Topic
Toothpick sequence
About: Toothpick sequence is a research topic. Over the lifetime, 2 publications have been published within this topic receiving 10 citations.
Papers
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AT&T1
TL;DR: In this paper, 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.
Abstract: 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 arise from enumerating active cells in cellular automata. Some unusual recurrences appear: a typical example is that instead of the Fibonacci recurrence, which we may write as
8 citations
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TL;DR: The game of Nim can be viewed as a cellular automata, where the total number of counters divided by 2 can be considered as a generation in which P-positions are born as discussed by the authors.
Abstract: 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 counters is a famous toothpick sequence based on the Ulam-Warburton cellular automaton We introduce 10 new sequences
2 citations
Performance Metrics
| Year | Papers |
|---|---|
| 2014 | 1 |
| 2010 | 1 |