit exhaustive analysis. We study model systems with different update rules and different topologies, to assess their ability to perform programmable pattern formation and their susceptibility to errors. We find that only a small subset of model systems permits local organizer cells to dictate any target pattern. These systems follow a common principle whereby a temporal pattern is transcribed into a spatial pattern. Our results establish a basis for the design of synthetic systems, and for more detailed models of programmable pattern formation closer to real systems.