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- Toothpick_sequence abstract "In geometry, the toothpick sequence is a sequence of 2-dimensional patterns which can be formed by repeatedly adding line segments ("toothpicks") to the previous pattern in the sequence.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.This process results in a pattern of growth in which the number of segments at stage n oscillates with a fractal pattern between 0.45n2 and 0.67n2. If T(n) denotes the number of segments at stage n, then values of n for which T(n)/n2 is near its maximum occur when n is near a power of two, while the values for which it is near its minimum occur near numbers that are approximately 1.43 times a power of two. 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.All of the bounded regions surrounded by toothpicks in the pattern, but not themselves crossed by toothpicks, must be squares or rectangles. It has been conjectured that every open rectangle in the toothpick pattern (that is, a rectangle that is completely surrounded by toothpicks, but has no toothpick crossing its interior) has side lengths and areas that are powers of two, with one of the side lengths being at most two.".
- Toothpick_sequence thumbnail Margolus_toothpick_animated.gif?width=300.
- Toothpick_sequence wikiPageExternalLink joshua-trees-and-toothpicks.
- Toothpick_sequence wikiPageExternalLink oeis.org.
- Toothpick_sequence wikiPageExternalLink toothlist.html.
- Toothpick_sequence wikiPageExternalLink toothpick.html.
- Toothpick_sequence wikiPageID "37137043".
- Toothpick_sequence wikiPageRevisionID "604907280".
- Toothpick_sequence hasPhotoCollection Toothpick_sequence.
- Toothpick_sequence subject Category:Cellular_automaton_patterns.
- Toothpick_sequence subject Category:Combinatorics.
- Toothpick_sequence comment "In geometry, the toothpick sequence is a sequence of 2-dimensional patterns which can be formed by repeatedly adding line segments ("toothpicks") to the previous pattern in the sequence.The first design is a single "toothpick", or line segment.".
- Toothpick_sequence label "Toothpick sequence".
- Toothpick_sequence sameAs m.0n4c9rn.
- Toothpick_sequence sameAs Q5579775.
- Toothpick_sequence sameAs Q5579775.
- Toothpick_sequence wasDerivedFrom Toothpick_sequence?oldid=604907280.
- Toothpick_sequence depiction Margolus_toothpick_animated.gif.
- Toothpick_sequence isPrimaryTopicOf Toothpick_sequence.
