User:H. H. P. M. P. Cole/Maximum number of 4-cell oscillators

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Forum thread

RULES

- No infinite series of only 4-cell objects

- No rules where the only 4-cell stable objects are still-lifes (so no B/S012345678)

- No objects (SLs, oscs, spaceships, and growing patterns that never stop) with minpop lower than 4 in the rule

- No explosive rules

- No 4-cell predecessors of other non-minpop-4 oscillators

- Rule HAS to be isotropic

- Rule must not be B0 (due to a loophole toroidalet found)

- The number of points you have is governed by the number of minpop 4-cell oscillators you have in your rule (due to a loophole Haycat found)

Score tabulation

  • Still life: 1 point
  • Oscillator: 0.5 X (period^2) points, rounded up
  • Spaceship: (period x 3)^2 points
  • Infinite growth: (period x 5)^2 points
Number of cells in neighbourhood Number of objects Periods/Speeds Points (Durnak System) Discoverer Isotropic rulestring RLE
4 Unsatisfiable
8 13 p1, p2, p3, p4, p6, p10 101 H. H. P. M. P. Cole and Haycat Durnak (independent discovery) B2-an3ceqry4c5a/S1c2-en3-n5a6a7c (Hensel notation) and B2-an3ceqry4ct5a/S1c2-en3-n5a6a7c
x=22, y = 35, rule = B2-an3ceqry4c5a/S1c2-en3-n5a6a7c 2o4b2o4bo5b3o$2o5b2o4b2o4bo$13bo4$2bo12bo3bobo$2o5b2o4b2o$o5bo2bo2bo6b obo5$bo$o$3bo$2bo3$bo$3bo2bobo$o6bo$2bo5bo4$obo$bobo5$2bo$o3bo$2bo!
12 40 p1, p2, c/1o 81 H. H. P. M. P. Cole B3aa.ab.ac.ad.ae.af.ag.ah.ai.aj.an.ao.ap.aq.ar.as.at/S2-a.b.j.k.m.n.o (Durnak-Cole notation)
x=149, y = 80, rule = R3,C2,S2,B3,N+ 2o13bobo13bo2bo$2o13bobo13bo2bo9$15bobo13bo2bo2$15bobo13bo2bo9$31bo2b o3$31bo2bo17$2b2o11b2o14b2o12bobo15bobo15b2o15b2o10bobo9b2o12b2o8bobo $bo2bo9bo3bo10bo4bo9bo3bo13bobo14b2o16bobo9bo2bo7bo2bo11b2o8b2o9$2b2o 11b2o14b2o12bobo15bobo15b2o15b2o10bobo9b2o12b2o8bobo2$bo2bo9bo3bo10bo 4bo9bo3bo13bobo14b2o16bobo9bo2bo7bo2bo11b2o8b2o9$2b2o11b2o14b2o12bobo 15bobo15b2o15b2o10bobo9b2o12b2o8bobo3$bo2bo9bo3bo10bo4bo9bo3bo13bobo14b 2o16bobo9bo2bo7bo2bo11b2o8b2o14$bo2b3o!
48 >=127 p1, p2, 2c/1o, (2,1)c/1o, 2c/1d 250 H. H. P. M. P. Cole (too long to put here)
