Log log log log? (Complete)

[Kiran]

I think it is possible to create a pattern that grows in cells O(log(log(log(...x...)))) for an arbitrary number of logs.
One way to do so would be to have a unit that would for example:
1) Accept gliders from the NW.
2) Send a salvo to the NE every time it gets a glider from NW.
3)That salvo would partly hit object A repelling it by three cells.
4)Part of the salvo would hit the more faraway object B repelling it by one cell.
5)When A catches up to B; A toggles and starts going toward the gun.
6)When A reaches the gun; it toggles back and starts moving NE again.
7)When A reaches the gun: the gun fires a glider SE.
Notice that A only needs to go incrementally one way and can zoom the other way as a spaceship.
Also it can be done orthogonally with *WSSs.
Many stages can be set up to get many logs, starting with a Caber Tosser (not a gun).
A modification of sawtooth 1 would do the trick:
What has to be modified is:
1) A "turtle" that moves incrementally (Pentadecathlon crane?).
2) A "gun" that fires only when triggered and passes on a glider when the loaf hits it.
Any other potential designs are welcome.

[Kazyan]

The problem I see is the glider or *WSS stream to move objects A and B. The spaceships within that stream travel at c/4 or c/2, and the signals you're sending to objects A and B will have their own population.

sqrt(log n) is the slowest possible growth rate AFAIK. Consider a pattern that grows more slowly (A), and then an "optimal" pattern (B) that enumerates all possible states of an n x n bounding box at a rate of one per generation, and when all states are enumerated, increments n. This is growth rate of sqrt(log n). Eventually, pattern B will overtake pattern A because A is slower, but since pattern B enumerates all possible states, one of them has to be pattern A...even though we know pattern B grows at a rate of sqrt(log n). This is a contradiction, so a rate slower than Pattern B--sqrt(log n)--cannot exist.

(I'm not a mathematician and my proof probably has several errors; feel free to point them out.)

[Kiran]

That is the reason why the first stage must be a Caber Tosser and not a gun:
The cordership moves linearly while B moves logarithmically so the cordership would eventually be much farther away.
Therefore the signal would have plenty of time to be absorbed by B before the glider would return to create a new signal.
As for the proof of sqrt(log(t)), that only applies to diametric growth, not population growth.

[Kazyan]

Alright, I'll build something along the lines of your idea and see if it works.

[Kiran]

The most promising version is to have A be a HWSS on the way to B and a loaf on the way back.
As for B, a pentadecathlon and four hives seems best.
The tricky part is making a variation on sawtooth 1 (plus four slide guns) that shoots a salvo only when triggered by a glider.
Also the phase of the pentadecathlon changes by four, so to fix the phase it must be shifted 15 times.
That becomes 30 if the same type of salvo is to be fired every time.
That does not affect the action because B still moves sub-linearly and A moves linearly to B.
It would probably be easier to make a toggle gun that turns off after 30 salvoes (120 ships) then to generate them separately.
It would be nice to make the crane out of two well separated halves and to have the loaf pass between them.
That would allow more space for an incremental sawtooth gun farther back but would require the two cranes to be timed separately.
Also, since the two sides halves can be arbitrarily far apart, the sawtooth can be directly between them.

[Kiran]

