Difference between revisions of "Sawtooth 1212"

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Its population in generation t = 18*21^n + 222 (n ≥ 0) is 7t/60 + 1290, but the population in generation 6*21^n + 193 (n ≥ 1) is only 1212. It works by using a [[spark]] from a [[turtle]] to turn a [[heavyweight spaceship]] into a [[loaf]], which is then pulled back by pairs of [[lightweight spaceship]]s. When the loaf is pulled all the way back, another heavyweight spaceship is fired towards the turtle, starting the cycle again. The heavyweight spaceship synthesis, which uses two [[glider]]s, [[Kok's galaxy]], and a [[figure eight]], is due to [[:Category:Patterns found by David Buckingham|David Buckingham]].
 
Its population in generation t = 18*21^n + 222 (n ≥ 0) is 7t/60 + 1290, but the population in generation 6*21^n + 193 (n ≥ 1) is only 1212. It works by using a [[spark]] from a [[turtle]] to turn a [[heavyweight spaceship]] into a [[loaf]], which is then pulled back by pairs of [[lightweight spaceship]]s. When the loaf is pulled all the way back, another heavyweight spaceship is fired towards the turtle, starting the cycle again. The heavyweight spaceship synthesis, which uses two [[glider]]s, [[Kok's galaxy]], and a [[figure eight]], is due to [[:Category:Patterns found by David Buckingham|David Buckingham]].
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==Image gallery==
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{|
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|[[Image:Sawtooth1_later.png|framed|left|Sawtooth 1 works by sending out a stream of c/2 lightweight spaceships to collide with a c/3 turtle, creating loaves along the way.]]
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|}
  
 
==External links==
 
==External links==
 
*[http://www.math.ntnu.edu.tw/act/math_camp/Lab/Life/sawtoot3.lif Sawtooth 1] Life 1.05 file and description
 
*[http://www.math.ntnu.edu.tw/act/math_camp/Lab/Life/sawtoot3.lif Sawtooth 1] Life 1.05 file and description

