Sawtooth 1846

Sawtooth 1846
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Pattern type	Sawtooth
Number of cells	1462
Bounding box	370 × 118
Expansion factor	25
Discovered by	Dean Hickerson
Year of discovery	1992
Rules Outer-totalistic rules B3/S23 only # of rules 20 = 1 Isotropic rules B3/S23 – B3/S234c
Pattern files Plaintext sawtooth1846.cells RLE sawtooth1846.rle

Sawtooth 1846 is an orthogonal sawtooth with expansion factor 25 that was found by Dean Hickerson on August 26, 1992. Its population in generations t near 30(25ⁿ) is about 59t/225 if t is odd, about 7t/10 if t is even but not equal to 46 (mod 60), and about 211t/900 if t = 46 (mod 60). However, the population in generation 6(25ⁿ) - 1125 (n ≥ 2) is only 1846. Slightly more specifically, the population in generation t = 30(25ⁿ) - 525 (n ≥ 1) is 59t/225 + 1951.

A shotgun produces a salvo of 4 eastward lightweight spaceships every 120 generations. Some are deleted; the others eventually catch up to a pair of unnamed c/3 orthogonal spaceships (see 60P3H1V0.3) and reflect off the their backs, forming westward middleweight spaceships. When a middleweight spaceship returns to the shotgun, it causes the deletion of 5 salvos. Notice the unusual eating of a pi-heptomino by two blocks that is used in this deletion). As a result of this reaction, the region between the shotgun and the spaceships alternately becomes full of spaceships and empty.

The c/3 spaceships were found by David Bell, who suggested this way of making a sawtooth.

