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What are the relations between the shape of a system of cities and that of fish school? Which events should happen in a cell in order that it participates to one of the finger of our hands? How to interpret the shape of a sand dune? This collective book written for the non-specialist addresses these questions and more generally, the fundamental issue of the emergence of forms and patterns in physical and living systems. Relying on the seminal works of D Arcy Thompson, Alan Turing and René Thom, it confronts major examples like plant growth and shape, intracellular organization, evolution of living forms or motifs generated by crystals. This book is essential to understand universal principles at work in the shapes and patterns surrounding us but also to avoid spurious analogies.