R-pentomino
From LifeWiki
| R-pentomino | |||||||||||
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| Pattern type | Methuselah | ||||||||||
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| Lifespan | 1103 generations | ||||||||||
| Number of cells | 5 | ||||||||||
| Bounding box | 3×3 | ||||||||||
| Discovered by | John Conway | ||||||||||
| Year of discovery | 1970 | ||||||||||
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The R-pentomino is a methuselah that was found by John Conway in 1970.[1] It is by far the most active polyomino with fewer than six cells; all of the others stabilize in at most 10 generations, but the R-pentomino does not do so until generation 1103, by which time it has a population of 116. The glider it releases in generation 69, noticed by Richard K. Guy, was the first glider ever observed.
Predecessors
The R-pentomino has several different small predecessors which are of note because they naturally have a longer lifespan. There are three 5-cell grandparents of the R-pentomino (which each have a lifespan of 1105 generations) and three 6-cell predecessors that evolve into the R-pentomino after 5 generations (and thus have a total lifespan of 1108).
 The three 5-cell grandparents of the R-pentomino. |  Three 6-cell predecessors that each evolve into the R-pentomino at generation 5. |
Evolution
The R-pentomino initially grows in all directions. A c/2 forward growth mechanism emerges at generation 7, and by generation 27 finally separates. From here on this part of the pattern proceeds along the B-heptomino evolution.
The lef-behind chaos is whittled down by generation 40 into two halves, one of which would produce traffic light and the other a honey farm, if left on their own. These however react with each other to produce a large cloud of further growth, and by generation 104 this consumes the block left behind by the B-heptomino. The third glider also escapes around this time, followed by a fourth at generation 156.
The Herschel from the initial B finishes by generation 176, having created a ship, two blocks and two gliders as usual. By generation 198, a small active intrusion close to these creates two beehives (one of which will be later destroyed) and the fifth escaping glider.
The next surviving objects to be created are a boat formed at generation 599, a block formed at generation 646 and a glider released at generation 699 (though several temporary blocks, blinkers, boats, beehives, traffic lights and two temporary gliders have been seen by this point).
A toad forms at generation 737 and a beacon at generation 744, but both are destroyed by the activity at generations 751 and 754 respectively.
The pi heptomino sequence pops in for a cameo at several points, the longest-surviving instance running between generations 784 and 803. The century sequence also makes a brief appearence, between generations 316 and 333.
The stable pattern that results from the R-pentomino has 116 cells and consists of eight blocks, six gliders, four beehives, four blinkers, one boat, one loaf, and one ship.
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See also
References
- ↑ Gardner, M. (1983). "The Game of Life, Part III". Wheels, Life and Other Mathematical Amusements: 219, 223, W.H. Freeman.
External links
- New Methuselah Records at Game of Life News
- R-pentomino at Eric Weisstein's Treasure Trove of Life
- R-pentomino at the Life Lexicon
