x = 73, y = 71, rule = B3/S23
64b2o$64b2o3$61b2o$61b2o8b2o$5bob2o62bo$5b2obo55b2o6bo$64b2o5b2o3$54bo
$53b3o$2o5b2o10bo36bo$2o5b2o11b2o32b2o$15bobobo35bo$4b2o9bobo$4b2o4$
27b2o$27b2o2$24b2o5b2o20b2o$24b2o5b2o20b2o2$56b2o$56b2o3$23bo29b2o$21b
obo29b2o$22b2o4$30bo$20bo9bobo$20b3o7b2o$23bo$22b2o4$25bo$23b2ob2o2$
22bo5bo2$22b2obob2o9$24b2o$24b2o$53bo$51bobo$52b2o5$53bo$54b2o$53b2o!
x = 54, y = 59, rule = B3/S23
$23b2o$23bo$11bobo7bobo$11bo2bo6b2o$2b2o10b2o$2b2o8bo3b2o$7b2o5b2o$6bo
4bo2bo$11bobo6$2bo$2b3o$5bo$4b2o$10bo4b2o5b2o10bo$11bo3b2o5b2o11b2o$9b
3o18bobobo$19b2o9bobo$19b2o4$42b2o$4b2o3b2o31b2o$6b3o$5bo3bo29b2o5b2o$
6bobo30b2o5b2o$7bo4$6b2o$6b2o30bo$36bobo$37b2o10$40bo$41bo$39b3o6$52b
2o$52b2o!
biggiemac wrote:Here's an appropriate 6hd gun at p120 with 8 fewer cells at minimum population than the twin bees version. If someone can line up the blocker/ship the same as before it could break 200.
x = 86, y = 98, rule = B3/S23
5bob2o$5b2obo3$77b2obo$77bob2o$10bo$2o3bo4b2o$2o2b2o5b2o$5b2o4bo$6bo3b
o$77b2o5b2o$77b2o5b2o2$80b2o$27b2o51b2o$27b2o2$24b2o5b2o$24b2o5b2o24b
2o$17bo39b2o12bo$18b2o51bobo$17b2o34b2o5b2o9b3o$53b2o5b2o11bo21$48bo$
46b2o$47b2o$54bo$52b3o$51bo$51b2o$46bo$45bo$45b3o7$46b2o3b2o$48b3o$47b
o3bo$48bobo$49bo4$49b2o$49b2o3$22b2o12bo4bo$34b2ob4ob2o$25bo10bo4bo$
14b4o$12b2o4b2o$12b2o5bo$14b2obobo$19bo$15bo3bo$15bo4bo$17b3o3bo$17b2o
4bo$23b2o$25bo$25b3o3$28bo$27bob5o$26b2o5bo$26b2o3bo2bo$34bo$28b2obo2b
o$31bo2bo$32b2o$32b2o!
x = 78, y = 87, rule = B3/S23
5bob2o$5b2obo3$69b2obo$69bob2o$6bo$2o3bo3b3o$2o2bo6bo$5bo5bo$6b2ob2o$
69b2o5b2o$69b2o5b2o2$72b2o$27b2o43b2o$27b2o2$24b2o5b2o$24b2o5b2o16b2o$
18bo30b2o9bobo$16bobo41bobobo$17b2o26b2o5b2o11b2o$45b2o5b2o10bo20$50bo
$39bo8b3o$39bobo5bo$39b2o6b2o3$45bo$44bobo$39bo3bo3bo$37b2o5b3o$38b2o
2b2o3b2o11$17b4o24b2o$15b2o4b2o22b2o$15b2o5bo$17b2obobo$22bo9bo4bo$18b
o3bo7b2ob4ob2o$18bo4bo8bo4bo$20b3o3bo$20b2o4bo$26b2o$28bo$28b3o3$31bo$
30bob5o$29b2o5bo$29b2o3bo2bo$37bo$31b2obo2bo$34bo2bo$35b2o$35b2o!
chris_c wrote:So far I've got a Sawtooth183 that reaches minimum population at generation 108 * (121^n - 1). Kudos to simsim for finding the quite shocking reduction of the p120 gun.
EDIT: Now Sawtooth181 with minimum population at 58 * (121^n - 1).
biggiemac wrote:So you've made a 163-cell predecessor to the sawtooth, but still only with a minimum repeating population of 201. Although something goes wrong with your pattern after two sawtooth iterations, it explodes..
Edit: Putting them side by side I see that your pattern deleted the gliders, making the phase different, and ultimately leading to instability.
