# Nim Fractals

@article{Khovanova2014NimF, title={Nim Fractals}, author={Tanya Khovanova and Joshua Xiong}, journal={J. Integer Seq.}, year={2014}, volume={17}, pages={14.7.8} }

We enumerate P-positions in the game of Nim in two different ways. In one series of sequences we enumerate them by the maximum number of counters in a pile. In another series of sequences we enumerate them by the total number of counters. We show that the game of Nim can be viewed as a cellular automaton, where the total number of counters divided by 2 can be considered as a generation in which P-positions are born. We prove that the three-pile Nim sequence enumerated by the total number of… CONTINUE READING

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