Total aperiodic
| Total aperiodic | |||||||||
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| Pattern type | Miscellaneous | ||||||||
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| Number of cells | 182 | ||||||||
| Bounding box | 59 × 57 | ||||||||
| Discovered by | Bill Gosper | ||||||||
| Year of discovery | 1997 | ||||||||
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A finite pattern is total aperiodic if it evolves in such a way that no cell in the plane is eventually periodic.
The first example was found by Bill Gosper on November 16, 1997. A few days later, on November 19, he found the much smaller example that consists of three copies of backrake 2 (by David Buckingham),[1] shown in the infobox. Two of the rakes release southwestbound gliders, which perform 90-degree kickbacks to the northwestbound outputs from the third rake. As each kickback happens farther away from the last one and shifts the central glider by one half-diagonal southwestwards, any cell in the plane will be covered by infinitely many gliders on their aperiodic lanes.
On June 24, 2004, Gosper found that a block can be added to the pattern to make the total periodic pattern shown below, in which every cell in the plane will eventually die and stay dead, albeit incredibly slowly. The block remains untouched for about 363 generations. It deletes the nth glider (and is shifted) at about generation 357.5+5.5n.[2]
| Total periodic (click above to open LifeViewer) RLE: here Plaintext: here |
A space nonfiller is also capable of touching every cell in the plane at least once and making them eventually OFF.
References
- ↑ Total aperiodic at Paul Callahan's Page of Conway's Life Miscellany
- ↑ Jason Summers' jslife oversize pattern collection.
External links
- Total aperiodic at the Life Lexicon
- Dean Hickerson. "Aperiodic patterns". Dean Hickerson's Game of Life page. Retrieved on June 4, 2022. Patterns with similar concept.
- Totally periodic pattern (discussion thread) at the ConwayLife.com forums