E- Cellular Automata and Artificial Life

    Since the beginning, von Neumann, considered cellular automata as tools to analyse the reproduction mechanisms of living being. Indeed, the properties of cellular automata permit to show and analyse some of the Living fundamental mechanisms.

    1- Emergence

    The notion of emergence appeared with the general systems theory¹². In a general way it is said that "the whole is greater than the sum of the parts" or "The global behaviour is greater than sum of the behaviours of the individual parts". These expressions mean that the complex association of elements induces the apparition of new phenomena and mechanisms. "At each level (of the prebiotic, biotic and social evolution) new properties appear that cannot be explained by the sum of the own properties of each part that constitute the whole. There is a qualitative gap (…) the property of emergence is linked to complexity. The increase of the diversity of elements, the increase of the number of links between these elements, and the game of non linear interactions lead to hardly predictable behaviours."¹³. The so-called "global" emergence then characterize the properties of a system that are new ones comparing to the properties of its isolate components, or organized in a different way. Life is undoubtedly part of these¹⁴.

    We examined previously the behaviour of a line of three vertical cells : at the first generation, we get three horizontal cells, at the second one, three vertical cells again. A line of three living cells then generates a cycle.

    This pattern is a "blinker". A blinker is not made up of a group of given cells, it is a dynamic pattern that emerges within the space of cellular automata. The blinker seems to be independent ; it is a specific structure, particular inside its environment.

    The rules of the game of life were determined so as to generate a wide diversity of unpredictable structures. The specialists listed a whole faun of patterns whose behaviours are astonishing. Complete libraries are available (see links). One of the most famous is the glider. A given five cells pattern self-reproduces every four generations one cell away.

    Even more than blinkers, gliders evoke emergence. It looks like a creeping animal, going all over the space on straight line. A glider is not a set of cells. At each generation, its cells are replaced. As the atoms that constitute you are not the ones you had at your birth, the components of the glider are constantly renewed. The application of the rules of the game of life induce the apparition of a dynamic, coherent and independent structure, with peculiar properties : this is the very nature of emergence. These properties can be used for specific aims. The glider is used to represent a signal, you will find an example in LogiCell.

    Another remarkable pattern is also to be noted : the glider gun. It is a set of cells generating gliders. It made it possible to demonstrate that the population of the game of life could grow indefinitely. The classical p30 gun is used as a generator in LogiCell.

Glider gun

12- Bertalanffy (von) L., Théorie générale des systèmes. Dunod, Paris, 1973.

13- Rosnay (de) J., Le macroscope. Vers une vision globale. Points, Seuil, Paris, 1975, pp.131-132. Translated by me.

14- Morin E., La Méthode. I-La Nature de la Nature., Points, Seuil, Paris 1977.