In these systems, the individual cells have internal states, but do not know the global state of the system. Programmable pattern formation is impressively exemplified in developmental biology, where relatively minor changes in the cis-regulatory regions of genes can reprogram the developmental process to yield dramatic changes in the morphology of the adult organism 1, 2. ![]() Our results establish a basis for the design of synthetic systems, and for more detailed models of programmable pattern formation closer to real systems. An alternative scheme employing several different rules can only form a fraction of patterns but is robust with respect to the timing of organizer cell inputs. These systems follow a common principle, whereby a temporal pattern is transcribed into a spatial pattern, reminiscent of the clock-and-wavefront mechanism underlying vertebrate somitogenesis. Only a small subset of systems permits local organizer cells to dictate any target pattern. We study systems with different update rules, different topologies, and different control schemes, to assess their ability to perform programmable pattern formation and their susceptibility to errors. ![]() Here, we explore schemes for programmable pattern formation within a theoretical framework, in which subunits process discrete local signals to update their internal state according to logical rules. A distinguishing feature of such systems, as compared to simpler physical pattern forming systems, is that their subunits are capable of information processing. Diverse complex systems, ranging from developing embryos to systems of locally communicating agents, display an apparent capability of “programmable” pattern formation: They reproducibly form a target pattern, but this target can be readily changed.
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