block by nitaku 1036b853c3f52b8994a4

Gosper hex tiling irregularity

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This experiment creates cells of an hexagonal tiling by following a standard Gosper curve. The drawing highlights groups of 7 and 49 (7^2) cells.

It can be noticed that a standard Gosper curve does not produce nice-looking shapes at each fractal recursion, whereas someone would expect a (quasi-)hexagonal shape. Compare this drawing to the previous example, in which a Node Gosper curve is used to solve this problem.

It seems easy to alter the L-system parameters of the standard Gosper curve to obtain the intended result: adding a cell or two at the beginning of the sequence seems to be enough, but, to the best of our knowledge, it is not sufficient (try changing the axiom and see what happens!). The Node Gosper curve use instead a different set of rules (commented out in the code).

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