Revision as of 03:42, 15 February 2009

Sawtooth 1
x = 173, y = 114, rule = B3/S23 39b2o$39bo16b2o$28b2o7bobo16bo$28bo2bo5b2o$14bobo15bo$12bo3bo15bo$12bo 19bo$5b2o4bo16bo2bo6b2o$5bo6bo15b2o8bobo15bo$12bo3bo22b3o13b3o$14bobo 23b2o13b3o$37b2o$37b3o13b2o3b2o$31bo21bo5bo$32bo$30b3o5b2o$38bo22b2o$ 55bo6bo$56bo5bobo7b2o$54b3o6b2o6b3o$9bobo56bob2o15bo$7bo3bo56bo2bo15bo bo$2o5bo15b2o43bob2o16bobo$o5bo16bo2bo24bo5bo13b3o14bo2bo3b2o$7bo19bo 23bo5bo14b2o14bobo4bo$7bo3bo15bo6b2o16bo3bo30bobo28b2o$9bobo15bo6bo18b 3o31bo31bo$23bo2bo76b2o14bobo9bo$23b2o78bo16b2o8b4o$38b2o52bobo6bobo 25b2obo8b2o$38bo53bo2bo5b2o25b3obobo6bo2bo$26b2o8bobo38bo17b2o32b2obo 12bo$28bo7b2o38bobo14bo3b2o20b2o9b4o11bo6b2o$15b2o12bo26b2o17bob2o16b 2o21bo2bo9bo13bo6bo$15bo13bo26bo17b2ob2o13bo2bo6b2o14bo22bo2bo$12b2o 15bo27b3o15bob2o13bobo6bo2bo13bo22b2o$4b2o5b3o14bo8b2o20bo11b2o3bobo 25bo13bob2o$4bo7b2o12b2o9bo24bo7bobo4bo26bo15bo8bo$15bo31b2o12bo8bo30b 2obo22b2o$15b2o30bo13b3o5b2o31bo25b2o$37b3o79b2o$29bo8b2o55bo23bo12b2o $30bo4b2o9b3o47b2o4b2o28bo$28b3o4b3o8b2o18b2o27b2o5bo41bo$36bobo10b2o 16bo74bobo$24b2o11b2o9b3o16bobo7b2o42b2o7b2o9bobo11b2o$24bo22bobo18b2o 5bo2bo42bo8b3o7bo2bo11bo$14bo32b2o25bo13bo43b2obo5bobo$13bobo58bo11b4o 42bo2bo6bobo$b2o10b2obo8bobo46bo12bob2o41b2obo8bo$bo11b2ob2o6bo2bo47bo 2bo6bobob3o31b2o5b3o$13b2obo6b2o52b2o8bob2o31bobo5b2o$13bobo5b2o3bo59b 4o8b2o22bo$14bo8b2o63bo9bobo20b2o$24bo2bo5b2o65bo$25bobo5bobo64b2o$35b o$35b2o2$53bo7b3o$53b2ob2obo2b2o$54bo4b3o$34b2ob2obo13bo3bobo2bo$33b2o 2b2ob2o12bo4bo4bo$41bo12bo4bo4bo$33b2o19bo3bobo2bo$33b2o5b2o12bo4b3o$ 40b2o11b2ob2obo2b2o$33bo13b3o3bo7b3o$33b2ob2o2b2o5b3o$34bob2ob2o6b3o$ 50b3o$50b3o$50b3o2$39b2o23b2o$38b3o23bo44bo27b2o$26bo8bob2o9b2o59bobo 26bo$26bobo6bo2bo9bo63b2o6b2o16bobo9bo$27bobo5bob2o25bo47b2o4bo3bo16b 2o8b4o$14b2o11bo2bo7b3o22b2obo45b2o3bo5bo24b2ob4o5b2o$14bo12bobo9b2o 25bo33b2o7bobo4b2obo3bo23b3ob2o3bo3bo2bo$26bobo37bo32bobo7bo7bo5bo24b 2ob2o3bo7bo$26bo36bo2bo32bo18bo3bo7b2o17b5o3bo6bo6b2o$37b2o25b2o32b2o 20b2o8bobo17bo3b3o7bo6bo$37bo43b2o27bo21bo27bo2bo$81bo26b2o22b2o26b2o$ 70b2o7bobo27b2o$70bobo6b2o54bo$57bobo13bo61b2o$56bo2bo5bo4bo2bo18b2o$ 55b2o9bo6bo17bo2bo41bo$53b2o3bo5b3o3bobo21bo40bobo$55b2o13b2o22bo39bo 2bo$49b2o5bo2bo31b2obo38bo2bo24bo$48bobo6bobo32bo67bobo$48bo66bobo18bo 7bobo13b2obo4b2o$47b2o34b2o29bo2bo17b2o6bo2bo13b2ob2o3bo$23bo24bob2o 30bobo7b2o6b2o11b2o10b2o15b2o16b2obo$23b2o23bobo30b3o8bo7bobo8b2o3bo8b o14b2o3bo14bobo$14b2o8b2o14bo5bobo2bo29b2o20bo9b2o27b2o17bo$14bo9b3o 13bobo3b2o2b2o32b2o14bo2bo10bo2bo18b2o5bo2bo$24b2o15bobo39b3o17bo11bob o17bobo6bobo$23b2o16bo2bo13b2o33b2o5bobo32bo$23bo17bobo16bo8b3o20bobo 5b2o32b2o$40bobo7b2o9bo9bo3bo7b2o7bo$40bo9bo10bo8bo4bobo5bo7b2o$61bo 16b2o$60bo17b2o$58b2o18b2o$75bobo4b2o$75bo6bobo$84bo$84b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
Pattern type Sawtooth
Number of cells 983
Bounding box 173×114
Discovered by Dean Hickerson
Year of discovery 1991

Sawtooth 1 is an orthogonal sawtooth with expansion factor 21 that was discovered by Dean Hickerson on April 10, 1991. It was the first sawtooth to be constructed.

Its population in generation t = 18*21^n + 222 (n ≥ 0) is 7t/60 + 1290, but the population in generation 6*21^n + 193 (n ≥ 1) is only 1212. It works by using a spark from a turtle to turn a heavyweight spaceship into a loaf, which is then pulled back by pairs of lightweight spaceships. When the loaf is pulled all the way back, another heavyweight spaceship is fired towards the turtle, starting the cycle again. The heavyweight spaceship synthesis, which uses two gliders, Kok's galaxy, and a figure eight, is due to David Buckingham.

Image gallery

Sawtooth 1 works by sending out a stream of c/2 lightweight spaceships to collide with a c/3 turtle, creating loaves along the way.

External links