Caber tosser

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A caber tosser is a pattern whose population is asymptotic to c · log(t) for some constant c, and that contains a glider (or other spaceship) bouncing between a slower receding spaceship and a fixed reflector that emits a spaceship (in addition to the reflected one) whenever the bouncing spaceship hits it.

As the receding spaceship gets further away, the bouncing spaceship takes longer to complete each cycle, and so the extra spaceships emitted by the reflector are produced at increasingly large intervals. More precisely, if v is the speed of the bouncing spaceship and u the speed of the receding spaceship, then each interval is (v + u) / (vu) times as long as the previous one. The population at time t is therefore n · log(t) / log((v + u) / (vu)) + O(1), where n is the population of one of the extra spaceships (which is assumed to be constant).

For example, the following caber tosser uses a bouncing c/4 diagonal glider and a receding c/12 diagonal 2-engine Cordership, so the ratio is (1/4 + 1/12) / (1/4 − 1/12) = 2. Because the Cordership has a period of 96, two period-48 glider guns and a 68P32 are used. The resulting m-th glider appears at generation 192 × 2m.

x = 64, y = 73, rule = B3/S23 17b3o$15b7o6bo$14b9o4bo$13bo7b3o2b2o$14b3o6bo3bo2bo$15b2o11b3o$18bo10b o$19bo18b2o$20bo17b2o4$obo$3o$2o15bo$17bo$16bo$3bo13b2o27bo$bobo12bo2b o27bo$b3o12bobo21bobo2bobo$4bo35bo4bo$5o12bo26bo$15bo2bo22b6o$16b4o23b 2obo$18b2o$16bo$15b2o29bo$15bo2bo$16b3o24b3o$17bo27bo$44bo2$5b2o$5b2o 2$49bo3bo$44bo2b2obobob2o2bo$42b2obobo2bobo2bobob2o$42b2o3bobo3bobo3b 2o$44b2o2bo5bo2b2o$13b2o$13b2o$27b2o$17bo10bo$15bobo10bobo$16b2o11b2o 4$44b2o2bo5bo2b2o$42b2o3bobo3bobo3b2o$11b2o8b3o5b2o11b2obobo2bobo2bobo b2o$7bo3b2o7bo8bo14bo2b2obobob2o2bo$3b2ob2o12bo2bo3bobo19bo3bo$2bobobo 11b2o3bo3b2o$3b2ob2o9bo4bo18bo$4b2o11bo3bobo17bo$2bob3o10bo4bo17bo$2ob o4b3o7b2o4bo9b2o16b2o4bo$20bo3bo10bo12bo3b2o3bob2o$20bo3bo10bobo9bobo 7bo$21b3o12b2o8b2ob2o8bo$27b2o12bo5bo2bo5b3o$14b2o11bobo10bob2o4bobo5b o$14b2o13bo10bob2o5bo8bo2b2o$29b2o10bobo11b4o4bo$41b2o12bo3bo2bo$41b4o 16bo$43b2o$36b2o7bo$35bobo7bo3b2o$35bo8bo4b2o$34b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 800 THUMBSIZE 2 ZOOM 10 ]]
A caber tosser starting from a 64 × 73 bounding box
(click above to open LifeViewer)
RLE: here Plaintext: here

The first caber tosser was built by Dean Hickerson in May 1991.

See also

External links