We investigate the evolutionary dynamics of an idealised model for the robust
self-assembly of two-dimensional structures called polyominoes. The model
includes rules that encode interactions between sets of square tiles that drive
the self-assembly process. The relationship between the model's rule set and
its resulting self-assembled structure can be viewed as a genotype-phenotype
map and incorporated into a genetic algorithm. The rule sets evolve under
selection for specified target structures. The corresponding, complex fitness
landscape generates rich evolutionary dynamics as a function of parameters such
as the population size, search space size, mutation rate, and method of
recombination. Furthermore, these systems are simple enough that in some cases
the associated model genome space can be completely characterised, shedding
light on how the evolutionary dynamics depends on the detailed structure of the
fitness landscape. Finally, we apply the model to study the emergence of the
preference for dihedral over cyclic symmetry observed for homomeric protein
tetramers