We explore the formation and evolution of wall structures in deformed crystals. We model the dynamics of the Nye dislocation density tensor starting from a smooth random initial deformation, by choosing a local velocity to be in the direction of net Peach-Koehler force on the dislocations. If dislocations are allowed to climb, polycrystalline structures form with sharp grain boundary-like walls. If dislocation climb is forbidden, cellular structures emerge with self-similar fractal morphology - closely resembling the cell wall patterns observed in experiments. We suggest that the fundamental distinction between cell walls and grain boundaries is that the former are intrinsically branched in a characteristic fractal fashion. Our model exhibits realistic cell refinement under strain, with cell sizes decreasing and misorientations increasing as external strain is applied. We analyze our results in view of previous experimental studies of cell morphologies, both those which observed fractal structures and those that used scaling collapses suggesting a single scale for sizes and misorientations. Our simulations simultaneously show fractal structures and scaling collapses. We suggest that self-similar cellular structures are best studied using correlation functions, rather than artificially dividing them into distinct cells.
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