Code: Select all

x = 2673, y = 1787, rule = B3/S23
2625bo$2624bobo$2624bobo$2625bo14$2616bo$2615bo$2615b3o32$2653bo$2653b
3o$2656bo$2655b2o$2642bo$2642b3o12b3o$2645bo11bo2bo$2644b2o10bo3bo$
2638b2o17bo2b2o$2639bo19bo$2639bobo15b2o$2640b2o14b3o$2656b4o3$2569bo
87bobo$2568bo87b2ob2o8b2o$2568b3o77b2o6b2obobo7bobo$2648b2o6b4ob2o8bo$
2656b5o10b2o$2657bo2b2o$2623b3o32b3o$2622bo2bo33bo$2625bo$2621bo3bo$
2625bo$2622bobo7b3o$2631bo2bo30b2o$2634bo30bobo$2634bo32bo$2607bo23bob
o33b2o$2605b3o$2604bo$2604b2o$2618bo$2616b3o$2615bo$2615b2o$2658bo$
2656b3o$2655bo$2655b2o$2661b2o$2661bo$2602b3o54bobo$2602bo2b2o52b2o$
2590b2o10bo2bo$2589bobo5b2o3bo2bo$2589bo7b2o2bo3bo$2588b2o12bo2bob2o$
2597b2o5b2o46b3o$2597b2o5b3o45bo2bo$2605b3o42bo4bo$2606b2o48bo8b2o$
2600b2o40b2o5bo5b2o8bo$2600b2o40b2o5bo5b2o6bobo$2653bo9b2o$2594b2o54b
2ob2o$2593bobo$2593bo57b2o$2592b2o56bo2bo$2598b2o$2599bo50bo2bo$2596b
3o52bob2o$2522bo73bo56b3o$2521bo116b2o10b2ob2o$2521b3o115bo10b2o2bo$
2636b3o12b3o$2636bo13b3o$2649b2o$2650bo$2647b3o$2647bo3$2606bo$2604b3o
$2603bo$2603b2o$2617bo$2615b3o$2614bo$2614b2o32bo$2604b2o40b3o$2597bo
6b2o39bo$2596b3o46b2o$2595bo2bo4bo47b2o$2596bobo3bobo7b3o36bo$2596bob
2ob2o8bo3bo33bobo$2596bob2o2bob2o5bo2bo34b2o$2595b3obo3b3o5bo2bo$2589b
2o5b3o5bo7bo$2588bobo6b2o3b2ob2o3b2o26b2o$2588bo14b4o31b2o$2587b2o15b
3o3$2639b3o13b2o$2604b2o36bo12bo$2604b2o47bobo$2639b2o12b2o$2645b2o$
2593b2o44b2o5b2o$2592bobo44bo2b5o$2592bo46bo3b3o$2591b2o47bo$2597b2o8b
2o32b2o$2598bo9bo$2595b3o10bobo4b4o$2595bo13b2o3bo2b2o9b2o$2613bo4bo
10bo$2602b2o10b2o10b3o$2603bo11b2o9bo$2475bo127bobo33b2o$2474bo129b2o
34bo$2474b3o160b3o$2620bobo14bo$2603b2o15bobo$2604bo9b2obo3bo4b2o$
2604bobo4bo3bo2bo7b2o$2605b2o5bo6b3o$2614bo2b2o$2618bob2o$2617b2o$
2613b2o3b2o$2613b3o18b2o$2611bo2bob3o15bobo$2612b3o21bo$2612b3o2bo18b
2o$2614b3o13b2o$2630bo$2631b3o$2633bo$2619b2o$2619bo$2620b3o$2622bo26$
2428bo$2427bo$2427b3o47$2381bo$2380bo$2380b3o47$2334bo$2333bo$2333b3o
30$47bo$46bobo$46bobo$47bo14$56bo2230bo$57bo2228bo$55b3o2228b3o32$19bo
$17b3o$16bo$16b2o$30bo$13b3o12b3o$12bo2bo11bo$12bo3bo10b2o$11b2o2bo17b
2o$13bo19bo$14b2o15bobo$14b3o14b2o$13b4o3$13bobo87bo2136bo$2b2o8b2ob2o
87bo2134bo$bobo7bobob2o6b2o77b3o2134b3o$bo8b2ob4o6b2o$2o10b5o$11b2o2bo
$12b3o32b3o$13bo33bo2bo$47bo$47bo3bo$47bo$38b3o7bobo$6b2o30bo2bo$5bobo
30bo$5bo32bo$4b2o33bobo23bo$65b3o$68bo$67b2o$54bo$54b3o$57bo$56b2o$14b
o$14b3o$17bo$16b2o$10b2o$11bo$11bobo54b3o$12b2o52b2o2bo$67bo2bo10b2o$
67bo2bo3b2o5bobo$67bo3bo2b2o7bo$64b2obo2bo12b2o$18b3o46b2o5b2o$17bo2bo
45b3o5b2o$17bo4bo42b3o$6b2o8bo48b2o$7bo8b2o5bo5b2o40b2o$7bobo6b2o5bo5b
2o40b2o$8b2o9bo$18b2ob2o54b2o$77bobo$20b2o57bo$19bo2bo56b2o$73b2o$19bo
2bo50bo$18b2obo52b3o$17b3o56bo73bo2042bo$18b2ob2o10b2o116bo2040bo$18bo
2b2o10bo115b3o2040b3o$19b3o12b3o$20b3o13bo$22b2o$22bo$23b3o$25bo3$66bo
$66b3o$69bo$68b2o$55bo$55b3o$58bo$24bo32b2o$24b3o40b2o$27bo39b2o6bo$
26b2o46b3o$20b2o47bo4bo2bo$21bo36b3o7bobo3bobo$21bobo33bo3bo8b2ob2obo$
22b2o34bo2bo5b2obo2b2obo$58bo2bo5b3o3bob3o$60bo7bo5b3o5b2o$33b2o26b2o
3b2ob2o3b2o6bobo$33b2o31b4o14bo$66b3o15b2o3$16b2o13b3o$17bo12bo36b2o$
17bobo47b2o$18b2o12b2o$26b2o$25b2o5b2o44b2o$26b5o2bo44bobo$27b3o3bo46b
o$32bo47b2o$30b2o32b2o8b2o$64bo9bo$54b4o4bobo10b3o$43b2o9b2o2bo3b2o13b
o$43bo10bo4bo$44b3o10b2o10b2o$46bo9b2o11bo$32b2o33bobo127bo1948bo$32bo
34b2o129bo1946bo$33b3o160b3o1946b3o$35bo14bobo$50bobo15b2o$45b2o4bo3bo
b2o9bo$45b2o7bo2bo3bo4bobo$51b3o6bo5b2o$54b2o2bo$51b2obo$54b2o$53b2o3b
2o10bo$37b2o18b3o8b3o$36bobo15b3obo2bo5bo$36bo21b3o6b2o$35b2o18bo2b3o$
41b2o13b3o$42bo$39b3o$39bo$52b2o$53bo$50b3o$50bo26$244bo1854bo$245bo
1852bo$243b3o1852b3o47$291bo1760bo$292bo1758bo$290b3o1758b3o47$338bo
1666bo$339bo1664bo$337b3o1664b3o47$385bo1572bo$386bo1570bo$384b3o1570b
3o35$1916bo$1915bobo$1915bobo$1916bo9$432bo1478bo$433bo1476bo$431b3o
1476b3o15$1944bo$1944b3o$1947bo$1946b2o$1914b3o16bo$1914bo2bo15b3o$
1914bo21bo$1914bo3bo16b2o$1887bo26bo14b2o$1887bobo25bobo5b3o4bo$1887b
2o34bo2bo3bobo$1923bo7b2o$1923bo$1924bobo3$1948bob2o8b2o$1939b2o5bob6o
6bobo$1939b2o5bo2b3ob2o7bo$1945bobo4bo9b2o$1944bobobo3b3o$1943bobo3b3o
bo$1944bo4b3o$1950b2o$1950b2ob2o$1950bo4bo2$1951bo5bo$1952bo2b2obo$
1958bo$1898bo59b2o$1896b3o$479bo1384bo30bo50bobo$480bo1382bo31b2o49b2o
$478b3o1382b3o43bo37bo$1907b3o$1906bo$1906b2o$1949bo$1947b3o$1946bo$
1893bo52b2o$1892b3o57b2o$1891bo3bo56bo$1890b2o2b2o54bobo$1891b2o57b2o$
1881b2o9b2o$1880bobo10b2o49b2o2bo$1880bo14bo47bo2bobo$1879b2o13b2o$
1938bo$1937bobo2bo4b2o$1938bob5o3bo$1896b2o41bob4o11b2o$1896b2o35b2o4b
2o7bo7bo$1933b2o7bo4b2o5bobo$1941b2o11b2o$1840bo44b2o$1840bobo41bobo$
1840b2o42bo$1883b2o$1889b2o$1890bo$1887b3o$1887bo$1929b2o$1930bo$1927b
3o$1927bo$521bo1418b2o$520bobo1418bo$520bobo1415b3o$521bo1416bo3$1897b
o$1895b3o$1894bo$1894b2o$1908bo$1906b3o$526bo1290bo87bo$527bo1288bo88b
2o32bo$525b3o1288b3o118b3o$1895b2ob2o36bo$1895b2ob2o36b2o$1894bobo45b
2o$1895bo6b2o38bo$1896b2o4b2o36bobo$1891b2o3b2o42b2o$1896b2o$1880b2o$
1879bobo10b2o2b3o30b2o$1879bo12b2o2b3o30b2o$1878b2o33bobo13b2o$1914b2o
12b2o$1914bo14b2o$1926bo2bo3b3o10b2o$493bo1420b2o10b3o4b5o8bo$491b3o
1419bobo11bo3b4o9bobo$490bo1439b2ob2o3bo5b2o$490b2o1425bo4bo11bobobo$
504bo16b3o1360b2o32bo3bob2o5bo6bo$502b3o15bo2bo1359bobo29b2o4bo4bob2o
3bo2b4o$501bo21bo1359bo37b2o6bob3o2b2o2bobo$501b2o16bo3bo1358b2o37bo4b
o3b4o7bo$507b2o14bo26bo1242bo94b2o8b2o22b3o$507bo4b3o5bobo25bobo1242bo
bo93bo9bo$505bobo3bo2bo34b2o1242b2o91b3o10bobo$505b2o7bo1371bo13b2o17b
2o$514bo1405bo$511bobo1379b2o11b2o9b3o$1894bo11b2o9bo$1894bobo33b2o$
476b2o8b2obo1405b2o34bo$475bobo6b6obo5b2o1404b2o2b3ob2o15b3o$475bo7b2o
b3o2bo5b2o1403b2o5bob2o15bo$474b2o9bo4bobo1401b2o9bo7bo$483b3o3bobobo
1401bo9bo3b2o$484bob3o3bobo1400bobo10b2o$486b3o4bo1402b2o6b2o2bo$486b
2o1417b2o4b2o$483b2ob2o1423b2o$482bo4bo2$480bo5bo1438b2o$479bob2o2bo
1439bobo$479bo1447bo$478b2o59bo1387b2o$539b3o1379b2o$489bobo50bo30bo
1196bo150bo$490b2o49b2o31bo1194bo152b3o$490bo37bo43b3o1194b3o152bo$
528b3o1379b2o$531bo1378bo$530b2o1379b3o$488bo1424bo$488b3o$491bo$490b
2o52bo$484b2o57b3o$485bo56bo3bo$485bobo54b2o2b2o$486b2o57b2o$544b2o9b
2o$489bo2b2o49b2o10bobo$489bobo2bo47bo14bo$542b2o13b2o$499bo$489b2o4bo
2bobo$489bo3b5obo$480b2o11b4obo41b2o$481bo7bo7b2o4b2o35b2o$481bobo5b2o
4bo7b2o$482b2o11b2o$551b2o44bo1148bo$551bobo41bobo1148bobo$553bo42b2o
1148b2o$553b2o$547b2o$547bo$548b3o$550bo$507b2o$507bo$508b3o$510bo$
496b2o$496bo$497b3o$499bo3$540bo$540b3o$543bo$542b2o$529bo$529b3o$532b
o87bo1102bo$498bo32b2o88bo1100bo$498b3o118b3o1100b3o$501bo36b2ob2o$
500b2o36b2ob2o$494b2o45bobo$495bo38b2o6bo$495bobo36b2o4b2o$496b2o42b2o
3b2o$540b2o$556b2o$507b2o30b3o2b2o10bobo$507b2o30b3o2b2o12bo$507b2o13b
obo33b2o$508b2o12b2o$507b2o14bo$490b2o10b3o3bo2bo$491bo8b5o4b3o10b2o$
491bobo9b4o3bo11bobo$492b2o5bo3b2ob2o$499bobobo11bo4bo$499bo6bo5b2obo
3bo32b2o$498b4o2bo3b2obo4bo4b2o29bobo$495bobo2b2o2b3obo6b2o37bo$496bo
7b4o3bo4bo37b2o$513b3o22b2o8b2o94bo1054bo$538bo9bo93bobo1054bobo$536bo
bo10b3o91b2o1054b2o$517b2o17b2o13bo$517bo$518b3o9b2o11b2o$520bo9b2o11b
o$506b2o33bobo$506bo34b2o$507b3o15b2ob3o2b2o$509bo15b2obo5b2o$524bo7bo
9b2o$527b2o3bo9bo$528b2o10bobo$529bo2b2o6b2o$525b2o4b2o$525b2o3$511b2o
$510bobo$510bo$509b2o$515b2o$516bo150bo1008bo$513b3o152bo1006bo$513bo
152b3o1006b3o$526b2o$527bo$524b3o$524bo19$691bo960bo$689bobo960bobo$
690b2o960b2o22$714bo914bo$715bo912bo$713b3o912b3o23$738bo866bo$736bobo
866bobo$737b2o866b2o22$761bo820bo$762bo818bo$760b3o818b3o23$785bo772bo
$783bobo772bobo$784b2o772b2o22$808bo726bo$809bo724bo$807b3o724b3o23$
832bo678bo$830bobo678bobo$831b2o678b2o22$855bo632bo$856bo630bo$854b3o
630b3o23$879bo584bo$877bobo584bobo$878b2o584b2o22$902bo538bo$903bo536b
o$901b3o536b3o23$926bo490bo$924bobo490bobo$925b2o490b2o22$949bo444bo$
950bo442bo$948b3o442b3o23$973bo396bo$971bobo396bobo$972b2o396b2o22$
996bo350bo$997bo348bo$995b3o348b3o23$1020bo302bo$1018bobo302bobo$1019b
2o302b2o22$1043bo256bo$1044bo254bo$1042b3o254b3o23$1067bo208bo$1065bob
o208bobo$1066b2o208b2o22$1090bo162bo$1091bo160bo$1089b3o160b3o23$1114b
o114bo$1112bobo114bobo$1113b2o114b2o22$1137bo68bo$1138bo66bo$1136b3o
66b3o23$1161bo7bo4bo7bo$1159bobo5b2ob4ob2o5bobo$1160b2o7bo4bo7b2o100$
1191b2o$1191b2o2$1204b2o$1204b2o$1189b2o5$1188b2o3b2o$1189b5o$1189b2ob
2o11bo$1189b2ob2o10b3o$1190b3o10b5o$1202b2o3b2o$1153b2o$1153b2o2$1140b
2o62b3o$1140b2o12bo49b3o$1153b3o39bo$1152bo3bo32bo3bobo11bo$1154bo33b
3o3b2o10bobo$1138b2o11bo5bo29b5o13bo3bo$1151bo5bo28bobobobo13b3o$1152b
o3bo29b2o3b2o11b2o3b2o$1153b3o2$1137b2o3b2o$1138b5o$1138b2ob2o$1138b2o
b2o9bo33b2o$1139b3o45bo$1184b3o11b2o$1152bo31bo12b3o9b2o$1152bobo41bob
o2bo2b2o3bo$1152b2o42b2o2b2o2b2o4b3o$1200b2o10bo$1149b2o43bo$1149b2o
41b3o$1138bo14b2o3b2o31bo$1137b3o51b2o$1136b5o13bo3bo$1135bobobobo13b
3o$1135b2o3b2o13b3o$1206b2o$1206b2o$1158b2o26b2o3b2o$1158bo27bo5bo$
1153b2o4b3o$1135b2o7b2o7b2o6bo25bo3bo15bo$1136bo3b2o4b4o38b3o15bobo$
1133b3o4b2o2b2ob3o55bo3bo$1133bo10bo61b3o$1204b2o3b2o4$1192bo$1190bobo
16bo$1191b2o16bo$1205b3obo$1187bo$1186b3o15bo$1185b5o14b2obo$1184b2o3b
2o8bo6b2o$1185b5o10bo$1135bo10bo38bo3bo8b3o$1135b3o4b2o2b2ob3o34bobo
17b2o3b2o$1138bo3b2o4b4o35b3o16b2o3b2o$1137b2o7b2o15bo25b2o16b5o$1161b
3o25bo18bobo$1160bo29b3o$1160b2o30bo15b3o2$1131b2o$1131b2o$1202bo8b2o$
1198b2o2b2ob3o3bo$1137b2o3b2o11b2o3b2o36b2o4b4o4b3o$1139b3o13bobobobo
40b2o10bo$1138bo3bo13b5o$1139bobo15b3o$1140bo17bo2$1130b3o8b3o$1129bo
3bo7b3o66b4o7bo$1128bo5bo70b2o7bo4b3o$1128bo5bo70b2o2b2o3bo3bo$1131bo
61bo15b2o2bo4b2o$1129bo3bo5b2o3b2o47b3o$1130b3o7b5o10b3o38bo$1131bo9b
3o10b2ob2o36b2o$1142bo11b2ob2o$1154b5o$1128b3o22b2o3b2o48bo$1128b3o76b
2o7bo$1127bo3bo75bobo5b3o$1195b2o3b2o12b5o$1126b2o3b2o11b2o49b2o3b2o
11b2o3b2o$1144bo51b5o3bo9b5o$1145b3o49bobo4b2o8b5o$1147bo5b2o48bobo8bo
2bo$1154bo42b3o13bo3bo$1151b3o59bo$1151bo36bo24bob2o$1183b3ob2o2b2o21b
o$1126b2o55b4o4b2o$1127bo59b2o11bo$1124b3o72bobo9b2o3b2o$1124bo6bo66bo
3bo8bo5bo$1131b2o66b3o$1119bobo8bobo10b2o52b2o3b2o8bo3bo$1119bo3bo19bo
6bobo60b3o$1109b2o12bo10b2o5bobo7b2o$1109b2o8bo4bo7bo2bo5b2o8bo$1123bo
7bo$1119bo3bo7bo$1119bobo9bo47b3o$1132bo2bo46bo$1134b2o42bo3bo23bob2o
3b2o$1177bobo2bo19b2o2b2obo3b2o$1147bo2b2o23bo2bobo4b2o15bo$1146bo3b2o
2b2o19bo3bo5b2o16b6o$1146bo7b2o19bo29bo3bo$1147b4o25b3o29b2o3$1172b2o
11b3o$1171b4o10b3o$1170bob2ob2obo5bo3bo$1108bo10b2o2bo51b2o2bo$1108b3o
4b2o2b2o3bo12bo7b4o21b2o2b2o2b3o2b2o3b2o20b3o$1111bo3b2o7bo12b3o4bo7b
2o16b4obo2b3o11b2o15bo3bo$1110b2o8b4o3bo12bo3bo3b2o2b2o15bo2bo3bo2bo
12b2o14bo5bo$1127b2o10b2o4bo2b2o15bo2b3o2bob4o29bo5bo$1126bobo4b2o20bo
7b3o2b3o2b2o2b2o10b2o$1133b2o20b2o5bo6bo2b2o14bobo17bo$1154bobo5b2o6bo
b2ob2obo11bo17b2o$1174b4o30b2o$1160bo14b2o30b2o2bo$1110b2o3b2o14b2o6b
2o3b2o13bobo28bo17bobo$1111b5o23bo5bo12bo3bo46b2o$1111b2ob2o43b3o$
1111b2ob2o24bo3bo12b2o3b2o$1112b3o26b3o62b2o3b2o$1130b2o3b2o16b2o32b3o
16b2o3b2o$1131b5o17b2o31bo3bo$1131b2ob2o49bo5bo16b3o$1131b2ob2o20b2o
27bo5bo16b3o$1114b3o15b3o20b2o31bo20bo$1114b3o40bo28bo3bo$1113bo3bo26b
o42b3o$1112bo5bo23b2ob2o41bo$1113bo3bo$1114b3o13b3o8bo5bo$1130b3o55b2o
18b2o$1129bo3bo7b2obob2o40b2o18b2o$1128bo5bo23bo$1129bo3bo23b3o$1130b
3o23b5o$1155b2o3b2o4$1115b2o40b3o$1115b2o27b2o11b3o$1144b2o2$1157b2o$
1130b2o25b2o$1130b2o!

