Toothpick sequence
In geometry, the toothpick sequence is a sequence of 2-dimensional patterns which can be formed with a recursive procedure: The first design is a single "toothpick", or line segment. Every design after the first can be formed by taking the previous design and, for every exposed toothpick end, placing another toothpick centered on that end at a right angle to the earlier toothpick.[1] This process results in a pattern of fractal growth[2] The structure of stages in the toothpick sequence often resemble the T-square fractal, or the arrangement of cells in the Ulam–Warburton cellular automaton.[1]
References
- ^ a b Applegate, David; Pol, Omar E.; Sloane, N. J. A. (2010). "The Toothpick Sequence and Other Sequences from Cellular Automata". Retrieved 18 September 2012.
{{cite journal}}: Cite journal requires|journal=(help) - ^ Cipra, Barry (2010). "What Comes Next?" (PDF). Science. 327. AAAS: 943. Retrieved 18 September 2012.
External links
- A list of integer sequences related to the Toothpick Sequence from the On-line Encyclopedia of Integer Sequences. (note: the IDs like A139250 are IDs within the OEIS, and descriptions of the sequences can be located by entering these IDs in the OEIS search page.)
- A java applet demonstrating the sequence