In a pre-previous post called “Think Inc”, I looked at the fractals created by a point first jumping halfway towards the vertex of a square, then using a set of increments to decide which vertex to jump towards next. For example, if the inc-set was [0, 1, 3], the point would jump next towards the same vertex, v[i]+0, or the vertex immediately clockwise, v[i]+1, or the vertex immediately anti-clockwise, v[i]+3. And it would trace all possible routes using that inc-set. Then I added refinements to the process like giving the point extra jumping-targets half-way along each side.

Here are some more variations on the inc-set theme using two and three extra jumping-targets along each side of the square. First of all, try two extra jumping-targets along each side and a set of three increments:

inc = 0, 1, 6

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inc = 0, 2, 6

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inc = 0, 2, 8

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inc = 0, 3, 6

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inc = 0, 3, 9

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inc = 0, 4, 8

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inc = 0, 5, 6

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inc = 0, 5, 7

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inc = 1, 6, 11

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inc = 2, 6, 10

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inc = 3, 6, 9

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Now try two extra jumping-targets along each side and a set of four increments:

inc = 0, 1, 6, 11

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inc = 0, 2, 8, 10

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inc = 0, 3, 7, 9

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inc = 0, 4, 8, 10

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inc = 0, 5, 6, 7

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inc = 0, 5, 7, 8

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inc = 1, 6, 7, 9

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inc = 1, 4, 6, 11

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inc = 1, 5, 7, 11

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inc = 2, 4, 8, 10

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inc = 3, 5, 7, 9

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And finally, three extra jumping-targets along each side and a set of three increments:

inc = 0, 3, 13

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inc = 0, 4, 8

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inc = 0, 4, 12

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inc = 0, 5, 11

inc = 0, 6, 9

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inc = 0, 7, 9

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Previously Pre-Posted

• Think Inc — an earlier look at inc-set fractals