Realistic pattern formations on rough surfaces
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We are interested in simulating patterns on rough surfaces. First, we consider periodic rough surfaces with analytic parametric equations, which are defined by some superposition of wave functions with random frequencies and angles of propagation. The amplitude of such surfaces is also an important variable in the provided eigenvalue analysis for the Laplace-Beltrami operator and in our numerical studies. Simulations show that the patterns become irregular as the amplitude and frequency of the rough surface increase. Next, for the sake of easy generalization to closed manifolds, we propose another construction method of rough surfaces by using random nodal values and discretized heat filters. We provide numerical evidence that both surface constructions yield comparable patterns to those found in real-life animals.
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