The pattern

x = 370, y = 118, rule = B3/S23 235b2o$236bo$222bo15b2o$220bobo15b3o11bo$166b2o50b2o18b2o12bobo$166bo 45bo5b2o16bo16bobo7bo$61bo40bo60b2o15bo31b2o4b2o15b2o16bo2bo6b2o$60bob o38bobo46bo11b3o15bobo37bobo30bobo3bo4b2o9bo$43b2o14bo3b2o36b2obo7b2o 34bobo12b2o18b2o37bo29bobo3b2o4b3o7b2o44bo$43bobo13bo3b2o3b2o19b2o10b 2obobo5bobo24bo7bobo16bo16b2o5bo44b2o15bo11b2o52bobo$44b3o12bo3b2o4bo 19bo11b2obo10bo22b2o6bo2bo16b2o15b2o4b2o44bo27b2o43b2o6b2o$34bo10b3o 12bobo38bobo8bo2bo8bo2bo9b2o4bo3bobo30bobo80bo43bo8b2o15bo31bo$34b2o8b 3o14bo40bo12bo7b2o2b2o7b3o4b2o3bobo29bo125bo6bo2b2o15b2o29bobo$43bobo 66bobo22b2o11bo145b2o8bo5b2o4bobo13b2o13b2o15b2o$43b2o67b2o24b2o156bo 9bo5bo7bo13b3o11b3o14bo$139bo94b2o71bo26b2o9bob2o17b2o$234bo73b2o23b2o 10bo2bo10bo5b3o$333bo11bob2o9b2o$208bo139b3o13bo2bo$207b3o23b3o113b2o 14bobo$31b2o72bo127b2o132bo$32bo71b2o130b2o128bo$32bobo6bo73bobo117b3o 126bobo$33b2o4bobo71bo3bo116bobo81b2o45bo$37b2o15b2o45b2o10bo12b2o31bo 47b3o12b2o5b2o3b2o82bo46b2o$37b2o16bo45bo2bo7bo14bo29bobo48bo13bo7bo$ 2o23b2o10b2o18b2o46bo7bo44b2o204bo2bo$bo23bo13bobo15b3o45bo7bo3bo36b2o 161b2obo47bo$bobo7bo10b2o17bo15b2o46bo9bobo36b3o161bobo44bo2b2o$2b2o7b obo7b3o10b2o19bo7b2o29b2o5bo2bo43bo3bo2bobo161bo44b4o$14b2o6b2o11bo18b 2o7bobo27bobo5b2o45b2o2b2o2b2o160b2o44b2obo$14b2o9bo39bo27bo58b2o164b 2o45bobo$14b2o9b2o38b2o25b2o224b2o45b3o$o10bobo352b2o$3o8bo351b2obo$3b o60bo59bo59bo59bo59bo58bo$2b2o61bo59bo59bo59bo59bo57bo$61bo3bo10bo44bo 3bo10bo44bo3bo10bo44bo3bo10bo44bo3bo57b3o$62b4o11bo44b4o11bo44b4o11bo 44b4o11bo44b4o60b2o$73bo3bo55bo3bo55bo3bo55bo3bo105bo2b2o$74b4o56b4o 56b4o56b4o106bo$52b2o311b2o$2b2o3b2o25b2o7b2o6b3o310b3o$2bo5bo25bo9bo 5bobo2bo3bo$35b9o6b2o2b2o2b2o32b2o$3bo3bo2b2o20b3o2b5o2b3o7b2o32b2o2b 2o2b2o$4b3o4b2o19bo2bo2b3o2bo2bo41bo3bo2bobo$10bo22b2o9b2o48b3o$94b2o 114bo6bo89bo$29b2o178b2obo2bob2o88bobo$28b2o10bobo167bobo2bobo89b2o$ 30bo8bo2bo168bo4bo$25b2o11b2o10b2o$7bo17bobo8b2o3bo9bo10bo$5b2ob2o6bo 11bo9b2o21b2o49b2o75bo47b2o$16b2o7bo2bo10bo2bo17b2o11bo38bo74bobo48bo$ 4bo5bo17bo11bobo16b3o4b2o3bobo29bo6bobo17bobo55b2o48bobo$25bobo32b2o4b o3bobo30bobo4b2o18bo2bo17b2o9b2o75b2o44bo$4b2o3b2o14b2o25b2o7b2o6bo2bo 16b2o15b2o7bo17b2o6b2o7bo2bobo3bobo2bo9bo109b2o$51bobo8bo7bobo16bo16b 2o6bobo14bo3b2o5bo7b3o9b3o8bo110bobo$51bo19bobo12b2o18b2o5bob2o16b2o 18b2o5b2o7bo2bo4bo$50b2o21bo11b3o15bobo6b2ob2o13bo2bo18bo2b5o2bo5b2obo 2bob2o$86b2o15bo9bob2o13bobo19b2o7b2o9b2o$89bo19b2o3bobo231b3o$89b2o 17bobo4bo233b2o$108bo54b2o58b2o58b2o63bo$107b2o53b4o56b4o56b4o61bo2b2o $8bo153b2ob2o55b2ob2o5b4o46b2ob2o5b4o54b2o$7b2o155b2o58b2o5bo3bo48b2o 5bo3bo51b3o$235bo59bo51bo$234bo59bo52bo$347b2obo$184b2o164b2o$184bo 122b2o40b3o$150b2o23b2o5bobo27bo4bo90bo40bobo$151bo22bobo5b2o26b2obo2b ob2o88bobo5b2o30b2obo$151bobo5bobo11bo36b2o6b2o89b2o5bo2bo28b4o$152b2o 5bo2bo10bo2bo33b3o4b3o100bo9bobo16bo2b2o$103b2o9b2o46b2o9bo146bo7bo3bo 19bo$103bobo7bobo44bo3b2o8bobo7bo135bo7bo13bo5bo2bo$94b2o10bo8bo5bo25b obo12b2o11b2o7b2o38bo91bo2bo7bo13b2o$94bo8bo2bo13bobo24bo3bo7bo2bo20bo bo3bo32bobo91b2o10bo20b2o$106bo13b2obo10b2o3b2o10bo7bobo27b2o30bobo17b o86bo3bo16bo$103bobo14b2ob2o7bo2bo3bobo10bo57bo4b2o3bo2bo16b2o88bobo 15bobo$103b2o15b2obo7bo7bo11bo37bo19b2o4bo5bobo15b2o77b2o30bo$120bobo 8bo15bo3bo3b2o31bobo18bobo10bobo13b3o9bo55bo12bo31bo$121bo9bo15bobo5bo bo30bo2bo32bo4bobo7b2o8b2o54b2o42bobo$125b2o5bo2bo21bo31bo2bo36b2o9b2o 106bo2bo$124bobo7b2o21b2o48b2o21bo10bo64bo$124bo64bo17bo97bobo41b3o$ 123b2o40b2o22b2o87b4o22bo2bo42b2o$164bo42bo2bo62b2o7bo20bo2bo20b2o20bo $153b2o8bo6bo6bo28bo2bo63bo3b2o3bo44bobo20b2o$153bo9bo5b2o4bobo28bobo 52b2o15bo2bo24bo10bo12bo7b2o8bobo$163bo5bo3b2o13bo18bo52bo2bo41b2o9bob o8bo2bo8bo9bo$164bo8b2o12b2o74bo52b2obo10bo$165b2o6b2o32b2o54bo52b2obo bo5bobo$175bobo29bo52b2obo52b2obo7b2o$177bo58bo24bo44b2o8bobo$235b2o 68bobo9bo$219bo14b2o8b2o59bo$217bobo13b3o9bo16bo41b2o$210bo5bobo15b2o 25b2o$210b2o3bo2bo16b2o$216bobo17bo$217bobo$219bo73bo$263bo29bobo$263b 2o14b2o15b2o$249b2o28bo16b2o4b2o$249bo2bo23b2o18b2o5bo$240b2o11bo13bo 7b3o15bobo$240bo12bo12b4o6b2o15bo$253bo11b2obobo8bo$249bo2bo11b3obo2bo 7b2o$249b2o14b2obobo$266b4o$267bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 3 WIDTH 1300 HEIGHT 500 QUALITY ]]

(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

• Dean Hickerson. "Sawtooths based on bouncing spaceships". Dean Hickerson's Game of Life page. Retrieved on April 30, 2022.
• Sawtooth 1846 at Paul Callahan's Page of Conway's Life Miscellany