x=265, y = 244, rule = R6,C2,S2,14,63,98-99,105,B3,10,21,147-148,154,NW07000001000031000001000007000000000000000000000000000000070001003100010007000001000000000000000000000001000001000701310107000100000000000001000000010000000031003100310000003100310031000000000100000001000000000000010007013101070001000001000000000000000000000001000007000100310001000700000000000000000000000000000007000001000031000001000007 6bobo10bo3bo8bo5bo14bobo13bobo17bobo15bo3bo33bobo25bobo12bobo2$6bobo10b o3bo8bo5bo12bo5bo9bo7bo9bo9bo9bo7bo27bobo29bo5bo10bobo7$253bo2$253bo2$ 253bo4$19bo3bo8bo5bo14bobo33bobo15bo3bo14bo3bo2$253bo2$19bo3bo8bo5bo12b o5bo27bo9bo9bo7bo10bo3bo14$32bo5bo14bobo13bobo17bobo15bo3bo14bo3bo14b obo10bobo12bobo12bobo6$32bo5bo12bo5bo9bo7bo9bo9bo9bo7bo10bo3bo12bobo14b o3bo10bo5bo10bobo11$4bo12bo14bo2$2bo3bo8bo14bo2$4bo16bo2$19bo18bo2$36b o6$260bo$17bo14bo79bo21bo$51bo39bo7bo158bo$118bo$49bo7bo31bo166bo$13b o7bo6bo79bo21bo2$38bo97bo2$17bo$51bo198bo$34bo75bo21bo$89bo9$192bo$155b o$33bo138bo17bo$50bo39bo62bo$170bo29bo$48bo18bo20bo11bo$180bo17bo$58b o6bo11bo$27bo11bo2$176bo$157bo2$52bo102bo$33bo$69bo20bo13$242bo$208bo 17bo$2bo110bo23bo18bo14bo15bo4bo18bo12bo13bo$o15bo15bo59bo4bo18bo37bo 14bo4bo10bo18bo$3bo47bo18bo4bo14bo18bo23bo91bo13bo$bo10bo4bo15bo15bo4b o13bo67bo33bo15bo18bo17bo13bo$26bo126bo$13bo94bo23bo18bo$27bo20bo18bo 19bo4$264bo$241bo20bo$208bo16bo34bo$113bo22bo17bo16bo15bo35bo13bo$16b o15bo59bo59bo16bo15bo18bo$51bo18bo19bo18bo22bo60bo18bo41bo$12bo36bo18b o29bo18bo57bo$26bo49bo148bo13bo$18bo15bo20bo80bo34bo15bo18bo16bo13bo$ 152bo$14bo94bo22bo17bo$28bo20bo18bo19bo4$241bo$208bo16bo$113bo22bo17b o16bo15bo35bo13bo$92bo59bo16bo15bo18bo$51bo18bo19bo18bo22bo$32bo16bo18b o$194bo18bo$99bo18bo57bo$26bo50bo148bo13bo$56bo80bo34bo15bo18bo16bo13b o$153bo$35bo74bo22bo17bo$50bo18bo19bo2$29bo16$15bo14bo76bo16bo7bo10bo $13bo33bo18bo7bo10bo7bo11bo16bo18bo7bo$19bo6bo18bo7bo10bo18bo63bo$17b o18bo89bo$107bo$32bo14bo18bo38bo$83bo10$108bo$106bo$85bo$83bo11bo2$110b o$108bo2$85bo9$3bo13bo14bo186bo$bo13bo14bo73bo17bo18bo46bo13bo$2bo45b o56bo33bo16bo15bo2bo13bo10bo14bo$o45bo2bo14bo2bo16bo2bo12bo17bo35bo2b o12bo13bo$15bo46bo19bo36bo79bo14bo$13bo122bo16bo15bo13bo13bo14bo$29bo 13bo53bo17bo18bo$27bo31bo$77bo4$203bo$142bo58bo$32bo107bo32bo$49bo35b o37bo47bo$28bo18bo35bo91bo$87bo31bo79bo$49bo147bo$136bo32bo$29bo89bo14b o$43bo$25bo51bo37bo3$219bo$143bo60bo$141bo60bo12bo$32bo73bo17bo33bo31b o$50bo35bo69bo17bo$48bo17bo17bo17bo17bo51bo13bo$26bo37bo2$87bo17bo51b o17bo13bo9bo12bo$29bo19bo17bo68bo60bo12bo$119bo14bo18bo$169bo13bo$23b o19bo53bo17bo$59bo17bo!