In Chapter 2, we demonstrate an analytical analysis of a previously published
research for a percolation simulation. In that research the effect of mutations on adaptability
was investigated in a bit-string model of invading species in a random environment. However,
analytical analysis was missing which will be the topic here. The Hausdorff dimensions are
calculated for the fractals and the conditions on invasion are analyzed analytically by
manipulation of partial differential equations. Thus, various conclusions may be reached
without having to run long simulations.
Keywords: Boundary value problems, Fractals, Hausdorff dimension, Monte carlo methods, Ordinary and partial differential equations, Percolation.
