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Published in:
2014 | OriginalPaper | Chapter
Complex Self-Reproducing Systems
Authors : Roderick Edwards, Aude Maignan
Published in: ISCS 2013: Interdisciplinary Symposium on Complex Systems
Publisher: Springer Berlin Heidelberg
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Abstract
Cellular automata and L-Systems are well-known formal models to describe the behaviour of biological processes. They are discrete dynamical systems, each of which can have complex and varied behaviour. Here, we study a class of substitutive systems incorporating properties of both cellular automata and L-systems, that exhibits self-reproducing behaviour. A one-dimensional array of cells is considered, each cell has a set of modes or states which are determined by a number from \(\mathbb {Z}/\mathbf{{n}}\mathbb {Z}^*\) (\(n\) prime). The behaviour of a cell depends on the states of its neighbours and obeys an additive rule. It has also a cell-division mode, which allows the line of cells to grow. The behaviour of such a model can be complex, but, using algebraic techniques, we prove that it can describe a reproducing system.