We investigate the dynamics of shape in growing systems - from bacteria to batteries - through the lenses of computational geometry, statistical mechanics, and soft matter physics, aiming to extract general principles of shape control. Living systems build remarkable structures (like you) with impressive robustness despite functioning in a wet, noisy environment. We imagine a future where the structures we use and live in can build and regulate their own complex morphology, the way biology does it. Our projects are baby steps in that direction, divided into three overlapping approaches: Data-driven description of shape changes, model-driven understanding of shape control, and application-driven control of emerging shapes.
Describing shape variation
As Blippi says, shapes are all around us (see video here), but how do we describe differences between shapes? How do we analyze time-evolving shapes? How do we learn the dynamics of shape from an incomplete observation of shape (e.g., images taken at different times without live tracking)?
These questions generate exciting collaborative projects between mathematicians, physicists, and biologists working with beautiful organisms, as the pictures above demonstrate.
Understanding shape generation
How do organisms grow into the right shape? What are the physical, geometric, and biochemical processes and principles underlying this miracle?
Controling shape emergence
How can we control the emergence of shape in living and artificial systems? As AGI (artificial general intelligence) is to human brains, Morphoryhtms is to human embryos. The goal of our group is to make baby steps in this direction by controlling living (e.g., plants), natrual (e.g., coastal morphodynamics) , and technological (e.g., electrochemical interfaces in batteries) systems.
Exploring the soft universe.