Abstract

The design of a soft-matter system can be recast as an input-output map, where the inputs are the parameters that fix the components and their interactions, and the outputs describe the outcome of a self-assembly process. By extending the coding theory from algorithmic information theory, we have recently shown [K Dingle, C. Camargo and AAL , Nat Comm. 9, 761 (2018)] that for many computable maps, the a priori probability P(x) that randomly sampled inputs generate a particular output x decays exponentially with the approximate Kolmogorov complexity $\tilde{K}(x)$ of that output. While Kolmogorov complexity is technically uncomputable, we show how to make approximations that work in practice, allowing for a tight upper bound on P(x). For soft matter systems, simplicity bias implies that randomly sampling design inputs will naturally lead to outputs that have low descriptional complexity. Since high symmetry structures typically have low descriptional complexity, simplicity bias implies that randomly picking design patterns can lead to the spontaneous emergence of highly symmetric self-assembled structure. We provide evidence for these trends for self-assembled RNA and protein structures.