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Economic models based on simple rules can result in complex and unpredictable deterministic dynamics with emergent features similar to those of actual economies. I present several such models ranging from cellular automaton and register machines to quantum computation. The additional benefit of such models is displayed by extending them to model political entanglement to determine the impact of allowing majority redistributive voting. In general, the insights obtained from simulating the computations of simple rules can serve as an additional way to study economics, complementing equilibrium, literary, experimental, and empirical approaches. I culminate by presenting a minimal model of economic complexity that generates complex economic growth and diminishing poverty without any parameter fitting, and which, when modified to incorporate political entanglement, generates volatile stagnation and greater poverty.