#C Sawtooth 179
#C Adam P. Goucher, 2015-10-25
x = 72, y = 83, rule = B3/S23
63b2obo$63bob2o6$63b2o5b2o$63b2o5b2o$7b2o$7b2o57b2o$66b2o2$10b2o$2o8b
2o$bo41b2o$o6b2o34b2o9bobo$2o5b2o45bobobo$39b2o5b2o11b2o$39b2o5b2o10bo
$18bo$17b3o$16bo$17b2o$17bo9$18b2o$18b2o2$15b2o$15b2o2$44bo$18b2o13bo
8b3o$18b2o13bobo5bo$33b2o6b2o3$39bo$38bobo$33bo3bo3bo$31b2o5b3o$32b2o
2b2o3b2o11$11b4o24b2o$9b2o4b2o22b2o$9b2o5bo$11b2obobo$16bo9bo4bo$12bo
3bo7b2ob4ob2o$12bo4bo8bo4bo$14b3o3bo$14b2o4bo$20b2o$22bo$22b3o3$25bo$
24bob5o$23b2o5bo$23b2o3bo2bo$31bo$25b2obo2bo$28bo2bo$29b2o$29b2o!
calcyman wrote:Shameless corollary snipe to re-establish myself at the head of the Sawtooth Hall of Fame
calcyman wrote:Shameless corollary snipe to re-establish myself at the head of the Sawtooth Hall of Fame:Code: Select allrle
#C Sawtooth 177
#C thunk, 2015-10-27
#C Pop=177 at T=15, 6975...
x = 68, y = 76, rule = B3/S23
59b2o$59b2o3$56b2o$56b2o8b2o$7b2o57bo$7b2o50b2o6bo$59b2o5b2o2$10b2o54b
2o$2o8b2o55bo$bo61bo$o6b2o53bo3bo$2o5b2o55b2o2$2o$o$4bo43b3o$bo3bo41bo
2bo$2b2o43bo3bo$46b2obobo$46b2ob2o$47b3o$17b3o$17bo2bo$16bo3bo29b2o$
16bobob2o27bo2bo$17b2ob2o25b5o$18b3o25b2ob3o$46b3o$47bobo$16b2o22bo7b
2o$15bo2bo10bo8b3o$16b5o8bobo5bo$16b3ob2o7b2o6b2o$19b3o$18bobo$18b2o
15bo$34bobo$29bo3bo3bo$27b2o5b3o$28b2o2b2o3b2o11$7b4o24b2o$5b2o4b2o22b
2o$5b2o5bo$7b2obobo$12bo9bo4bo$8bo3bo7b2ob4ob2o$8bo4bo8bo4bo$10b3o3bo$
10b2o4bo$16b2o$18bo$18b3o3$21bo$20bob5o$19b2o5bo$19b2o3bo2bo$27bo$21b
2obo2bo$24bo2bo$25b2o$25b2o!
thunk wrote:Well, corollary sniping is fun!Code: Select all#C Sawtooth 177
#C thunk, 2015-10-27
x = 68, y = 77, rule = B3/S23
59b2o$59b2o3$56b2o$56b2o8b2o$7b2o57bo$7b2o50b2o6bo$59b2o5b2o2$10b2o$2o
8b2o$bo46b3o$o6b2o40bo$2o5b2o40b3o4$17b3o$18bo$16b3o4$48b2o$48b2o2$51b
2o$51b2o2$18b2o$18b2o28b2o$40bo7b2o$15b2o21b3o$15b2o20bo$37b2o2$18b2o
5bobo$18b2o5b2o$26bo5$24bo$24bobo5b2o3b2o$24b2o8b3o$33bo3bo$34bobo$35b
o4$35b2o$6b4o25b2o$4b2o4b2o$4b2o5bo$6b2obobo10bo4bo$11bo8b2ob4ob2o$7bo
3bo10bo4bo$7bo4bo$9b3o3bo$9b2o4bo$15b2o$17bo$17b3o3$20bo$19bob5o$18b2o
5bo$18b2o3bo2bo$26bo$20b2obo2bo$23bo2bo$24b2o$24b2o!
thunk wrote:Well, corollary sniping is fun!
chris_c wrote:Well done! Note that I would suggest the following as the canonical version of your pattern. Population is 177 at 48 * (121^n-1).
calcyman wrote:I imagine this record will be extremely difficult to improve further. We either need a smaller shotgun, or a smaller spaceship, or a completely different tractor-beam mechanism.
thunk wrote:...
chris_c wrote:Very good. It seemed impossible to me to get the phases matched up like that. Well done! Note that I would suggest the following as the canonical version of your pattern. Population is 177 at 48 * (121^n-1).
Scorbie wrote:If I got it right, all the components are in its minimal phase, so there won't be any more improvements with trivial (i.e. without change of mechanism) collorary sniping, right??