This is a failed prototype that shows separation of the slide guns as well as the loaf tractor beam.

By the way, could someone please post an rle of Sqrt(log(t)) diameter, my browser cannot open the files.

[Kiran]

What if actual turtles are used?
This would be much simpler to build (no need to bother with pentadecathlon cranes) and would also cause a much slower growth rate.
B shall be a turtle (or other ship slower then C/2).
A should be a *WSS on the way to b and a loaf on the way back.
Each loaf pulling salvo would be triggered by the previous stage and the arrival of the loaf would trigger the next stage
If starting with a caber tosser the signal population would be asymptomatically constant, thus that would not be a problem.
I think the growth rate is O(log****(t)) but cannot find it exactly, in any case it would be the slowest ever constructed (besides constant).
What is the growth rate, is my guess correct?

[Kiran]

Prototype:

Code: Select all

x = 280, y = 202, rule = B3/S23
216b2o21bo$217bo19bobo$217bobo8bo2b2o3bobo$218b2o7b2o2bo3bo2bo14b2o$
226b2o8bobo14bobo$213bo11b3o9bobo16bo11bobo$211bobo12b2o11bo13bo2bo10b
o2bo$201b2o6b2o16b2o27bo9b2o$200bo8b2o17bo24bobo8b2o3bo9bo$199bo5bo3b
2o42b2o11b2o10b2o$189bo9bo5b2o4bobo7b2o44bo2bo$189b2o8bo6bo6bo7bobo44b
obo$200bo22bo$201b2o20b2o8$195bobo$195bo2bo$186b2o10b2o11b2o$186bo9bo
3b2o8bobo$198b2o9bo$195bo2bo10bo2bo$195bobo11bo$210bobo5b2o$106b2o23bo
19b2o58b2o5bobo$107bo23bobo86bo$107bobo4b2o18b2o4b2o78b2o$108b2o6bo17b
2o5bo$117bo16b2o$117bo8bo4bobo$117bo9bo3bo$116bo5bo2b3o$114b2o114bo$
109b2o116bo3b2o$109bo23b4o26b4o59b2o2bo$132bo3bo25bo3bo59b2o$136bo29bo
60bo$132bo2bo26bo2bo61b2o$121b2o104bo$122b2o104bo$121bo18b2o2b3o2b2o
77b3o$140bo2b5o2bo76bo$106b2obob2o17b2o9b9o76b2o3bo$106bo5bo16b2o7b3o
9b3o73b2o$107bo3bo19bo6bo2bo7bo2bo74bob2o$108b3o3bo24b2o9b2o74b2ob2o$
114b2o40b2o67bo3bo$113bobo40bo70bobob2o$149bo4bobo70bo3bo$138bo9bobo3b
2o75bo$132bobo2b2o9b2obo76bobo$131bo2bo2bobo8b2ob2o74bo$130b2o16b2obo
74b3o$111bo16b2o3bo14bobo58bo$111bo18b2o17bo59bobo16bo$110bobo11b2o5bo
2bo75bo17bo2bo$109b2ob2o9bobo6bobo91b2o2b2o$108bo5bo8bo107bo$111bo10b
2o$108b2o3b2o78bo$194bo$209b2o$208bobo$76bo4b2o127bo$75bobo2bobo7b2o$
74bo2b4o9bo$74bobo4bo6bobo$73b2ob2o2b2o6b2o21b2o$71bo39b2o$68bo2b4ob2o
$68b3o3bob2o$71bo$70b2o$112b2o$47b2o63bo$48bo61bobo$35bo11bo58b2o2b2o
82b2o$35b3o9b2o57b2o85bobo$38bo156bo$25b2o10b2o$26bo$26bobo$12b2o13b2o
$12b2o36b2o$50b2o2$6b2o$6b2o$10b2o70b2o28b2o$10b2o64b2o4bobo9b2o16bobo
$77bo6bo8bobo18bo$60b2o12b3o7b2o7bo20b2o63b2o$41b2o18bo12bo17b2o4b2o
78bobo$5b2o34bo16b3o35bo2bo80bo$5b2o35b3o13bo37b2o$44bo60b2o$105b2o7$
115b2o$115bo$12b2o99bobo$13bo99b2o49b2o$10b3o150bobo$10bo154bo2$95bo$
2o93b3o$bo96bo$bobo15b2o76b2o$2b2o15b2o2$90b2o$91bo$91bobo$92b2o2$149b
2o$148bobo$150bo$89b2o19b2o$89b2o19b2o$20b2o$20bobo$22bo62b2o24b2o$22b
2o62bo24bo$86bobo23b3o$87b2o26bo$110b4obo$110bo2b2o$4bo103bobo$3bobo
102b2o$3bo130b2o$2b2o60bo68bobo$62b3o70bo$61bo$61b2o$32bo34bo$32b3o32b
3o$35bo34bo$12b2o20b2o33b2o$12b2o65b2o$21b2o56bo$19bo2bo54bobo$19b2o4b
2o44b2o4b2o$3b2o20bo44bo2bo39bo$4bo18bobo45b2o40bobo$4bobo16b2o34b2o
53bo4b2o$5b2o52b2o57bobo$120bo2$82b2o$82b2o4$34b2o32b2o3b2o$34b2o11b2o
20bo3bo$47bo18b3o5b3o$11b2o35b3o15bo9bo$7b2o2b2o37bo40bo$6bobo69b2o10b
obo$6bo23b2o45bobo10bo2bo10b2o$5b2o23bo46bo13b2o10bobo$31b3o42b2o27bo$
33bo3$81b2o$80bobo$80bo15bo$79b2o14bobo2$92bob2obo$92b3obo$96b2o$97bo$
89b2o4b3o$88bobo10b2o$90bo9b2o$102bo$76b2o$75bobo$65b2o7b3o4b2o4bo$65b
2o6b3o4bo2b2obobo20b2o9bo$74b3o4b3obo3bo18b4o7bobo$75bobo4b2obo3bo13bo
bo2bo2b3o5b2obo4b2o$76b2o6b2o3bo12bo2bo2b2o9b2ob2o3b2o$86bobo12b2o9bo
6b2obo$87bo11b2o3bo8bo5bobo$101b2o10bo6bo$102bo2bo$103bobo!

Does not have input mechanism to move loaf in increments.

[Kiran]

Possible input mechanism:

Code: Select all

x = 188, y = 53, rule = B3/S23
151bo$151b4o$145b2o5b4o7bo$140bo3bo2bo4bo2bo6bobo$139b8o5b4o4b2o3bo$
122b2o14b2obob2o6b4o5b2o3bo9b2o10bo$122bo2bo11b3obo2bo6bo8b2o3bo9b2o8b
2o$114b5o7bo11b2obobo18bobo21b2o$113bo5bo6bo12b4o20bo$113bo3b2o7bo7bo
5bo11bobo$114bo7bo2bo9bo16b2o$122b2o9b3o17bo6$142bo$140bobo$141b2o26$
13bo2bo26bo2bo26bo2bo26bo2bo$17bo29bo29bo29bo$13bo3bo25bo3bo25bo3bo25b
o3bo$14b4o26b4o26b4o26b4o$b4o26b4o26b4o26b4o$o3bo25bo3bo25bo3bo25bo3bo
$4bo29bo29bo29bo$o2bo26bo2bo26bo2bo26bo2bo!

[Kiran]

Another input mechanism:

Code: Select all

x = 74, y = 13, rule = B3/S23
50bobo$51b2o$51bo5$2b2o28b2o28b2o$2ob2o25b2ob2o25b2ob2o$4o5bo2bo17b4o
5bo2bo17b4o5bo2bo$b2o10bo17b2o10bo17b2o10bo$9bo3bo25bo3bo25bo3bo$10b4o
26b4o26b4o!

Sawtooth 633 may be easier to use because no extra ship in necessary at the start of the cycle.

[Alexey_Nigin]

I decided to complete the project.

Below are the parts, like Legos, which you can assemble differently to get different growth rates.

Part 1:

Code: Select all

x = 199, y = 180, rule = B3/S23
78bo7bo$77b3o5bobo$76b2ob4o2bo2bo$77b3o2bo$78bo2b2o2bo$82b2obobo$86bo
10b2o$97b2o5$62bo$61b3o$60b2ob2o40b2o$61b3o41b2o$62bo$62bobo$62b4o$65b
o2$61b2ob2o5b3o$60bo5bo46b2o$61bo3bo9b2o36b2o$62bo14bo$71b4obo$52bo7bo
10b5o$51b3o5bobo$50b2ob4o2bo2bo39bo$51b3o2bo14bobo27bobo$52bo2b2o2bo
11bobo27bo2b2o$56b2obobo10bo26b7o$60bo10bobo24bo2bo3bo$72b2o23b3o2b7o$
72bo26b3o2bo$95bo4b2ob2o$94b2o5b3obo2bo$93bob2o5b3ob2o$93bo2b2o7bo$91b
4ob3o$90bo2bobo2b2o$56bo34bobobob3o$55b4o6b2o25b2ob3obo$54bo4bo4b3ob2o
22b4o2bobo$53b2o10b2ob3o24bo3bo$54bobob2o4b3ob2o25bo3bo$55b3o6b2o29bo
2bo$56bo5$59b2o$59b2o$76bo$75bobo$75bo2b2o$73b7o$72bo2bo3bo$71b3o2b7o$
67b2o4b3o2bo$67b2o5b2ob2o$75b3obo2bo$76b3ob2o$79bo4$75b2o$75b2o36$188b
2o$188b2o8$189bo$188b3o$187b5o$156bo29b2o3b2o$155b2o$155bobo2$188b3o$
188b3o2$191bo$190bobo$189bo3bo$190b3o$183bo4b2o3b2o$183bobo$183b2o7$
188b2o8bo$174b2o13bo6b3o$186b3o6bo$186bo8b2o4$176bo$174b3o$173bo$173b
2o11bo$185b2o3b2o3b2o$185bobo$4b2o155bo29bo3bo$3bo2bo153bo31b3o$3bo2bo
153b3o8bo8bo11b3o$b2ob2ob2o161b3o7b2o$o2bo2bo2bo159b5o5bobo$o2bo2bo2bo
158bobobobo16bo$b2ob2ob2o159b2o3b2o15b3o$3bo2bo182bo3bo$3bo2bo184bo$4b
2o167b2o13bo5bo$173b2o13bo5bo$175bo13bo3bo$173b3o14b3o$171bo$171b5o$
172b2o3$170b2o3b2o$171b5o$171b2ob2o$171b2ob2o14b2o$172b3o15b2o6$173b2o
$173b2o!

