Chaos, Artificial Life and Risk Mathematics

31 Pages Posted: 15 Aug 2010

Date Written: August 15, 2010


The current work addresses the importance of chaos theory and artificial life as scientific bases for the development of a mathematical research of risk in the systems, within the framework of risk science and risk mathematics. It is argued, in particular, that a combination of chaos theory and artificial life may provide for a theoretical basis for the understanding of systemic situations of risk.

It is presented, within the context of category computation theory, a notion of morphic incompressibility and it is addressed how statistical laws emerge in chaotic dynamics, which becomes morphically compressible at the statistical level, while being morphically incompressible at the individual orbits' level. The issue of the systemic origins of chaos is addressed in connection with this dual (orbit) incompressibility/(statistical) compressibility.

Through the introduction of a one-dimensional game of life, that combines a coupled map lattice and a cellular automaton, in a model of an artificial ecosystem, it is, then, shown that artificial life can be effectively combined with chaos theory, in order to support the development of a mathematical theory of risk.

Keywords: Chaos, artificial life, risk, risk science, risk mathematics, morphic incompressibility, coupled map lattices, cellular automata, game of life

Suggested Citation

Gonçalves, Carlos Pedro dos Santos and Madeira, Maria Odete, Chaos, Artificial Life and Risk Mathematics (August 15, 2010). Available at SSRN: or

Carlos Pedro dos Santos Gonçalves (Contact Author)

Lusophone University of Humanities and Technologies ( email )

Campo Grande 376, 1749-024 Lisbon, Portugal

Maria Odete Madeira

Massacritica, Lda. ( email )



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