D’Arcy Thompson set the mathematical foundation for describing and classifying the astonishing
diversity of shapes and form in the living world. A century later, our understanding of biological processes at the molecular level has been vastly improved and yet a complete understanding on how particular biological forms are generated during development, and how they change over evolutionary time remains mostly unknown. A unifying feature of all higher organisms is that they start as a single cell, a zygote, and autonomously develop into an individual, without external input. The genome provides a template that steers development towards the desired body plan.
The formation of large structures such as tissues and organs are a result of a complex set of guided collective mechano-chemical processes. To select a specific morphology, the number of possible shapes must be substantial. Furthermore, the transition between them should be feasible at a reasonably low cost, which is hard to achieve in equilibrium. In this talk, using active mechanics as a framework, I will explore how out of equilibrium competing processes can help biology-inspired shapes to access morphologies that are unavailable if restricted to the adiabatic evolution alone. We argue that the out of equilibrium regime studied here is of interest in developing physical understanding of morphogenesis.