Part 2:

Code: Select all

x = 248, y = 93, rule = B3/S23
9b2o$8bo2bo$8bo2bo$6b2ob2ob2o$5bo2bo2bo2bo$5bo2bo2bo2bo$6b2ob2ob2o$8bo
2bo108b2o$8bo2bo107b3o$9b2o105bob2o15bo$103bo12bo2bo8b3o4bobo$102bobo
11bob2o16bobo$92b2o7bob2o14b3o2b2o2bo7bo2bo3b2o$35bo55bobo6b2ob2o15b2o
2bo3bo7bobo4b2o$34bobo53bo6b3obob2o20bo2bo6bobo$33bob2o15b2o27b2o7bo2b
o2bo2bo2bobo20b2o8bo$9b2o16b2o3b2ob2o14bobo27b2o7bo6b2o4bo$9b2o16b2o4b
ob2o13bo6b2o32bobo$34bobo13bo2bo2bo2bob2o29b2o63bo$35bo5bo8bo6b2o2b2o
10b2o42bo39b3o$41bobo7bobo19bobo28bobo10bobo40bo$41b2o9b2o14b2o6bo11bo
bo14b2o10b2o40b2o$60bo6bo2bo2bo2bo10bo2bo4bo9bo$60b4o4b2o6bo9b2o5b2o$
44bo16b4o8bobo8b2o3bo8b2o$43bobo5b2o8bo2bo8b2o11b2o10b2o$34bo6b2o3bo
14b4o13bo8bo2bo57b2o5b2o7b3o$33bo7b2o3bo4bobob2o3b4o12b2o10bobo21bo35b
2o5b2o7bo$7b5o21b3o5b2o3bo5b2o3bo2bo16b2o34b2o50bo$6bob3obo25b2o3bobo
10bo55b2o38b2o19b2o$7bo3bo25bobo4bo8bo2bo95b2o19b2o$8b3o26bo136bo$9bo
26b2o132b4o$169bo3bo$26bo36bo5bobo97b3o$26bobo6b2o4bo4b2o16bo4b2o100b
2o$7bo18b2o6bo2bobo3bobo2bo13b3o5bo102bo$7bo26b3o9b3o125bo4b2o56bobo$
6bobo5bo22b2o5b2o29b2o96bo5b2o52b3o3bo$5b2ob2o2bobo21bo2b5o2bo28b2o
156b2o5b2o$4bo5bo2b2o21b2o7b2o172b2o8bo6bo3b2o$7bo211b3o7bob2o2b2obo$
4b2o3b2o60bo55bo92bo2bobob2o2bo6bo3bo$23b2o28b2o14bobo11b2o28b2o13b2o
89b2o2b2o3b4o3bo6bo2bo$22b4o13b2o11b4o14b2o10b4o26b4o11b2o88bo2b2o2bo
2bo8b6o2bobo$22b2ob2o10b2ob2o10b2ob2o25b2ob2o25b2ob2o100bo2b2o3bo18bo
2bo$o23b2o11b4o13b2o28b2o28b2o101bo2b2o2bo2bo8b6o2bobo$3o35b2o52b4o26b
4o93b2o2b2o3b4o3bo6bo2bo$3bo5b2o80bo3bo25bo3bo94bo2bobob2o2bo6bo3bo$2b
2o5bo85bo29bo93b3o7bob2o2b2obo$10b3o47b2o29bo2bo26bo2bo94b2o8bo6bo3b2o
$12bo4b2o41bo5bo111bo54b2o5b2o$18b2o32bo5bobo5b2o111bo53b3o3bo$17bo34b
obo3b2o5bobo9b2o98b3o48bo8bobo$35bo17bobo22bo147b3o$2b2obob2o26b2o16bo
2bo21bobo7b2o135bo$2bo5bo21b2o4b2o15bobo17b2o4b2o7b2o135b2o$3bo3bo18b
2o2b2o4b3o13bobo17b2o11b2o10bo4bo$4b3o3bo15b2o2b2o4b2o7bobo4bo21bo9b3o
10bo4bobo$10b2o23b2o9b2o37b2o10bo7b2o$9bobo23bo10bo41b2o2b2o11b2o4b2o$
88b2o2bo2b2o8b2o4b2o116b2o5b2o$93b4o5bobo124b2o5b2o$94bo7bo117bo$217b
3o12b2o$213b2obo15b2o$7bo43bo161bo4bo$7bo43b2o161b3o$6bobo30bobo8bobo$
5b2ob2o29bo3bo165b2o$4bo5bo18b2o12bo10b2o153b2o$7bo21b2o8bo4bo7bo2bo7b
o24b2o9b2o$4b2o3b2o32bo7bo7b2o3bo22b2o9bobo104b2o5b2o$39bo3bo7bo6bo5bo
17bo6bo7b3o4b2ob3o95b2o5b2o$39bobo9bo7b5o17bobo12b3o4bo2b4o$6bo45bo2bo
18b2o3b2o3bo12b3o4b2o$6bo47b2o18b2o3b2o3bo13bobo$5bo73b2o3bo14b2o$81bo
bo$82bo$7b2o$7b2o200bo$208b2o$53b2o153b3o$52bo2bo154b2o$52bo2bo154b2o$
50b2ob2ob2o$49bo2bo2bo2bo$49bo2bo2bo2bo$50b2ob2ob2o$52bo2bo$52bo2bo$
53b2o!

Part 3:

Code: Select all

x = 432, y = 181, rule = B3/S23
4b2o$3bo2bo$3bo2bo$b2ob2ob2o$o2bo2bo2bo$o2bo2bo2bo$b2ob2ob2o$3bo2bo$3b
o2bo$4b2o27$82bo$82b3o$85bo$84b2o$246b2o31bo$87bo156bo2bo29bobo$86b3o
142bobo9bo7b5o19b2o18b2o$85bo3bo141bo3bo7bo6bo5bo12b2o4b2o17bo3bo32bo$
84bob3obo144bo7bo7b2o3bo12b2o4b2o16bo5bo31b3o$85b5o131b2o8bo4bo7bo2bo
7bo21bobo4bo8bo3bob2o2b2o29bo$221b2o12bo10b2o31bo3bo9bo5bo3b2o17b2o9b
2o$107b2o122bo3bo47b3o2bo5bo3bo23b2o33bo$107bo29bobo91bobo8bobo12b2o8b
2o26b2o58b3o$97bo7bobo29bo3bo101b2o11bo2bo7b2o85bo$92bo4b4o4b2o14bo19b
o101b3o13bo94b2o9b2o$92bo5b4o17b4o14bo4bo4b2o96b2o12bo105b2o$98bo2bo
16bobob2o4bo12bo5b2o97b2o8b2obo6b3o8b2o54b2o3b2o$98b4o15bo2bob3o5b2obo
3bo3bo103bo10b2o8b2o9b2o54b2o3b2o$97b4o16b2obob2o5b4obo2bobo129b2o$76b
2o19bo17b3ob4o6b2o2b2o115bo17b3o10b2o52b3o$76bo37bobo4bo27b2o100b2o4b
2o8bobo11bobo15b2o34b3o14bo13bo$63bo10bobo37bo34bo2bo97b2o5b2o8b2o12bo
17b2o20b3o12bo14b3o10b2ob2o$62bobo9b2o37b2o112bo10bo81bo3bo25b5o$52b2o
6b2o3bo83bo2bo74b2o9b2o79bo5bo23b2o3b2o7bo5bo$51bobo4b2obo3bo11b3o68bo
2bo70b2o4b2o7bobo4bo75bo3bo$50b3o4b3obo3bo13bo55bo3bobo6bobo67b2o2b2o
4b3o13bobo74b3o39b2obob2o$41b2o6b3o4bo2b2obobo13bo56b2o3b2o7bo68b2o2b
2o4b2o15bobo51b3o19b3o$41b2o7b3o4b2o4bo70bobo3bo86b2o16bo2bo39b3o8b3o
32bo16b3o$51bobo95b2o76bo17bobo40bo9bo3bo29b2o17b3o14bo$52b2o95b2o93bo
bo4b2o36bo43b2o30bo2bo$121b2o121bo6bobo43b2o3b2o46bo17bo$66bo10b2o41b
3o3b2obo22b2o99bo65b3o15b3o9bobo12b2o$64bobo10b2o38bob2o5bo3bo2bo19bo
99b3o62b2ob2o13bo3bo7bo3bo11bo$65b2o43b2o5bo2bo4bo4bo2b2o18bobo5bo94bo
13b2o46b2ob2o12bo5bo7b3o12bobo$68b2o40b2o5bob2o4b4o5b2o18b2o4bobo92b2o
8bo5bo24b2o20b5o4b2o6bo5bo5b2o3b2o4bo6b2o$44b2o22b2o6b3o41b3o3bo7b3o
22bob2o38b2o53b3o7b2o3bobo5bo16bobo18b2o3b2o3b2o9bo17bobo$45bo30b2o43b
2o11b2o22b2ob2o10b2o26b3o53bobo5b2o5b2o4bobo15bo39bo3bo16b2o$45bobo5bo
8b2o15b2o52b2o8b2o14bob2o10b2o12bo15b2obo15b2o33bobo17bob2o56bo27b2o3b
2o$46b2o3bobo6bo2bo14b3o52bo9bobo14bobo22bobo4b3o8bo2bo5b2o8b2o34bo17b
2ob2o10b2o45bo2bo18b2o3bo5bo$50bobo7bo3bo2b2o8bobo65bo15bo22bobo16b2ob
o5b2o63bob2o10b2o3bo44bo18b2o$49bo2bo7bo2b2o2b3o7b2o66b2o31b2o3bo2bo7b
o2b2o2b3o74bobo37b2o13bobo4bo25bo3bo$50bobo16b2obo105b2o4bobo7bo3bo2b
2o52b2obob2o3bobo11bo54b2o5b3o23b3o$51bobo4b3o8bo2bo112bobo6bo2bo57bo
5bo4b2o66bo8bo$53bo15b2obo114bo8b2o16b2o40bo3bo5bo80b2o$67b3o6b2o136b
2o41b3o20bo16b3o20b2o26bo$67b2o7bobo135b2o62bobo15bo3bo19b2o4bo2b2o14b
3o$78bo74b2o60bo63b2o14bo5bo23bo3b2o2b2o10bo5bo18b2o$78b2o65bo5bo2bo
44b2o4bo8bobo6bo71bo5bo23bo7b2o15bo19bo$67b2o76b2o51bobo2bobo7b2obo5b
3o73bo27b4o20b3o18b3o$67bo76bobo4bo2bo20b2o23bo3b2o15b5o37bo32bo3bo72b
o$58b2o5bobo84bo2bo20bo43b2o3b2o28b2o6b2o32b3o66bo30bo$56bo2bo5b2o86bo
bo20bobo7b2o26b2o5b5o30bo5bobo3b2o28bo65b3o30b3o$43bobo9bo89bo8bo22b2o
6bobo26b2o5bo3bo27b3o10bo2bo93bo36bo$43bo3bo7bo88b2o38b3o4b2o4bo24bobo
28bo103bo5b2o9b2o12b2o9b2o$33b2o12bo7bo88bobo6b2o28b3o4bo2b2obobo24bo
42bo2bo27b2o56b3o16b2o12b2o$33b2o8bo4bo7bo2bo6b2o69b2o14b2o14bobo12b3o
4b3obo3bo57b2o8bo2bo26b2o55bo$47bo10b2o6bo2bo68b2o30b2o13bobo4b2obo3bo
57b2o9bobo83b2o$43bo3bo89bo32bo6bo8b2o6b2o3bo25bo43bo$43bobo8bobo9bo2b
o105bobo18bobo8b2o14b2ob2o$55b2o8bo2bo107b2o19bo9bobo8bo49b2o81b2o5b2o
bob2o$55bo9bobo84b2o55bo7bo4bo5bo39b2o88bo5bo22b3o11b3o$66bo84b2o56b2o
6b3o116bo22bo3bo22b2ob2o9bo3bo$130bo22bo68b2obob2o35b2o69bo24b3o23b2ob
2o8bo5bo$66b2o17bobo30b2o10b2o9b2o20b2o98b2o70b3o11b2o3b2o30b5o8bo5bo$
66b2o16bo33b2o9bobo10bo18bo3bo82bo16bo29bo53b2o3b2o16b2o3b2o6b2o3b2o
10bo$84bo36b2o12b2o5bobo7bo7bo5bo81b2o46b2o102bo3bo$39bo10bo33bo2bo33b
3o10bo3bo4b2o7bobo4b2obo3bo80bobo45b2o54b3o19bo3bo23b3o$39b2o9b2o32b3o
34b2o10bo5bo15b2o3bo5bo184b3o20b3o10b2o13bo$30b2o2b2o4b2o7bobo4bo54b2o
5b2o13bo3bo2bo14b2o4bo3bo7b2o60b2o19b2o14b2o9bo68bo21b3o9b5o$30b2o2b2o
4b3o13bobo51bobo5b2o13bo21b2o6b2o8bobo46b2o10bobo20bo13b4o7bobo78bo22b
o$34b2o4b2o15bobo50bo23bo3bo3bo9bobo20bo47bo9bo6b2o4bo10bobo6bobo2bo2b
3o5b2obo78bo23b3o12b3o$39b2o16bo2bo48b2o24b2o3b2obo8bo22b2o43b3o10bo2b
o2bo2bo2bobo10b2o5bo2bo2b2o9b2ob2o8bobo37bo26b3o25bo12b3o$39bo17bobo
83bo76bo12bo6b3obob2o16b2o9bo6b2obo10b2o37bobo11b2o37b2o12bo3bo$56bobo
4b2o78b2o81b2o6bobo6b2ob2o14b2o3bo8bo5bobo3b2o6bo38b2o13bo37b2o6bobo$
56bo6bobo159bobo7b2o7bob2o16b2o10bo6bo4bobo19bo36b3o27bo18b2o3b2o3b2o$
65bo159bo19bobo8b2o7bo2bo21bo17bobo36bo28b3o18bo$65b2o157b2o20bo9bobo
7bobo21b2o17b2o10bo35b5o14b3o4b2o3b2o$258bo61bo35bob3obo6b2o12bobobobo
$258b2o60b3o34bo3bo7b2o3b2o3b2o3b5o5bobo$126bo2bo56bo2bo168b3o13b2o3b
2o4b3o7b2o$125bo59bo173bo26bo8bo$125bo3bo55bo3bo$108b4o13b4o39b4o13b4o
39b4o56b4o64b2o5bo13bo28b2o$108bo3bo55bo3bo55bo3bo55bo3bo64bo5bobo10bo
bo27bo$108bo59bo59bo59bo65b3o6b2o13b2o27b3o$109bo2bo56bo2bo56bo2bo56bo
2bo61bo23b2o29bo$129b3o57b3o57b3o57b3o65b3o$113bo10bobobo3bo40bo10bobo
bo3bo40bo10bobobo3bo40bo10bobobo3bo63bobo7b2o$84bobo24b3o10bo7bo38b3o
10bo7bo38b3o10bo7bo38b3o10bo7bo54b2o7b2o8b2o4bo2b2o$85b2o23bo3bo15b2o
5bo32bo3bo15b2o5bo32bo3bo15b2o38bo3bo15b2o51b2o2b2o2b2o18bo3b2o2b2o$
85bo24bo4b3o19bobo30bo4b3o19bobo30bo4b3o52bo4b3o65b2o2bo2bobo18bo7b2o$
88b2o20b2obob3o8bo10b2o31b2obob3o8bo10b2o31b2obob3o8bo43b2obob3o8bo62b
3o20b4o$88b2o22bo3b2o54bo3b2o54bo3b2o54bo3b2o71b2o$113bobo57bobo57bobo
57bobo113bobo$142bo267b2o$142bobo265bo$108b4o5b2o23b2o24b4o5b2o49b4o5b
2o49b4o5b2o49b4o5b2o59bo$108bo3bo3b2ob2o47bo3bo3b2ob2o47bo3bo3b2ob2o
47bo3bo3b2ob2o47bo3bo3b2ob2o56bobo$108bo8b4o47bo8b4o47bo8b4o47bo8b4o
47bo8b4o55bob2o10b2o$109bo2bo5b2o27bo21bo2bo5b2o49bo2bo5b2o49bo2bo5b2o
49bo2bo5b2o55b2ob2o10b2o$147bobo266bob2o$147b2o268bobo$94b2o8b2o8b2o8b
2o8b2o8b2o8b2o8b2o8b2o8b2o181b2o49bo$93bobo7bobo7bobo7bobo7bobo7bobo7b
obo7bobo7bobo7bobo153b2o2bo24bo$93bo9bo9bo9bo9bo9bo9bo9bo9bo9bo151b2o
2b2o3bo23bobo5b2o$92b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o151b2o7bo
24b2o5bobo$330b2o8b4o35bo11bobo20b3o$330b2o44bo2bo10bo2bo19b2ob2o$379b
o9b2o22b2ob2o$353bo14bo7bobo8b2o3bo20b5o$351b3o13b2o7b2o11b2o21b2o3b2o
$350bo11b2o3bobo11bo8bo2bo5b2o$330bo19b2o10bo2bo13b2o10bobo5bobo$330bo
9bo39b2o19bo$329bobo8b2o20bo2bo35b2o$328b2ob2o6bobo19bo2bo51b2o$327bo
5bo27bobo$330bo31bo11b2o$327b2o3b2o6bo33b2o$339b2o7bo13b2o50b2o$339bob
o5b3o12b2o22b2o26b2o$332b3o11b5o33bo3bo$332bob2o9b2o3b2o23bo7bo5bo8b2o
$334b2o10b5o24bobo4b2obo3bo8b2o$333b2o11b5o13b2o12b2o3bo5bo$331bobo12b
o2bo14b2o12b2o4bo3bo$329b2o2bo11bo3bo28b2o6b2o$345bo29bobo$345bob2o26b
o$346bo3$330b5o8b2o3b2o$329bob3obo7bo5bo$330bo3bo$331b3o10bo3bo$332bo
12b3o4$332b2o$332b2o9b2o$344bo$341b3o$341bo!

