Difference between revisions of "Parabolic sawtooth"

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m (Removed Life 1.05 and 1.06)
m (Expansion factor is not applicable)
 
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|bx          = 126
 
|bx          = 126
 
|by          = 114
 
|by          = 114
 +
|e            = n/a
 
|discoverer  = Dean Hickerson
 
|discoverer  = Dean Hickerson
 
|discoveryear = 1991
 
|discoveryear = 1991

Latest revision as of 21:51, 27 January 2019

Parabolic sawtooth
x = 126, y = 144, rule = B3/S23 34b2o11b2o36b2o18b2o$34bo12bo37bo19bo6$16b2o16bo$16bo16b3o$33b3o36b2o 29bo5bo$72bo11b3o16b2o3b2o$31b2o3b2o6b2o3b2o32bo3bo$31bo5bo44bo5bo16b 3o$45bo3bo32bo5bo16b3o$46b3o57bo$46b3o24bo10bo$35bo35b2ob2o7b2o$34bo$ 34b3o33bo5bo$14b5o$13bob3obo50b2o3b2o5b3o$14bo3bo26bo5bo30b3o$15b3o15b o5bo4b3o5bo28bo3bo$16bo16bo5bo4b3o3b3o$34bo3bo41b2o3b2o20b3o6b2o$35b3o 4b2o3b2o57bo3bo5bo$42bo5bo56bo5bo$5b2o7bo90bo5bo$5bo8bo$13bobo$12b2ob 2o99b3o$11bo5bo98b3o$14bo23b2o7b2o23b2o3b2o36bo3bo$11b2o3b2o20bo8bo24b o5bo$5bo33b3o6b3o31b2o23b2o5b2o3b2o$4b3o27b2o5bo8bo4b2o16bo3bo4bo24bo$ 4b3o28bo19bo18b3o21b2o$35bobo5bo9bobo42bo$2b2o3b2o27b2o4bobo8b2o$2bo5b o32bob2o$40b2ob2o$13b2o26bob2o13bo$13bo9b2o17bobo12bo40bo$4bo15bo4b4o 14bo13b3o14b2o4bobo13b2ob2o$5bo13b2o2b2ob3o36b2o7bo5b2o$3b3o17bo37b4o 4b2o10bo13bo5bo$61b3ob2o2bo18bo2bo$66bo16b2o2b2o3bo2b2o3b2o14bo5bo$83b o8bo23b2o3b2o$o5bo81b4o$o5bo111b3o$bo3bo21bo15bo74b3o$2b3o22b2o15bo74b o$26bobo13b3o3$34bo$34b3o$37bo$36b2o55b2o3b2o2b2o$25b2o66bo5bo2bo$26bo 32bo9b2o51bo$57bobo10bo23bo3bo22b3o$23bo2bo31b2o10bobo5bo16b3o22b5o$3b 2o3b2o14bo2bo43b2o3b4o39b2o3b2o$3b2o3b2o15bobo8bo5bo34bob2o9b2o$4b5o 17bo9bo5bo32bobob3o8bo$5bobo29bo3bo35bob2o$25b2o11b3o35b4o32b2o$5b3o 17bo30bo21bo33bobo$57b2o37b2o11b2obobo$56b2o38bo12bobobo$111bo$111b2o$ 8bo43b2o57b3o$7bobo42bo23bo34b3o3b2o3b2o$6bo3bo63bobo34b3o3b2o3b2o$7b 3o28b2o35b2o34b2o5b5o$5b2o3b2o26bo15b2o55bo7bobo$54bo32b2o20bobobo$45b 2o5bobo32bo21b2obobo4b3o$44b3o5b2o19bo38bobo$32bo8bob2o29bo37b2o$32bob o6bo2bo27b3o$20b2o11bobo5bob2o$20bo12bo2bo7b3o$33bobo9b2o63b2o7b2o$32b obo75bo8bo$32bo$8b2o33b2o$8bo34bo12b2o51b3o$55bo2bo50b2o$47b2o6bo56b2o $48b2o5bo55b3o$47bo7bob2o51bobo$57bo52b2o3$56b2o$56bo2$28bobo$28bo3bo$ 18b2o12bo10b2o$18bo14bo7bo2bo21b2o42b2o$32bo7bo11b2o12bo43bo$28bo3bo7b o11bo$28bobo9bo$41bo2bo20b3o$43b2o20b2o$68b2o$34bo32b3o$34bobo29bobo$ 17b2o18b2o4b2o21b2o41b2o$19bo17b2o4bo65bo$20bo16b2o9b3o23bo$9b2o9bo8bo 4bobo13bo22b2o$9bo10bo9bo3bo14bo7b2o13b2o8b2o$19bo8b3o26b3o11b3o8bo$ 17b2o40b2obo9b2o$59bo2bo10b2o$59b2obo11bo$50b2o5b3o$49bobo5b2o$49bo44b o$48b2o40b2o2b2ob3o$90bo5b4o$86b2o6b2o$85bobo18b2o$22b2o60b3o19bo$24bo 59b2o21b3o$14b2o9bo13bo47b2o20bo$14bo10bo13bobo44b3o$25bo16b2o4b2o12b 2o$24bo17b2o4bo13b3o$22b2o18b2o9b2o9b2obo11bo6b2o$39bobo11bo10bo2bo10b 2o6bo$39bo24b2obo9b2o$62b3o11b3o$62b2o13b2o$78b2o5b2o$79bo5bobo$87bo$ 87b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
Pattern type Sawtooth
Number of cells 889
Bounding box 126×114
Expansion factor n/a
Discovered by Dean Hickerson
Year of discovery 1991

Parabolic sawtooth is a diagonal sawtooth that was discovered by Dean Hickerson on June 26, 1991. It is of special note because unlike most other sawtooths, its graph of population versus generation number is a sawtooth graph with parabolic (as opposed to linear) envelope and its population returns to 1208 in amounts of time that are quadratically spaced (as opposed to exponentially spaced, like most sawtooths). It can be reduced by using the Simkin glider gun instead of the Gosper glider gun-based p120 guns.

The pattern works by repeating the following operation for each n ≥ 0:

  • A 4-glider salvo is sent southeast toward a block A, arriving in generation 20n2 + 144n + a[n mod 3], where a[0]=a[2]=131 and a[1]=91.
  • Block A is pushed 1 unit southeast and another block, B, is created upstream from block A. Every 108 generations, 2 gliders hit B and pull it 3 units northwest. Eventually block B gets deleted by a glider, at generation 20n2 + 180 n + b[n mod 3], where b[0]=193, b[1]=223, and b[2]=227.
  • Another 4-glider salvo is sent toward block A.

The population is minimal around the time block B is deleted. The minimum repeating population that appears is 1208 in generations 180n2 + 540n + 210 and 180n2 + 660n + 450. The population is maximal around the time block B is created: there are about n/30 2-glider salvos on their way toward block B around generation t = 20n2 + 144n, so the population is about n/3 ~ sqrt(t/180) at that time.

Videos

About 250,000 generations of the parabolic sawtooth's evolution

External links