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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."
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