Feynman Lectures on Computation
Feynman Lectures on Computation
Combinatorial view of digital convexity
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
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We consider the shuffle operation on paths and study some parameters. In the case of square lattices, shuffling with a particular periodic word (of period 2) corresponding to paperfoldings reveals some characteristic properties: closed paths remain closed; the area and perimeter double; the center of gravity moves under a 45^@? rotation and a 2 zoom factor. We also observe invariance properties for the associated Dragon curves. Moreover, replacing square lattice paths by paths involving 2k@p/N-turns, we find analogous results using more general shuffles.