Abstract:
Since D'Arcy Thompson wrote his influential treatise "On growth and form", now 100 years ago, much more is understood about the mechanisms that lead to some of the beautiful patterns observed in nature. This talk will describe a few examples, including phyllotactic growth, bacterial colony formation, and recurrent precipitation (Liesegang's patterns), that share a common feature: the interplay of growth and pattern forming processes. This interplay poses challenges for scientists trying to model and predict phenomena, but also leads to promising engineering strategies, for instance in the manufacturing of nanodot arrays. Rather than dwelling on microscopic details in the physical or biological modeling of these processes, the talk will try to show in examples how mathematics can exhibit simple, universal mechanisms, often hidden in complex models, that can produce a vast array of beautiful patterns. A leitmotiv will be the description of fronts that select patterns in their wake, their bifurcations, and their universal scaling laws.
Thackeray 703