The daughter of CELIA, the french flag and the firing squad

Abstract

In earlier work (1, 2) we have reported on a program, called CELIA, for simulating the behavior of linear iterative arrays of cells. The action of a cell is influenced by both its neighbors. Our main application area was biology, where the program can be used to test hypotheses about the developmental rules for organisms. More recently we have been applying our program to test proposed solutions to some fairly complicated biologically based problems. We have investigated (3) whether one can achieve regulative global polarity in organisms without polarity in individual cells, by solving the French flag problem of Wolpert (4) using only symmetric elements. In our attempted simulation of pigmentation patterns on the shells of sea-snails, we have found it necessary to find a solution to a generalized version of the firing squad synchronization problem (3), in which the firing squad is growing while it is trying to synchronize itself. We found that our original program CELIA was somewhat awkward for simulating such complicated situations. A new program has been devised where the state of the individual cells is described by an array of attributes, such that each attribute itself may be a list structure. The present paper reports on these changes and explains how they turn out to be useful in the applications mentioned above.

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