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1 Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Prace Informatyczne

1 2000

1 Karcz-Dulęba I.

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The Cantor set generated by a simple evolutionary model

100%

Karcz-Dulęba I.

2000

tom z. 10

29-36

Distributions of traits in a population provide important information about evolution of the population itself. In this paper an analysis of traits distributions in a phenotypic evolution is presented. A very simple model of evolution is under consideration - infinite populations evolve in one dimension space of a bimodal fitness function. The analysis of dynamic behavior of a population yields an interesting result concerning generation of the subsequent distributions. It appears that every normal distribution generates two offspring normal distributions. The evolutionary process initialized with a single normal distribution grows up to 2t normal distributions after t generations. The evolution of normal distributions is described equivalently by evolution of their parameters: means and variances. The evolution of distributions' means resembles fractals generated by an Iterated Function System (IFS). Equations describing the location of distrbutions' means in the next generation define contractive affine transformations. The defined iterative system maps the interval [0,1] into the Cantor set after infinite number of iterations.