Abstract
The formation of a wide variety of patterns is controlled by the strength of the gradient of a field at the interface between the structure and the outside. For example, the rate of growth in aggregation processes [1, 2] depends on the concentration of diffusing particles, in solidification [3] it depends on the temperature gradient, in dielectric breakdown [4] it is proportional to some power of the electric field, in electrodeposition [5, 6] it depends on the gradient of the electrical voltage, and in viscous fingering [7, 8] it is the pressure gradient. It has long been speculated [9] that concentration gradients of nutrients, light and energy resources are the factors controlling the development of a variety of biological patterns as well, even though much less is known about pattern formation in biological systems [9].
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Family, F. (1988). Growth by Gradients: Fractal Growth and Pattern Formation in a Laplacian Field. In: Landau, D.P., Mon, K.K., Schüttler, HB. (eds) Computer Simulation Studies in Condensed Matter Physics. Springer Proceedings in Physics, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93400-1_8
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DOI: https://doi.org/10.1007/978-3-642-93400-1_8
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