Freywa wrote: Well, thunk, I implore to know what your real name and (optionally) location is for the sake of posterity. Conway's Life is still very much academic in nature.
thunk wrote:Scorbie wrote:If I got it right, all the components are in its minimal phase, so there won't be any more improvements with trivial (i.e. without change of mechanism) collorary sniping, right??
I think so too. The only B60 phases with smaller population are 39 and 40 ticks after the initial Herschel position, and none of those work in the sawtooth--at 40 ticks, there end up being two sets of gliders in the pattern when the block is finally deleted (10 cell penalty), and at 100 ticks, the FNGs have not yet been deleted by the boat-bits.
thunk wrote:Just so you know, demanding to out people in public is rather rude. Many people have reasons for not wanting to divulge their birth name, and I'm not the first (Guam comes to mind) to prefer pseudonymity.
thunk wrote:Anyway, a nym didn't prevent this guy from being published.
x = 158, y = 74, rule = B3/S23
54b2obo$54bob2o2$12b2o$12b2o$46bo$46b2o$15b2o28bobo6b2o5b2o$5b2o8b2o
37b2o5b2o$6bo$5bo6b2o22bo20b2o$5b2o5b2o23b2o18b2o$36bobo2$149b2o$22b3o
10b2o112b2o$23bo11b3o$21b3o11b2ob2o$30b2o3b2ob2o106b2o$30b2o4bob2o106b
2o8b2o$37bo59b2o57bo$97b2o50b2o6bo$149b2o5b2o2$100b2o$90b2o8b2o$91bo
46b3o$23b2o65bo6b2o40bo$23b2o65b2o5b2o40b3o$45bo$20b2o21b3o$20b2o20bo$
2b4o36b2o63b3o$2o4b2o100bo$2o5bo15b2o5bobo73b3o$2b2obobo15b2o5b2o$7bo
23bo$3bo3bo$3bo4bo129b2o$5b3o3bo126b2o$5b2o4bo$11b2o16bo111b2o$13bo15b
obo5b2o3b2o97b2o$13b3o13b2o8b3o$38bo3bo65b2o$39bobo66b2o28b2o$16bo23bo
89bo7b2o$15bob5o83b2o21b3o$14b2o5bo83b2o20bo$14b2o3bo2bo104b2o$22bo17b
2o44b4o$16b2obo2bo17b2o42b2o4b2o16b2o5bobo$19bo2bo61b2o5bo16b2o5b2o$
20b2o64b2obobo24bo$20b2o5bo4bo58bo$25b2ob4ob2o52bo3bo$27bo4bo54bo4bo$
89b3o3bo$89b2o4bo18bo$95b2o17bobo5b2o3b2o$97bo16b2o8b3o$97b3o23bo3bo$
124bobo$125bo$100bo$99bob5o$98b2o5bo$98b2o3bo2bo18b2o$106bo18b2o$100b
2obo2bo$103bo2bo$104b2o6bo4bo$104b2o4b2ob4ob2o$112bo4bo!
thunk wrote:EDIT: Forgot to count the pentadecathlon sparks. Though the twin bees sparks weren't counted in Sawtooth 213 or 201.
dvgrn wrote:Luckily, sawteeth are not glider guns -- their bounding boxes are always increasing in any case. And clearly there's something of an established tradition to measure the bounding box without any transitory sparks, unless they're actually present in the T=0 generation. So I've added the new Sawtooth 189 record as 67x57 in the LifeWiki and left all the old bounding-box measurements unchanged.
x = 62, y = 56, rule = B3/S23
53b2obo$53bob2o2$11b2o$11b2o3$14b2o28b2o7b2o5b2o$4b2o8b2o37b2o5b2o$5bo
37bobo$4bo6b2o28bo14b2o$4b2o5b2o24b2obob2o12b2o$38bob2o$39bo2$33b2o$8b
2o23b2o$8bobo$8bo20b2o5b2o$29b2o5b2o4$21b3o$21bo2bo$21bob2o4$20b2o12bo
9bo$20bo2bo10bobo5b3o$2b4o15b3o10b2o5bo$2o4b2o33b2o$2o5bo$2b2obobo14b
2o$7bo14b2o$3bo3bo26bo4bo$3bo4bo23b2o5bo$5b3o3bo21b2o3bobo$5b2o4bo25b
2ob2o$11b2o23bo5bo$13bo25bo$13b3o20b2o3b2o3$16bo21bo$15bob5o16bo$14b2o
5bo15bo$14b2o3bo2bo$22bo$16b2obo2bo16b2o$19bo2bo16b2o$20b2o$20b2o5bo4b
o$25b2ob4ob2o$27bo4bo!
thunk wrote:Since we don't need the buckaroo to be synchronized with the pd, the pd can be moved one cell further in, resulting in a bounding box of 62*56...
