Complexity from simple rules.

I am a DPhil student at the Rudolf Peierls Centre for Theoretical Physics, University of Oxford, working with Prof. Ard Louis.

My research asks a deceptively simple question: if you hand a set of building blocks a short list of local rules for how to stick together, what can they build? I study this through three-dimensional polycube models of programmable self-assembly, where a small set of local interaction rules can generate a surprisingly large space of possible structures. Exploring that space computationally, I look at how the rules of assembly map onto the structures that emerge, and how properties such as symmetry, assembly complexity, and designability are distributed across it.

In parallel, I work on a different way of asking a similar question: given a finished structure, how many different sequences of steps could have built it while keeping it connected the whole way through? This is a problem in graph theory and combinatorics, and I've used it to count successive vertex orderings of graphs, and even to work out how many ways there are to assemble a jigsaw puzzle.

More broadly, I'm drawn to questions that don't sit neatly inside one discipline, where physics, biology, mathematics and computer science each offer a different lens on the same underlying puzzle: why are some structures easy to reach, while others stay stubbornly out of reach?