Patterns with Open Branches or Closed Networks: Growth in Scalar or Tensorial Fields
In a variety of physical systems in which there is growth, patterns are spontaneously generated. Since it is also during their growth that living entities acquire their shapes, it is tempting to consider possible relations between the two types of morphogenesis. This direction of research was initiated by D’Arcy Thompson (1917) in his classical book “On Growth and Form”. To the present day it is still an important and open problem. The fact that biological growth is under the control of genetic factors does not abolish the fact that it also obeys the laws of physics. Many situations of biological morphogenesis can thus involve an interplay between genetic determination and physical self-organisation. This is, of course, well beyond the field of the present article. We limit ourselves here to the description of some recent results concerning branches and meshworks in physical systems and discuss a few biological systems, mostly in botany, where these results may be relevant.
KeywordsTensorial Field Transverse Crack Secondary Vein Main Vein Hele Shaw Cell
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