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Many facts were at the origin of the present monograph. The ftrst is the beauty of maple leaves in Quebec forests in Fall. It raised the question: how does nature create and reproduce such beautiful patterns? The second was the reading of A. Lindenmayer's works on L systems. Finally came the discovery of "the secrets of DNA" together with many stimulating ex- changes with biologists. Looking at such facts from the viewpoint of recursive numerical systems led to devise a simple model based on six elementary operations organized in a generating word, the analog of the program of a computer and of the genetic code of DNA in the cells of a living organism. It turned out that such a model, despite its simplicity, can account for a great number of properties of living organisms, e.g. their hierarchical structure, their ability to regenerate after a trauma, the possibility of cloning, their sensitivity to mutation, their growth, decay and reproduction. The model lends itself to analysis: the knowledge of the generating word makes it possible to predict the structure of the successive developmental stages of the system; and to synthesis: a speciftc type of structure can be obtained by systematically constructing a generating word that produces it. In fact the model here proposed is coherent with the fundamental assumptions of cellular biology and in particular with recent discoveries concerning DNA, which in the light of our model behaves like a very elaborate generating word.