According to my calculations the overall effect is an example of a discrete dynamical system in mathematics. The patterns are created by time restrictions on stochasticity. A dynamical system is a tuple (T, M, Φ) where T is a monoid, written additively, M is a set and Φ is a function Φ: U subset T X M to M with I(x) = { t in T: (t,x) in U } Φ (0,x) = x, Φ (t_2,Φ (t_1,x)) = Φ (t_1 + t_2, x) for t_1, t_2, t_1 + t_2 in I(x), The function Φ(t,x) is called the evolution function of the dynamical system: it associates to every point in the set M a unique image, depending on the variable t, called the evolution parameter. M is called phase space or state space, while the variable x represents an initial state of the system. In my field which is mathematical ecology, it is quite a trick to differentiate between the patterns that arise from a discrete dynamical system and those that arise from interactions between species as those interactions are ameliorated by habitat. - author - not me haha
Posted on: Thu, 31 Jul 2014 10:12:45 +0000
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