Unfortunately, the minimum population is increased still further to 195, achieved in gens 38*(121^n-1) (every cycle now).
dvgrn wrote:Luckily, sawteeth are not glider guns -- their bounding boxes are always increasing in any case. And clearly there's something of an established tradition to measure the bounding box without any transitory sparks, unless they're actually present in the T=0 generation.
#C Canonical Sawtooth 177 with reduced bounding box:
x = 74, y = 58, rule = B3/S23
64b4o2$66b2o$62b2o$62b2o8b2o$13b2o57bo$13b2o50b2o6bo$65b2o5b2o2$16b2o$
6b2o8b2o$7bo46b3o$6bo6b2o40bo$6b2o5b2o40b3o4$23b3o$24bo$22b3o4$54b2o$
54b2o2$57b2o$57b2o2$24b2o$24b2o28b2o$46bo7b2o$21b2o21b3o$21b2o20bo$43b
2o$2b4o$2o4b2o16b2o5bobo$2o5bo16b2o5b2o$2b2obobo24bo$7bo$3bo3bo$3bo4bo
$5b3o3bo$5b2o4bo18bo$11b2o17bobo5b2o3b2o$13bo16b2o8b3o$13b3o23bo3bo$
40bobo$41bo$16bo$15bob5o$14b2o5bo$14b2o3bo2bo18b2o$22bo18b2o$16b2obo2b
o$19bo2bo$20b2o$20b2o4b10o!
calcyman wrote:Where do you stand on the following variant of Sawtooth 177? It attains its minimum repeating population of 177 in generation 0, so it's canonical, and is 74-by-58 instead of 74-by-60. But it feels incredibly disingenuous in a way that is impossible to capture mathematically...
calcyman wrote:If anyone can see any reason why this shouldn't be considered the canonical Sawtooth 177, speak now...
dvgrn wrote:Also the T=1 population doesn't match the pattern that all future sawtooth cycles will follow -- there are a couple of extra cells still present in the pre-pentadecathlon.
x = 74, y = 58, rule = B3/S23
64b4o2$66b2o$62b2o$62b2o8b2o$13b2o57bo$13b2o50b2o6bo$65b2o5b2o2$16b2o$
6b2o8b2o$7bo46b3o$6bo6b2o40bo$6b2o5b2o40b3o4$23b3o$24bo$22b3o4$54b2o$
54b2o2$57b2o$57bo$59bo$24b2o$24b2o28b2o$46bo7bo$21b2o21b3o9bo$21b2o20b
o$43b2o$2b4o$2o4b2o16b2o5bobo$2o5bo16b2o5b2o$2b2obobo24bo$7bo$3bo3bo$
3bo4bo$5b3o3bo$5b2o4bo18bo$11b2o17bobo5b2o3b2o$13bo16b2o8b3o$13b3o23bo
3bo$40bobo$41bo$16bo$15bob5o$14b2o5bo$14b2o3bo2bo18b2o$22bo18b2o$16b2o
bo2bo$19bo2bo$20b2o$20b2o4b10o!
dvgrn wrote:So I'm afraid the definition of "canonical" is going to have to carry all the weight of defending sawtooth initial bounding boxes against optimizations from the Dark Side. Anyone else have a better defense?
calcyman wrote:thunk wrote:Scorbie wrote:If I got it right, all the components are in its minimal phase, so there won't be any more improvements with trivial (i.e. without change of mechanism) collorary sniping, right??
I think so too...
Yes, I'm pretty certain it is optimal based on present technology.
dvgrn wrote:Luckily I think that's not an issue for Sawtooth 189, since the spaceship is already as close as it can safely get to the pentadecathlon.
#C population 177 at T=0, 336720, 4930254240, ... 23*(121^2N-1)...
x = 73, y = 60, rule = B3/S23
64b2o$64b2o3$61b2o$61b2o8b2o$12b2o57bo$12b2o50b2o6bo$64b2o5b2o2$15b2o$
5b2o8b2o$6bo46b3o$5bo6b2o40bo$5b2o5b2o40b3o4$22b3o$23bo$21b3o4$53b2o$
53b2o2$56b2o$56b2o2$23b2o$23b2o28b2o$45bo7b2o$20b2o21b3o$20b2o20bo$2b
4o36b2o$2o4b2o$2o5bo15b2o5bobo$2b2obobo15b2o5b2o$7bo23bo$3bo3bo$3bo4bo
$5b3o3bo$5b2o4bo$11b2o16bo$13bo15bobo5b2o3b2o$13b3o13b2o8b3o$38bo3bo$
39bobo$16bo23bo$15bob5o$14b2o5bo$14b2o3bo2bo$22bo17b2o$16b2obo2bo17b2o
$19bo2bo$20b2o$20b2o5bo4bo$25b2ob4ob2o$27bo4bo!
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