1. Introduction.

Morphogenesis is a branch of mathematics, of chaos theory actually, inspired by the problem of biological morphogenesis, the mystery of pattern formation in biological nature. For example, how did the leopard get its spots? Today most biologists believe that a leopard gets its spots from its mother leopard, through the information of DNA alone, in the process of embryogenesis.

But only a few decades ago, vitalists and organicists considered the idea that there are immaterial fields of intelligence which collaborate with DNA: morphogenetic fields. Around 1954, this idea was revived by the late theoretical biologist, Conrad Waddington. The renowned French mathematician Rene Thom, inspired by Waddington, provided mathematical models for Waddington's field theory of embryogenesis around 1966. In the process, he introduced Waddington's teleological notion of attractor into the history of mathematics, a crucial contribution to dynamical systems theory (also known as chaos theory) and its applications.

And more recently, it has been revised and extended by Rupert Sheldrake in a sequence of books. The morphic field is the name given by Sheldrake, generically, to morphogenetic, mental, and social fields. And in 1992 he proposed this field as the medium for telepathic communications observed between animals, for example, between people and their pets. More importantly, one goal of his work is the depolarization of the conflict between the sciences and the major world religions which necessary results from the mechanistic and materialistic paradigm rampant in the scientific community of today.

In this paper we report on our recent computer simulation of a mathematical model for this kind of communication. This model is derived from an electromagnetic field on a two-dimensional, flat torus, in which are placed two conductors. We simulate the perception by conductor A of a transient wave triggered by a sudden change of shape in conductor B. This mode of communication is monopolar. A change of shape is transmitted through the field, without oscillation by either conductor. A transient carries the information, and we may regard this is a possible model for morphic resonance, as defined by Sheldrake.

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|| 1. Introduction || 2. Vibrations and morphogenesis || 3. Reaction-diffusion models || 4. Wave-diffusion models || 5. Simulation results || 6. Conclusion || Acknowledgments/Bibliography