Branching is probably the most common mode of growth in Nature. From plants to river networks, from lung and kidney to snow-flakes or lightning sparks, branches grow and blossom everywhere, in every realm of Nature. When Galileo Galilei stated that the geometry ofNature was written in terms ofplanes, cones and spheres, he missed one essential pattern of Nature: the tree. However, the tree has been recognized as a "scientific" objet very early, ever since the classical times. Pliny, Strabo or Theophrastus were weIl aware ofthe existence of"dendrites", i. e., stones in the shape of plants or corals, although the existence of such stones was a puzzle to them. In his book Prodromus Cristallographiae, in which the very word cristallography appears in print for the first time (1711), Mauricius CapeIler, a Swiss naturalist, shows in between facetted crystals, several examples of dendritic crystals. He seemed already to believe in the existence of a general class of branching structures (arbusculatum in modum) in Nature. In the same spirit, his friend Jean-Jacques Scheuchzer had demonstrated experimentally that viscous fingering could generate geological dendrites (1699). At the time of Renaissance, Leornardo da Vinci was quite interested in the resemblance between trees and vessels (1508), and later, Nicola Steno did not hesitate in considering branched deposits of silver found in mines as a close relative of snow.

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From the contents: Patterns with Open Brances or Closed Networks: Growth in Scalar or Tensorial Fields.- Branching in Plants.- Inside the Buds: The Meristems.- Two Symmetries Linking Biological and Physical Branching Morphogenesis.- Establishing a Growth Axis in Fucoid Algae.- Shape Stability During Osmotic Growth.- On Transcellular Ionic Currents.- Branched Patterns in Geology: Rivers and Other Systems.- Neuronal Arborization.- Chemical Waves and Dendrites and Navigation During Self-Wiring of Neural Nets.- The Mouse Embryonic Lung: A Biological Example of Branching Morphogenesis.- Branched Structures, Acinus Morphology and Optimal Design of Mammalian Lungs.- Quantitative Studies of Branching Morphogeneses in the Developing Kidney.- Morphogenic Responses of Mammary Epithelial cells Grown in Biological Semi-Solid Substrates.