Open the first part in Golly, then add a few copies of part two to the bottom-right. If you want to get a pattern with a-bit-larger-than-linear growth rate, add part three to the very bottom. Always paste components in such a way that decorative still lifes overlap.

I will not post completed patterns: it's your turn to play!

[Kiran]

I decided to complete the project.

I thought everyone gave up on it.

Thanks a lot Alexey!
Should it be added to the Wiki?
Any thoughts for a good name?
Is the growth rate actually log****(t)?

[gmc_nxtman]

Any thoughts for a good name?

Logging Camp
Standard name (log***(t) growth
Logger
Iterative sawtooth

Just suggestions.

Should it be added to the Wiki?

In my humble opinion, definitely. This is a very impressive construction. Great job to both of you for the idea and build

[gameoflifeboy]

This is amazing. With one "part 2" mechanism, it seems that each glider shoots out at approximately 2 to the power of the generation that the previous glider shot out, similar to the wickstretchers in this pattern. With two of them, each glider shoots out at approximately 2 tetrated to the generation that the previous one shot out. With three of them, each glider shoots out at about 2 pentated to the generation the previous one shot out, and so on.
If I'm not mistaken, this is much slower than any finite number of iterated logs on the generation number, even if only one "part 2" mechanism is used.

[biggiemac]

Well in up-arrow notation, log 2^x = x, log 2^^x = 2^^(x-1), so log* 2^^x = x. And log* 2^^^x = 2^^^(x-1), etc. So if g_{n+1} = 2(k^)g_n where k^ is some specified number of up arrows, then to get n in terms of g, you take log-(k-1 stars) g_{n+1} = g_n, iterate this n times to get log-(k stars) g_n = n. The nth glider is emitted at a generation such that log-(k stars) g_n = n. So the pattern increases at log**..**t, where the number of stars is the number of part 2. Correct me if any of this is wrong.

[simsim314]

First of all nothing is complete I don't see any pattern posted or in this case script should be posted (I think) to call it complete.

Should it be added to the Wiki?

I think not. There are many not standard infinite growths which are not in the wiki. This one has no historical or other value, no extreme novelty in the construction and nothing that was too impressive (maybe actually building the solution would change my mind).

As far as I see Alexey posted a puzzle for basic components that's it. You're still in the middle. I've posted the basic components for replicator and all slow salvo and arm recipes for it... I did't think my replicator is complete.

[Alexey_Nigin]

Iterative sawtooth

Since it's not a sawtooth, I wouldn't call it a sawtooth in order not to cause ambiguity.

As far as I see Alexey posted a puzzle for basic components that's it. You're still in the middle. I've posted the basic components for replicator and all slow salvo and arm recipes for it... I did't think my replicator is complete.

You're a bit wrong. I have actually posted step-by-step instructions which allow you to create completed patterns in 15 seconds. Here is an example:

