Abstract
Stochastic evolutionary growth and pattern formation models are treated in a unified way in terms of algorithmic models of nonlinear dynamic systems with feedback built of a standard set of signal processing units. A number of concrete models is described and illustrated by numerous examples of artificially generated patterns that closely imitate wide variety of patterns found in the nature.
Highlights
Problems of pattern formation and growth of forms belong to the most fundamental problems in theoretical biology and other natural sciences [1,2,3,4]
We show that quite simple algorithmic models are capable of generating a wide variety of patterns, which closely remind patterns frequently found in the nature such as dendrite patters, labyrinth and zebra skin patterns, papillary patterns, fingerprints and alike
Linear filters (LF)-Point-wise nonlinearity (PWN)-models allow to generate textures with correlation function controlled by the linear filter impulse response and with a given distribution density controlled by the nonlinear unit
Summary
Problems of pattern formation and growth of forms belong to the most fundamental problems in theoretical biology and other natural sciences [1,2,3,4]. The combination of the 'primary" pseudo-random number generator and the point-wise nonlinearity with a threshold transfer function forms the unit 2Drandb(P), which implements an operation of generating, out of the primary pseudo-random numbers, binary numbers zeros and ones with a given probability P of ones On such an array of binary numbers, the linear filter with impulse response as shown in Figure 3 computes the number of ones in the 3 × 3 neighborhood (8-neighbor sum S8) of each pixel defining the threshold level of the pointwise nonlinearity. Combination of the threshold type point-wise nonlinearity and a linear filter in cascade with the primary pseudorandom number generator (Figure 18a) forms PWN-LF models They generate patterns of randomly distributed filter impulse responses. LF-PWN-models allow to generate textures with correlation function controlled by the linear filter impulse response and with a given distribution density controlled by the nonlinear unit Patterns generated by this model are very reminiscent of natural crystals, cells and cell wall patterns
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