# The Toothpick Sequence and Other Sequences from Cellular Automata

@article{Applegate2010TheTS, title={The Toothpick Sequence and Other Sequences from Cellular Automata}, author={David L. Applegate and O. Pol and N. J. A. Sloane}, journal={arXiv: Combinatorics}, year={2010} }

A two-dimensional arrangement of toothpicks is constructed by the following iterative procedure. At stage 1, place a single toothpick of length 1 on a square grid, aligned with the y-axis. At each subsequent stage, for every exposed toothpick end, place an orthogonal toothpick centered at that end. The resulting structure has a fractal-like appearance. We will analyze the toothpick sequence, which gives the total number of toothpicks after n steps. We also study several related sequences that…

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