Trapped knight path with wavy color

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Very cool! Very nice coloring. I had done something similar some time ago. I made a function that can give you all kinds of configuration of points. Have a look at https://resources.wolframcloud.com/FunctionRepository/resources/LatticePointsArrangement

See the Neat Example.

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There is also a triangular variation in the Numberphile video. Your function will help a lot with different sequence pattern and different starting point. I found a Medium article reveals some chaos nature of this problem: https://maartenmortier.medium.com/the-trapped-knight-revisited-132c034a8a28

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