Figure 1

Traditional and new process of analysis based on simulation studies of a model for pattern formation. Starting with a point P in parameter space (represented by the black dot) given by a chosen set of parameter values, the stable solution X is obtained by integrating the dynamical model dx/dt = F(x, P), x(0) = x⁰. The second step is to represent each X by a point in Solution Space (phase space). Using a convenient graphical mapping, X defines a Graphical Pattern that can be inspected and analysed visually. So far this is conventional procedure. To analyse and classify the patterns, new concepts, variables and names are necessary to describe the interesting macroscopic and emergent properties of the patterns in a Pattern Descriptor (PD) space. Each pattern descriptor is then given a numeric value according to chosen criteria. This permits the mapping of each point P in parameter space onto a point in the PD space in terms of a PD model derived by various multivariate methods (see text). Being approximate and probabilistic in nature, this mapping by the statistical prediction model only indicates a certain domain in parameter space (coloured) which will produce patterns resembling a given pattern.