Using Irrational Square Roots to Create Planar Walks

Since the digits in any base of an irrational number such as never exhibit periodicity, they can be used to create a nonterminating infinite walk. Using base 4 allows a coding of the four directions. The walk shown corresponds to the first digits of , where is the positive integer that is not a perfect square. The walks start at the green point and end at the red point.

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