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Mathematically, they provide fashions in every subclass of dynamical programs (integrable, regular, chaotic, and so on). Unfortunately, these fashions do not make widespread knot theoretic computations accessible. We now have used both one-way-infinite and bi-infinite trajectories to be able to reconstruct adjacency, within the guise of common prefixes and grazing sequences, respectively. We use the Chebyshev knot diagram model of Koseleff and Pecker with a view to introduce a random knot diagram model by assigning the crossings to be constructive or adverse uniformly at random. Namely we say that two polygonal billiards (polygons) are order equal if every of the billiards has an orbit whose footpoints are dense within the boundary and the 2 sequences of footpoints of these orbits have the same combinatorial order. The next definition introduces a new relation on the set of all merely connected polygons. Figure 11: The failure of collinearity to detect adjacency in non-convex polygons. Figure 11: Results of applying LWD to an ergodic Bunimovich stadium. Positive crossings are shown on the left of Figure 2; detrimental crossings appear on the right. The i