On the Stochastic Geometry of Growth

Vincenzo Capasso ()
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Vincenzo Capasso: University of Milan, MIRIAM and Dept. of Mathematics

Chapter 4 in Morphogenesis and Pattern Formation in Biological Systems, 2003, pp 45-57 from Springer

Abstract: Abstract The pioneering book by D’Arcy Thompson, entitled “On Growth and Form” [13], was perhaps the first to consider applying (deterministic) mathematics to problems in biology, in particular those problems associated with the growth of biological objects. However most people nowadays are aware of the fact that we cannot ignore stochasticity in real biological phenomena. The scope of this chapter is to introduce relevant nomenclature and mathematical methods for the analysis of geometries related to stochastic birth-and-growth processes, thus providing a guided tour in a selected bibliography. First of all let us introduce the current terminology in this framework. The most important chapters of mathematical interest in this context are the following, for which we refer to the relevant literature: While MORPHOGENESIS (PATTERN FORMATION) deals with the mathematical modelling of the causal description of a pattern (a direct problem) [11, 14] (see Fig. 4.1), STOCHASTIC GEOMETRY deals with the analysis of geometric aspects of “patterns” subject to stochastic fluctuations (direct and inverse problems) [1, 12] (see Figs. 4.2, 4.3).

Keywords: Hausdorff Dimension; Boolean Model; Stochastic Fluctuation; Stochastic Geometry; Random Object (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-4-431-65958-7_4

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