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In the regular square lattice create a walk moving according the value of a counter. Consider two types of walks: In the first walk advance forward one unit if the counter is a composite number and rotate 90 degrees if the counter is a prime. In the second, move forward if the number is prime and rotate 90 degrees if not. The walks resemble random walks.

Is someone else has more information about these walks?

First walk:

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Second walk:

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