Code: Select all

x = 481, y = 414, rule = B3/S23
83bo7bo$82b3o5bobo$81b2ob4o2bo2bo$82b3o2bo$83bo2b2o2bo$87b2obobo$91bo
10b2o$102b2o5$67bo$66b3o$65b2ob2o40b2o$66b3o41b2o$67bo$67bobo$67b4o$
70bo2$66b2ob2o5b3o$65bo5bo46b2o$66bo3bo9b2o36b2o$67bo14bo$76b4obo$57bo
7bo10b5o$56b3o5bobo$55b2ob4o2bo2bo39bo$56b3o2bo14bobo27bobo$57bo2b2o2b
o11bobo27bo2b2o$61b2obobo10bo26b7o$65bo10bobo24bo2bo3bo$77b2o23b3o2b7o
$77bo26b3o2bo$100bo4b2ob2o$99b2o5b3obo2bo$98bob2o5b3ob2o$98bo2b2o7bo$
96b4ob3o$95bo2bobo2b2o$61bo34bobobob3o$60b4o6b2o25b2ob3obo$59bo4bo4b3o
b2o22b4o2bobo$58b2o10b2ob3o24bo3bo$59bobob2o4b3ob2o25bo3bo$60b3o6b2o
29bo2bo$61bo5$64b2o$64b2o$81bo$80bobo$80bo2b2o$78b7o$77bo2bo3bo$76b3o
2b7o$72b2o4b3o2bo$72b2o5b2ob2o$80b3obo2bo$81b3ob2o$84bo4$80b2o$80b2o
36$193b2o$193b2o8$194bo$193b3o$192b5o$161bo29b2o3b2o$160b2o$160bobo2$
193b3o$193b3o2$196bo$195bobo$194bo3bo$195b3o$188bo4b2o3b2o$188bobo$
188b2o7$193b2o8bo$179b2o13bo6b3o$191b3o6bo$191bo8b2o4$181bo$179b3o$
178bo$178b2o11bo$190b2o3b2o3b2o$190bobo$9b2o155bo29bo3bo$8bo2bo153bo
31b3o$8bo2bo153b3o8bo8bo11b3o$6b2ob2ob2o161b3o7b2o$5bo2bo2bo2bo159b5o
5bobo$5bo2bo2bo2bo158bobobobo16bo$6b2ob2ob2o159b2o3b2o15b3o$8bo2bo108b
2o72bo3bo$8bo2bo107b3o74bo$9b2o105bob2o15bo42b2o13bo5bo$103bo12bo2bo8b
3o4bobo40b2o13bo5bo$102bobo11bob2o16bobo41bo13bo3bo$92b2o7bob2o14b3o2b
2o2bo7bo2bo3b2o33b3o14b3o$35bo55bobo6b2ob2o15b2o2bo3bo7bobo4b2o31bo$
34bobo53bo6b3obob2o20bo2bo6bobo38b5o$33bob2o15b2o27b2o7bo2bo2bo2bo2bob
o20b2o8bo41b2o$9b2o16b2o3b2ob2o14bobo27b2o7bo6b2o4bo$9b2o16b2o4bob2o
13bo6b2o32bobo$34bobo13bo2bo2bo2bob2o29b2o63bo17b2o3b2o$35bo5bo8bo6b2o
2b2o10b2o42bo39b3o16b5o$41bobo7bobo19bobo28bobo10bobo40bo15b2ob2o$41b
2o9b2o14b2o6bo11bobo14b2o10b2o40b2o15b2ob2o14b2o$60bo6bo2bo2bo2bo10bo
2bo4bo9bo71b3o15b2o$60b4o4b2o6bo9b2o5b2o$44bo16b4o8bobo8b2o3bo8b2o$43b
obo5b2o8bo2bo8b2o11b2o10b2o$34bo6b2o3bo14b4o13bo8bo2bo57b2o5b2o7b3o$
33bo7b2o3bo4bobob2o3b4o12b2o10bobo21bo35b2o5b2o7bo$7b5o21b3o5b2o3bo5b
2o3bo2bo16b2o34b2o50bo12b2o$6bob3obo25b2o3bobo10bo55b2o38b2o19b2o3b2o$
7bo3bo25bobo4bo8bo2bo95b2o19b2o$8b3o26bo136bo$9bo26b2o132b4o$169bo3bo$
26bo36bo5bobo97b3o$26bobo6b2o4bo4b2o16bo4b2o100b2o$7bo18b2o6bo2bobo3bo
bo2bo13b3o5bo102bo$7bo26b3o9b3o125bo4b2o56bobo$6bobo5bo22b2o5b2o29b2o
96bo5b2o52b3o3bo$5b2ob2o2bobo21bo2b5o2bo28b2o156b2o5b2o$4bo5bo2b2o21b
2o7b2o172b2o8bo6bo3b2o$7bo211b3o7bob2o2b2obo$4b2o3b2o60bo55bo92bo2bobo
b2o2bo6bo3bo$23b2o28b2o14bobo11b2o28b2o13b2o89b2o2b2o3b4o3bo6bo2bo$22b
4o13b2o11b4o14b2o10b4o26b4o11b2o88bo2b2o2bo2bo8b6o2bobo$22b2ob2o10b2ob
2o10b2ob2o25b2ob2o25b2ob2o100bo2b2o3bo18bo2bo$o23b2o11b4o13b2o28b2o28b
2o101bo2b2o2bo2bo8b6o2bobo$3o35b2o52b4o26b4o93b2o2b2o3b4o3bo6bo2bo$3bo
5b2o80bo3bo25bo3bo94bo2bobob2o2bo6bo3bo$2b2o5bo85bo29bo93b3o7bob2o2b2o
bo$10b3o47b2o29bo2bo26bo2bo94b2o8bo6bo3b2o$12bo4b2o41bo5bo111bo54b2o5b
2o$18b2o32bo5bobo5b2o111bo53b3o3bo$17bo34bobo3b2o5bobo9b2o98b3o48bo8bo
bo$35bo17bobo22bo147b3o$2b2obob2o26b2o16bo2bo21bobo7b2o135bo$2bo5bo21b
2o4b2o15bobo17b2o4b2o7b2o135b2o$3bo3bo18b2o2b2o4b3o13bobo17b2o11b2o10b
o4bo$4b3o3bo15b2o2b2o4b2o7bobo4bo21bo9b3o10bo4bobo$10b2o23b2o9b2o37b2o
10bo7b2o$9bobo23bo10bo41b2o2b2o11b2o4b2o$88b2o2bo2b2o8b2o4b2o116b2o5b
2o$93b4o5bobo124b2o5b2o$94bo7bo117bo$217b3o12b2o$213b2obo15b2o$7bo43bo
161bo4bo$7bo43b2o161b3o$6bobo30bobo8bobo$5b2ob2o29bo3bo165b2o$4bo5bo
18b2o12bo10b2o153b2o$7bo21b2o8bo4bo7bo2bo7bo24b2o9b2o$4b2o3b2o32bo7bo
7b2o3bo22b2o9bobo104b2o5b2o$39bo3bo7bo6bo5bo17bo6bo7b3o4b2ob3o95b2o5b
2o$39bobo9bo7b5o17bobo12b3o4bo2b4o$6bo45bo2bo18b2o3b2o3bo12b3o4b2o$6bo
47b2o18b2o3b2o3bo13bobo$5bo73b2o3bo14b2o$81bobo$82bo$7b2o$7b2o200bo$
208b2o$53b2o153b3o$52bo2bo154b2o$52bo2bo154b2o$50b2ob2ob2o$49bo2bo2bo
2bo$49bo2bo2bo2bo$50b2ob2ob2o$52bo2bo$52bo2bo$53b2o27$131bo$131b3o$
134bo$133b2o$295b2o31bo$136bo156bo2bo29bobo$135b3o142bobo9bo7b5o19b2o
18b2o$134bo3bo141bo3bo7bo6bo5bo12b2o4b2o17bo3bo32bo$133bob3obo144bo7bo
7b2o3bo12b2o4b2o16bo5bo31b3o$134b5o131b2o8bo4bo7bo2bo7bo21bobo4bo8bo3b
ob2o2b2o29bo$270b2o12bo10b2o31bo3bo9bo5bo3b2o17b2o9b2o$156b2o122bo3bo
47b3o2bo5bo3bo23b2o33bo$156bo29bobo91bobo8bobo12b2o8b2o26b2o58b3o$146b
o7bobo29bo3bo101b2o11bo2bo7b2o85bo$141bo4b4o4b2o14bo19bo101b3o13bo94b
2o9b2o$141bo5b4o17b4o14bo4bo4b2o96b2o12bo105b2o$147bo2bo16bobob2o4bo
12bo5b2o97b2o8b2obo6b3o8b2o54b2o3b2o$147b4o15bo2bob3o5b2obo3bo3bo103bo
10b2o8b2o9b2o54b2o3b2o$146b4o16b2obob2o5b4obo2bobo129b2o$125b2o19bo17b
3ob4o6b2o2b2o115bo17b3o10b2o52b3o$125bo37bobo4bo27b2o100b2o4b2o8bobo
11bobo15b2o34b3o14bo13bo$112bo10bobo37bo34bo2bo97b2o5b2o8b2o12bo17b2o
20b3o12bo14b3o10b2ob2o$111bobo9b2o37b2o112bo10bo81bo3bo25b5o$101b2o6b
2o3bo83bo2bo74b2o9b2o79bo5bo23b2o3b2o7bo5bo$100bobo4b2obo3bo11b3o68bo
2bo70b2o4b2o7bobo4bo75bo3bo$99b3o4b3obo3bo13bo55bo3bobo6bobo67b2o2b2o
4b3o13bobo74b3o39b2obob2o$90b2o6b3o4bo2b2obobo13bo56b2o3b2o7bo68b2o2b
2o4b2o15bobo51b3o19b3o$90b2o7b3o4b2o4bo70bobo3bo86b2o16bo2bo39b3o8b3o
32bo16b3o$100bobo95b2o76bo17bobo40bo9bo3bo29b2o17b3o14bo$101b2o95b2o
93bobo4b2o36bo43b2o30bo2bo$170b2o121bo6bobo43b2o3b2o46bo17bo$115bo10b
2o41b3o3b2obo22b2o99bo65b3o15b3o9bobo12b2o$113bobo10b2o38bob2o5bo3bo2b
o19bo99b3o62b2ob2o13bo3bo7bo3bo11bo$114b2o43b2o5bo2bo4bo4bo2b2o18bobo
5bo94bo13b2o46b2ob2o12bo5bo7b3o12bobo$117b2o40b2o5bob2o4b4o5b2o18b2o4b
obo92b2o8bo5bo24b2o20b5o4b2o6bo5bo5b2o3b2o4bo6b2o$93b2o22b2o6b3o41b3o
3bo7b3o22bob2o38b2o53b3o7b2o3bobo5bo16bobo18b2o3b2o3b2o9bo17bobo$94bo
30b2o43b2o11b2o22b2ob2o10b2o26b3o53bobo5b2o5b2o4bobo15bo39bo3bo16b2o$
94bobo5bo8b2o15b2o52b2o8b2o14bob2o10b2o12bo15b2obo15b2o33bobo17bob2o
56bo27b2o3b2o$95b2o3bobo6bo2bo14b3o52bo9bobo14bobo22bobo4b3o8bo2bo5b2o
8b2o34bo17b2ob2o10b2o45bo2bo18b2o3bo5bo$99bobo7bo3bo2b2o8bobo65bo15bo
22bobo16b2obo5b2o63bob2o10b2o3bo44bo18b2o$98bo2bo7bo2b2o2b3o7b2o66b2o
31b2o3bo2bo7bo2b2o2b3o74bobo37b2o13bobo4bo25bo3bo$99bobo16b2obo105b2o
4bobo7bo3bo2b2o52b2obob2o3bobo11bo54b2o5b3o23b3o$100bobo4b3o8bo2bo112b
obo6bo2bo57bo5bo4b2o66bo8bo$102bo15b2obo114bo8b2o16b2o40bo3bo5bo80b2o$
116b3o6b2o136b2o41b3o20bo16b3o20b2o26bo$116b2o7bobo135b2o62bobo15bo3bo
19b2o4bo2b2o14b3o$127bo74b2o60bo63b2o14bo5bo23bo3b2o2b2o10bo5bo18b2o$
127b2o65bo5bo2bo44b2o4bo8bobo6bo71bo5bo23bo7b2o15bo19bo$116b2o76b2o51b
obo2bobo7b2obo5b3o73bo27b4o20b3o18b3o$116bo76bobo4bo2bo20b2o23bo3b2o
15b5o37bo32bo3bo72bo$107b2o5bobo84bo2bo20bo43b2o3b2o28b2o6b2o32b3o66bo
30bo$105bo2bo5b2o86bobo20bobo7b2o26b2o5b5o30bo5bobo3b2o28bo65b3o30b3o$
92bobo9bo89bo8bo22b2o6bobo26b2o5bo3bo27b3o10bo2bo93bo36bo$92bo3bo7bo
88b2o38b3o4b2o4bo24bobo28bo103bo5b2o9b2o12b2o9b2o$82b2o12bo7bo88bobo6b
2o28b3o4bo2b2obobo24bo42bo2bo27b2o56b3o16b2o12b2o$82b2o8bo4bo7bo2bo6b
2o69b2o14b2o14bobo12b3o4b3obo3bo57b2o8bo2bo26b2o55bo$96bo10b2o6bo2bo
68b2o30b2o13bobo4b2obo3bo57b2o9bobo83b2o$92bo3bo89bo32bo6bo8b2o6b2o3bo
25bo43bo$92bobo8bobo9bo2bo105bobo18bobo8b2o14b2ob2o$104b2o8bo2bo107b2o
19bo9bobo8bo49b2o81b2o5b2obob2o$104bo9bobo84b2o55bo7bo4bo5bo39b2o88bo
5bo22b3o11b3o$115bo84b2o56b2o6b3o116bo22bo3bo22b2ob2o9bo3bo$179bo22bo
68b2obob2o35b2o69bo24b3o23b2ob2o8bo5bo$115b2o17bobo30b2o10b2o9b2o20b2o
98b2o70b3o11b2o3b2o30b5o8bo5bo$115b2o16bo33b2o9bobo10bo18bo3bo82bo16bo
29bo53b2o3b2o16b2o3b2o6b2o3b2o10bo$133bo36b2o12b2o5bobo7bo7bo5bo81b2o
46b2o102bo3bo$88bo10bo33bo2bo33b3o10bo3bo4b2o7bobo4b2obo3bo80bobo45b2o
54b3o19bo3bo23b3o$88b2o9b2o32b3o34b2o10bo5bo15b2o3bo5bo184b3o20b3o10b
2o13bo$79b2o2b2o4b2o7bobo4bo54b2o5b2o13bo3bo2bo14b2o4bo3bo7b2o60b2o19b
2o14b2o9bo68bo21b3o9b5o$79b2o2b2o4b3o13bobo51bobo5b2o13bo21b2o6b2o8bob
o46b2o10bobo20bo13b4o7bobo78bo22bo$83b2o4b2o15bobo50bo23bo3bo3bo9bobo
20bo47bo9bo6b2o4bo10bobo6bobo2bo2b3o5b2obo78bo23b3o12b3o$88b2o16bo2bo
48b2o24b2o3b2obo8bo22b2o43b3o10bo2bo2bo2bo2bobo10b2o5bo2bo2b2o9b2ob2o
8bobo37bo26b3o25bo12b3o$88bo17bobo83bo76bo12bo6b3obob2o16b2o9bo6b2obo
10b2o37bobo11b2o37b2o12bo3bo$105bobo4b2o78b2o81b2o6bobo6b2ob2o14b2o3bo
8bo5bobo3b2o6bo38b2o13bo37b2o6bobo$105bo6bobo159bobo7b2o7bob2o16b2o10b
o6bo4bobo19bo36b3o27bo18b2o3b2o3b2o$114bo159bo19bobo8b2o7bo2bo21bo17bo
bo36bo28b3o18bo$114b2o157b2o20bo9bobo7bobo21b2o17b2o10bo35b5o14b3o4b2o
3b2o$307bo61bo35bob3obo6b2o12bobobobo$307b2o60b3o34bo3bo7b2o3b2o3b2o3b
5o5bobo$175bo2bo56bo2bo168b3o13b2o3b2o4b3o7b2o$174bo59bo173bo26bo8bo$
174bo3bo55bo3bo$157b4o13b4o39b4o13b4o39b4o56b4o64b2o5bo13bo28b2o$157bo
3bo55bo3bo55bo3bo55bo3bo64bo5bobo10bobo27bo$157bo59bo59bo59bo65b3o6b2o
13b2o27b3o$158bo2bo56bo2bo56bo2bo56bo2bo61bo23b2o29bo$178b3o57b3o57b3o
57b3o65b3o$162bo10bobobo3bo40bo10bobobo3bo40bo10bobobo3bo40bo10bobobo
3bo63bobo7b2o$133bobo24b3o10bo7bo38b3o10bo7bo38b3o10bo7bo38b3o10bo7bo
54b2o7b2o8b2o4bo2b2o$134b2o23bo3bo15b2o5bo32bo3bo15b2o5bo32bo3bo15b2o
38bo3bo15b2o51b2o2b2o2b2o18bo3b2o2b2o$134bo24bo4b3o19bobo30bo4b3o19bob
o30bo4b3o52bo4b3o65b2o2bo2bobo18bo7b2o$137b2o20b2obob3o8bo10b2o31b2obo
b3o8bo10b2o31b2obob3o8bo43b2obob3o8bo62b3o20b4o$137b2o22bo3b2o54bo3b2o
54bo3b2o54bo3b2o71b2o$162bobo57bobo57bobo57bobo113bobo$191bo267b2o$
191bobo265bo$157b4o5b2o23b2o24b4o5b2o49b4o5b2o49b4o5b2o49b4o5b2o59bo$
157bo3bo3b2ob2o47bo3bo3b2ob2o47bo3bo3b2ob2o47bo3bo3b2ob2o47bo3bo3b2ob
2o56bobo$157bo8b4o47bo8b4o47bo8b4o47bo8b4o47bo8b4o55bob2o10b2o$158bo2b
o5b2o27bo21bo2bo5b2o49bo2bo5b2o49bo2bo5b2o49bo2bo5b2o55b2ob2o10b2o$
196bobo266bob2o$196b2o268bobo$143b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b
2o181b2o49bo$142bobo7bobo7bobo7bobo7bobo7bobo7bobo7bobo7bobo7bobo153b
2o2bo24bo$142bo9bo9bo9bo9bo9bo9bo9bo9bo9bo151b2o2b2o3bo23bobo5b2o$141b
2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o151b2o7bo24b2o5bobo$379b2o8b4o
35bo11bobo20b3o$379b2o44bo2bo10bo2bo19b2ob2o$428bo9b2o22b2ob2o$402bo
14bo7bobo8b2o3bo20b5o$400b3o13b2o7b2o11b2o21b2o3b2o$399bo11b2o3bobo11b
o8bo2bo5b2o$379bo19b2o10bo2bo13b2o10bobo5bobo$379bo9bo39b2o19bo$378bob
o8b2o20bo2bo35b2o$377b2ob2o6bobo19bo2bo51b2o$376bo5bo27bobo$379bo31bo
11b2o$376b2o3b2o6bo33b2o$388b2o7bo13b2o50b2o$388bobo5b3o12b2o22b2o26b
2o$381b3o11b5o33bo3bo$381bob2o9b2o3b2o23bo7bo5bo8b2o$383b2o10b5o24bobo
4b2obo3bo8b2o$382b2o11b5o13b2o12b2o3bo5bo$380bobo12bo2bo14b2o12b2o4bo
3bo$378b2o2bo11bo3bo28b2o6b2o$394bo29bobo$394bob2o26bo$395bo3$379b5o8b
2o3b2o$378bob3obo7bo5bo$379bo3bo$380b3o10bo3bo$381bo12b3o4$381b2o$381b
2o9b2o$393bo$390b3o$390bo!

