Sawtooth 562

Sawtooth 562
x = 114, y = 74, rule = B3/S23 50b2o21bo$51bo19bobo$51bobo8bo2b2o3bobo$52b2o7b2o2bo3bo2bo14b2o$60b2o 8bobo14bobo$47bo11b3o9bobo16bo11bobo$45bobo12b2o11bo13bo2bo10bo2bo$35b 2o6b2o16b2o27bo9b2o$34bo8b2o17bo24bobo8b2o3bo9bo$33bo5bo3b2o42b2o11b2o 10b2o$23bo9bo5b2o4bobo7b2o44bo2bo$23b2o8bo6bo6bo7bobo44bobo$34bo22bo$ 35b2o20b2o8$29bobo$29bo2bo$20b2o10b2o11b2o$20bo9bo3b2o8bobo$32b2o9bo$ 29bo2bo10bo2bo$29bobo11bo$44bobo5b2o$2o23bo19b2o5bobo$bo23bobo26bo$bob o4b2o18b2o4b2o18b2o$2b2o6bo17b2o5bo$11bo16b2o$11bo13bobo$11bo13bo$10bo $8b2o54bo$3b2o56bo3b2o$3bo56b2o2bo$60b2o$61bo$61b2o$61bo$62bo$34b2o2b 3o2b2o11b2o4b3o$34bo2b5o2bo10bobo3bo$2obob2o28b9o11bo4b2o3bo$o5bo25b3o 9b3o7b2o4b2o$bo3bo26bo2bo7bo2bo14bob2o$2b3o3bo24b2o9b2o14b2ob2o$8b2o 40b2o7bo3bo$7bobo40bo10bobob2o$43bo4bobo10bo3bo$32bo9bobo3b2o15bo$26bo bo2b2o9b2obo16bobo$25bo2bo2bobo8b2ob2o14bo$24b2o16b2obo14b3o$5bo16b2o 3bo14bobo$5bo18b2o17bo18bo$4bobo11b2o5bo2bo33bo2bo$3b2ob2o9bobo6bobo 31b2o2b2o$2bo5bo8bo21bo25bo$5bo10b2o20b2o$2b2o3b2o18b2o8b2o4b2o5bo$27b o8b3o4b2o3bobo29bo$37b2o4b2o2bobo30bobo$38b2o6bo2bo16b2o15b2o4b2o$39bo 7bobo16bo16b2o5bo$48bobo12b2o18b2o$50bo11b3o15bobo$63b2o15bo$6bo59bo$ 5b2o59b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
View static image
Pattern type	Sawtooth
Number of cells	415
Bounding box	105 × 74
Expansion factor	6
Discovered by	Dean Hickerson Tim Coe
Year of discovery	1992
Rules Outer-totalistic rules B3/S23 only # of rules 20 = 1 Isotropic rules B3/S23 – B3/S236ei
Pattern files Plaintext sawtooth562.cells RLE sawtooth562.rle

Sawtooth 562 is an orthogonal sawtooth with expansion factor 6 that was found by Dean Hickerson and Tim Coe on August 14, 1992. Its population in generations t near 28(6ⁿ) is about t/5 if t is odd and about 3t/20 if t is even. However, its population in generation 14(6ⁿ) - 84 (n ≥ 2) is only 562. Even more specifically, the population in generation t = 28(6ⁿ) + 12 (n ≥ 1) is 3t/20 + 555, which drops to t/5 + 599 in the next generation.

It works by using a spark from a period-4, speed c/4 orthogonal spaceship, found by Tim Coe, to turn one lightweight spaceship into a loaf, which is then pulled back by subsequent pairs of lightweight spaceships (see tractor beam). When the loaf is pulled all the way back, it gets deleted and the cycle begins again.

The pattern

x = 114, y = 74, rule = B3/S23 50b2o21bo$51bo19bobo$51bobo8bo2b2o3bobo$52b2o7b2o2bo3bo2bo14b2o$60b2o 8bobo14bobo$47bo11b3o9bobo16bo11bobo$45bobo12b2o11bo13bo2bo10bo2bo$35b 2o6b2o16b2o27bo9b2o$34bo8b2o17bo24bobo8b2o3bo9bo$33bo5bo3b2o42b2o11b2o 10b2o$23bo9bo5b2o4bobo7b2o44bo2bo$23b2o8bo6bo6bo7bobo44bobo$34bo22bo$ 35b2o20b2o8$29bobo$29bo2bo$20b2o10b2o11b2o$20bo9bo3b2o8bobo$32b2o9bo$ 29bo2bo10bo2bo$29bobo11bo$44bobo5b2o$2o23bo19b2o5bobo$bo23bobo26bo$bob o4b2o18b2o4b2o18b2o$2b2o6bo17b2o5bo$11bo16b2o$11bo13bobo$11bo13bo$10bo $8b2o54bo$3b2o56bo3b2o$3bo56b2o2bo$60b2o$61bo$61b2o$61bo$62bo$34b2o2b 3o2b2o11b2o4b3o$34bo2b5o2bo10bobo3bo$2obob2o28b9o11bo4b2o3bo$o5bo25b3o 9b3o7b2o4b2o$bo3bo26bo2bo7bo2bo14bob2o$2b3o3bo24b2o9b2o14b2ob2o$8b2o 40b2o7bo3bo$7bobo40bo10bobob2o$43bo4bobo10bo3bo$32bo9bobo3b2o15bo$26bo bo2b2o9b2obo16bobo$25bo2bo2bobo8b2ob2o14bo$24b2o16b2obo14b3o$5bo16b2o 3bo14bobo$5bo18b2o17bo18bo$4bobo11b2o5bo2bo33bo2bo$3b2ob2o9bobo6bobo 31b2o2b2o$2bo5bo8bo21bo25bo$5bo10b2o20b2o$2b2o3b2o18b2o8b2o4b2o5bo$27b o8b3o4b2o3bobo29bo$37b2o4b2o2bobo30bobo$38b2o6bo2bo16b2o15b2o4b2o$39bo 7bobo16bo16b2o5bo$48bobo12b2o18b2o$50bo11b3o15bobo$63b2o15bo$6bo59bo$ 5b2o59b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 6 WIDTH 800 HEIGHT 650 ]]

(click above to open LifeViewer) RLE: here Plaintext: here

Image gallery

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  The number of alive cells plotted versus the number of elapsed generations roughly forms an ever-increasing sawtooth graph.

External links

• Sawtooth 562 at Paul Callahan's Page of Conway's Life Miscellany