From the Chaos to Quasiregular Patterns
Phase portraits of dynamical systems produce certain kinds of patterns in their phase space. With help of web mapping it is possible to cover the plane with tiling of arbitrary quasicrystal symmetry. The connection between web-mapping and stationary Beltrami flows is established. New type of flows with quasicrystal symmetry is introduced. These flows have chaotic streamlines which display in real space different paterns with q-fold symmetry. Stochastic web is the region of space which separates the meshes of the pattern and inside of which Lagrangian turbulence of admixed particles is realized.
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