If you posted such instructions for your replicator or whatever, I would call it complete.

This one has no historical or other value

Well, in my humble opinion, this is the first constructive proof that Life supports infinitely many asymptotic growth rates.

[simsim314]

I have actually posted step-by-step instructions which allow you to create completed patterns in 15 seconds.

I can post a step by step instruction to complete it in few hours.

If you posted such instructions for your replicator or whatever, I would call it complete.

I would call it 15 second from completion. My replicator is few hours from completion. And dvgrn's quadratic replicator is few days from completion.

Thx for the complete pattern.

this is the first constructive proof that Life supports infinitely many asymptotic growth rates

Well putting it this way... I think it's not enough for Wiki yet, as there was no historical quest for such pattern, and the construction is not that novel. But it's definitely interesting finding, and I would recommend to post it in the collections.

I'm not sure if Wiki is extremely partial because of intentional effort to make it clean and minimalistic with the major discoveries only, or just not enough effort was made to make it more complete.

In any case, there are many interesting not trivial designs for different growth rates, this one definitely has respectful place among them.

EDIT Thinking of it again, the infinite growth rates article in wiki is not such a good quality one.

1. One should replace all the "?" with patterns from here, and open articles for them.

2. SqrtGun Should definitely be added as Dean worked extremely hard to optimize this one.

3. Patterns from this thread

4. Sqrt(log(t)) That comes in online archives large patterns in golly.

5. Then this pattern should be added into the infinite growth rate part. One should post explicit example of few growth rate, with link to here. Opening extra article after 1. - 4. is definitely an option (but link to here will suffice as well).

Creating a script for higher logⁿ(t) should be simple and should be considered a good practice for infinite collections.

[calcyman]

This one has no historical or other value, no extreme novelty in the construction and nothing that was too impressive

No, what Alexey et al have done is very impressive, has historical value (rediscovering and deepening concepts discussed by Gabriel Nivasch and Dean Hickerson in 2006) and is extremely novel. It is quite a deep concept and deserves to be explained clearly and pedagogically. I shall attempt to do so in the remainder of this post, after first addressing a slight attribution issue:

Well, in my humble opinion, this is the first constructive proof that Life supports infinitely many asymptotic growth rates.

No, Gabriel Nivasch did that in 2006. He constructed patterns with growth rate O(t^(1/2^n)) for all n. His idea (which he named the quadratic filter) was similar to (but simpler than) yours, and will make an excellent illustrative example. So, without further ado, allow me to begin:


How slow can you grow?

Let's consider patterns which emit gliders very slowly. One familiar example is the caber tosser, which emits the nth glider at generation f(n) = Θ(2^n). Another is Dean Hickerson's sqrtgun, which emits the nth glider at generation f(n) = Θ(n^2). The most trivial example is an ordinary glider gun, with f(n) = Θ(n). We'll call this function the slowness rate, which we will denote by S.

Notation note: The big theta Θ means 'is asymptotically proportional to'.

For instance, we could write:

• S(caber tosser) = f, where f(n) := Θ(2^n)

Notation note: The symbol := means 'is defined to be'.

Now this is quite verbose and annoying, and is easier to encapsulate in a single expression. The following two are alternative ways to express this:

• S(caber_tosser)(n) = Θ(2^n)
• S(caber_tosser) = λn.Θ(2^n)

The first of these is what we get by doing a literal replacement of f by its definition. The second is a way to 'rearrange the equation' to express S(caber_tosser), using lambda notation.

Notation note: λx.y means 'the function mapping x to y'.

S is a higher-order operator mapping patterns to growth rates. There's also something that we can do to certain patterns, called piping by analogy with Unix. This simply sends the output of the thing on the left to the input of the thing on the right. Gabriel designed a 'quadratic filter' which can be piped onto the end of a pattern to create a slower growth rate. Specifically, it has the following property:

• S(X | quadratic_filter) = S(X)^2

And here's an example constructed by Gabriel:

• S(sqrt_gun | quadratic_filter) = S(sqrt_gun)^2 = λn.Θ(n^2)^2 = λn.Θ(n^4).

For explicitness, you may want the actual RLE of the pattern, a working sqrtsqrtgun:

Code: Select all

x = 640, y = 464, rule = B3/S23
116b2o21b2o$115bobo21bo$114bo13bobo6bobo$102bo11bo2bo6b2o2bo2bo5b2o$
99b4o11bo8bobo5b2o$90bo7b4o13bobo3bo3bo3bo3b2o$89bobo6bo2bo14b2o2b2ob
3o5b2o$88bo3b2o4b4o21b2o3bo2bo25b2o$77b2o9bo3b2o5b4o25bobo26b2o$77b2o
9bo3b2o8bo$89bobo$90bo23bo$99bobo12bobo$100b2o12b2o$100bo$117b2o$108b
2o7b2o$108bo$105b2o3bo7bo$104b2ob2obo6bobo$106bob2o6bo2bo$115bo2bo2$
91bo23bo2bo$90b4o23b2o$89b2ob4o5b2o$78b2o8b3ob2o3bo3bo2bo$78b2o9b2ob2o
3bo7bo8bobo$90b5o3bo6bo9b2o$91bo3b3o7bo9bo$101bo2bo5b2o$101b2o7bobo$
112bo$60b2o27bo22b2o$60b2o25b2o$88b2o2$63bo$62bo$46b2o14bo$46b2o$80bob
o$47bo10b2o3b2o15b2o$46bobo12bo19bo$46bobo9bo5bo36b2o$47bo11b2ob2o36b
2o$60bobo39bo$61bo$44b2obob2o10bo$26b2o16bo5bo367bo$26b2o17bo3bo367bob
o$46b3o368bobo$418bo$64b2o$413b2o7b2o$64bo2bo344bo2bo5bo2bo$58b3o352b
2o7b2o$57bo3bo4b2o76bobo241b3o$45bo10bo5bo82b2o241b3o27bo$44bo11b2obob
2o82bo243bo27bobo$44b3o342bo27bobo$24b5o360bo28bo$23bob3obo29bo328bobo
$24bo3bo29bobo100bo$25b3o30bobo98b3o$26bo20b5o7bo98bo229bobo$37bo8bob
3obo106bo229bo$37bobo7bo3bo7b2o95bo2bo229bo$37b2o9b3o8b2o94bo233bo$24b
o17b2o5bo105bobo218bo11b3o$8b2o14bo17b2o112bo218b3o10b3o$8b2o13bobo5bo
10b2o7b2o$22b2ob2o2bobo11bo7bo$21bo5bo2b2o10bobo7b3o19b2o77b2o3b2o215b
3o$6bo17bo16b2obo9bo19bo78bobobobo$7bo13b2o3b2o26bobo5bo9bobo79b5o216b
obo$7bo47b2o4bobo8b2o12bo68b3o217bobo$42b2o16bob2o23b2o67bo$23bo18b2o
15b2ob2o22b2o287b3o$5b2o3b2o11bo36bob2o$8bo13bo38bobo$5bo5bo50bo69b2o
241b3o$6b2ob2o23b2o95b3o237bo4bo$7bobo14b2o8b2o92bob2o238bobo$8bo15b2o
95b2o5bo2bo24b2o200b2o9bo3b2o6b2o$8bo112b2o5bob2o24b2o200b2o9bo3b2o5bo
bo$35bo95b3o6b2o227bo3b2o7bo10bo$34bobo95b2o6bobo227bobo19b3o$33bo3bo
104bo228bo19b2obo$33b5o8bo95b2o232b2o13b3o$32b2o3b2o7b2o327bobo14b2o$
10bobo20b5o7bobo20b3o282b3o21bo48b2o$11b2o21b3o33bo283bo71bo$5b3o3bo
23bo33bo284bo61b2o6bobo$4bo3bo344b3o59bobo5b3o$3bo5bo395b2o7bo6b3o$3b
2obob2o75b2o266b3o49b2o7bo2bo2bo2bo$72b2o10b2o267b3o58bo6b2o$18bo52bob
o12bo328bobo$19b2o52bo279b3o60b2o$16b2obo334bo$32b2o27bo292bo$18b2o13b
o25bobo291b3o$2b2o14bo11b3o15b2o10b2o287bo$30bo17b2o298bobo$336b2o10b
2obo7bo$116bo219b2o10b2ob2o6b2o$117b2o229b2obo6bobo$10b2o99bo4b2o230bo
bo$9bobo8b4o51b2o34b3o235bo$2o3b2o4bo3b2o7bo50b3o36bo217bo$2b3o10b2o2b
2o3bo52b2obo32b2o217bo$bo3bo13b2o2bo53bo2bo250b3o19b3o$2bobo72b2obo
274bo$3bo63b2o6b3o6b2o268bo$66bobo6b2o7bobo244b3o34bo$4b3o8bo10b2o38bo
19bo245bo35b2o$4b3o8b3o4b2o2b2o2b2o4b2o22b2o3b2o19b2o27b3o214bo34bobo$
18bo3b2o2bo2bobo3bobo22bobo51bo3bo213bo$17b2o9b3o6bo22bo52bo5bo212bo$
28b2o44b2o37b2obob2o20bo190b3o$2b2o3b2o31bobo27b2o2b2o2b2o58b3o$3b5o
33b2o27bobo2bo2b2o57bo$4b3o34bo29b3o9b2o8bo22bo21bo192b3o$5bo46bo19b2o
9b2o8b3o19bobo17bo2bo187bo5bo$19b3o28bobo43bo18bobo16bo191bobo3bo80b2o
$18bo3bo4b2o19b2o45b2o19b3o15bobo177b2o11bobo83b2o$17bo5bo3b2o19b2o12b
2o48b2o4b2o15bo178b2o11bo2bo5b3o$17b2obob2o24b2o12b2o47bobo4bo208bobo
8bo$43b2o5bobo60bo5b3o204bobo8bo$30b3o9bobo7bo68bo10b2o3b2o187bo$23bo
6bo11bo89bobobobo254bo$5b2o15b2o7bo9b2o32b2o56b5o171b3o80b3o$5b2o68bob
o5b3o48b3o255bob2o9bo8bo$21bob2o50bo6bo3bo48bo172bo3bo18b2o60b3o2bo5b
2o7b3o$20bo2b2o56bo5bo8b5o207bo3bo17bobo60b2o3b3o3bobo5b5o$20b4o57bo5b
o7bob3obo230bo68bo9bobobobo$38b2o32b2o22bo3bo18bo189b3o88b2o9b2o3b2o$
38bobo20b2o8bobo7bo15b3o18bo226b2o$19b2o3b2o12bo22bo11bo7b2o15bo19b3o
225b2o$22bo26bo9bobo19b2o226b3o33bo65b2o$19bo5bo21b4o8b2o19b2o2bo50b2o
274b2o$20b2ob2o12bobo6bobob2o29bobo11b2o38b2o171bo3bo97bo$21bobo13bo3b
o3bo2bob3o29b2o12bo211bo3bo97b3o$22bo18bo4bobob2o41b3o289b2o13b2o3b2o
7bo$22bo4b2o8bo4bo4b4o13b3o26bo209bo5b3o73b2o14b5o4b5o$27b2o12bo7bo16b
o12b2o3b2o217bobo87bo7b2ob2o6b2o$37bo3bo23bo13b2o3b2o206b2o12b2o84b3o
6b2ob2o$37bobo62bo189b2o12b2o6b2o69bo5b2obo7b3o$51b2o28b3o18bobo39bo
161b2o7b2o67b3o4b3o15b2o3b2o$22b2o27b2o4bo23b3o19bobo36b3o158bobo8bo
68bo3bo4b2o16b5o$22b2o16b2o6b2o6b5ob2o18bo7b2o11bo2bo34bo145bo15bo81bo
24b2ob2o$40b2o5b3o5bo2b2o4bo25b2o11bobo35b2o144b3o92bo5bo21b2ob2o$48b
2o5b2o8bo36bobo4b2o179bo91bo5bo22b3o6b2o$51b2o4bo7bo8b2o26bo6bobo177b
2o92bo3bo32b2o$51b2o12bo8b2o35bo272b3o12bo$64bo46b2o148bo137bobo3bo$
62b2o17b2o176bobo46b3o78b2o8b2o3b3o$81b2o167bo7bobo49bo79b2o11b5o$249b
2o6bo2bo11b2o35bo79bo12bobobobo2b2o$248b2o4b2o2bobo11b2o18bo30bo78b2o
3b2o2b2o7b3o$238b2o7b3o4b2o3bobo29b3o29b2o70b2o22b2ob2o$238b2o8b2o4b2o
5bo28b5o27bobo70bobo21b2ob2o$249b2o38b2o3b2o99bo23b5o$250bo167b2o3b2o$
262bo124bo$262b2o122b3o18b2o$108b2o142bo6b2ob2o27b3o92b3o18bo$108b2o
21b2o117bobo38b3o114b3o$123b2o6b2o110b2o4bobo6bo2bo122b2o3b2o11b3o5bo
8b2o$124b2o117b2o3bo2bo7bobo27b2o5bo87b2o3b2o11bo$123bo125bobo7bo2bo
27bo4b2o106bo9bo$250bobo7bo2bo23b3o5bobo114bobo$252bo10bo23bo99bo12bob
o8bob2o$261bo124bobo11bo2bo6b2ob2o$131bo253b2o4b2o10b2o6bob2o105b2o$
130b3o252b2o4b2o8bo3b2o5bobo104bo2bo$108bo8bo12b3o114bobo135b3o8b2o5b
2o8bo105bo$107b3o6b2o128bo2bo3b2o131bobo6bo4bo2bo115bo$106b5o7b2o8b2o
3b2o102b2o6b2o5b3ob2o2b2o24b2o99b2o11bobo116bobo$105b2o3b2o8bo7b2o3b2o
102b2o4b2o3bo3bo3bo3bobo14bo7bobo231bobo$106b5o7bobo124b2o5bobo8bo14bo
8bo232bo$106b5o8bo126bo2bo2b2o6bo2bo7b2o3b3o$107bo2bo17b2o117bobo13bo
7b2o27b2o$107bo3bo15bobo49bo80bobo38b2o214b2o3b2o$111bo14b2o49b3o80b2o
38bo216bo5bo$108b2obo7bo7b2o47bo$110bo7b3o6b2o47b2o151b2o187bo3bo$117b
5o8b3o125bo62bo7bo2bo186b3o$116b2o3b2o135b3o59bo3b2o7bo9bobo$107b2o3b
2o3b5o139bo58bo5bo6bo7bo3bo$107bo5bo3bo3bo138b2o59b5o7bo7bo$118bobo
208bo2bo7bo4bo8b2o$108bo3bo6bo6b2o3b2o165b2o18b2o9b2o10bo12b2o$109b3o
185bobo17b2o22bo3bo176b2o$127bo3bo164b3o20bo12bobo8bobo176bo$118b2o8b
3o164b3o34b2o189b3o$118b2o8b3o165b3o34bo191bo$288b2o7bobo5b2o$287bobo
8b2o5bobo28bo$287bo19bo27bobo$110b2o174b2o19b2o24b2o3bo$110b2o16b2o13b
2o118b3o67b2o3bo9b2o$128b2o13b2o21b2o77b2o18bo67b2o3bo9b2o$158bo7b2o
76bobo17bo70bobo$158b2o70bo12b3o4b2ob3o80bo$157bobo65bo4b4o8b3o4bo2b4o
$225bo5b4o8b3o4b2o$220b2o9bo2bo9bobo86b2o9b2o$220b2o9b4o10b2o85b2o9bob
o$230b4o8bo84bo6bo7b3o4b2ob3o$166bo63bo12bo82bobo12b3o4bo2b4o$149bobo
13b3o73b3o75b2o3b2o3bo12b3o4b2o$149bob2o11b5o150b2o3b2o3bo13bobo$141b
5o5b2obo8bobobobo154b2o3bo14b2o$140bob3obo5bo2bo7b2o3b2o69bo5b2o79bobo
$141bo3bo6bo2bo82bobo4b2o80bo$142b3o9bo83b2obo$143bo19b2o61b2o10b2ob2o
$144b2o17b2o33bo27b2o10b2obo$144bobo15bo33bobo39bobo$144bobo15b3o32b2o
40bo$145bo20bo$152b5o5b5o$151bob3obo6b2o64b2o9b2o$142b2obob2o3bo3bo73b
obo7bobo$142bo5bo4b3o65b2o2b2o6bo8bo5bo$143bo3bo6bo6b2o3b2o53b2obo2bo
2bo2bo13bobo$144b3o15b5o58b2o6bo13b2obo4b2o$162b2ob2o63bobo14b2ob2o3b
2o$162b2ob2o63b2o15b2obo$153b2o8b3o81bobo$153b2o93bo4$145b2o$145b2o16b
2o$163b2o18$295bo$293bobo$284bo7bobo$283b2o6bo2bo11b2o161b2o162bo$282b
2o4b2o2bobo11b2o159bo2bo161bobo$272b2o7b3o4b2o3bobo170bo7b5o153bobo$
272b2o8b2o4b2o5bo170bo6bo5bo153bo$283b2o181bo7b2o3bo$284bo172b3o7bo2bo
7bo149b2o7b2o$296bo159b2ob2o8b2o156bo2bo5bo2bo$297bo158b2ob2o38bo128b
2o7b2o$286bo8b3o158b5o37b4o$284bobo168b2o3b2o19b2o14b2obobo130bo$277b
2o4bobo195bo2bo11b3obo2bo2b2o124bobo$277b2o3bo2bo187b5o7bo11b2obobo3b
2o124bobo$283bobo171b2o13bo5bo6bo12b4o131bo$284bobo169b5o11bo3b2o7bo7b
o5bo$286bo169bo6b2o8bo7bo2bo9bo$293b2o163b3o3bo16b2o9b3o$293b2o165bo3b
obo9bo$458b2o5b2o8b4o$281bobo174b2o14b2ob4o5b2o$280bo2bo3b2o184b3ob2o
3bo3bo2bo$271b2o6b2o5b3ob2o2b2o178b2ob2o3bo7bo$271b2o4b2o3bo3bo3bo3bob
o156b2o3b2o15b5o3bo6bo10bo$279b2o5bobo8bo155bobobobo16bo3b3o7bo8bobo$
280bo2bo2b2o6bo2bo7b2o147b5o5bobo19bo2bo5b2o3b2o$281bobo13bo7b2o148b3o
7b2o19b2o7bobo$294bobo159bo8bo31bo$294b2o201b2o$270bo201bo$270bobo202b
o$253b2o18b2o44bo4b2o146bo14bo2bo15bob2o7bo2bo86bo2bo$251bo3bo17b2o4b
2o36bobo4b2o149bo15bo13bo3bo11bo41b4o44bo$245b2o3bo5bo16b2o4b2o37b2o
154bob3o8bo3bo10bo4b2o8bo3bo40bo3bo40bo3bo$245b2o2b2obo3bo8bo4bobo183b
2o14b4o2bo9b4o13b2o11b4o44bo41b4o$250bo5bo9bo3bo185b2o19bo24bo2bo56bo
2bo$251bo3bo5bo2b3o198bo155b8o$253b2o209b2o155bob4obo$453b2o8b2o4b2o5b
o144b8o$453b2o7b3o4b2o3bobo130b2o$261bo201b2o4b2o2bobo11b2o119b2o$261b
obo200b2o6bo2bo11b2o118bo$250b2o12b2o199bo7bobo$250b2o12b2o208bobo$
264b2o210bo125b2o$261bobo5b2o332b2o$261bo7b2o331bo3$265b2o343bo4bo$
253b2o9bobo341b2ob4ob2o$253b3o10bo343bo4bo$244b2o9b2obo11bo69bo235b2o$
244bo5bo4bo2bo10b2o70bo233bobo$249bo5b2obo9b2o4b2o62b2o5b2o230bo$245bo
3bo3b3o11b3o4b2o2b2o58b3o4b3o$247bo5b2o13b2o4b2o2b2o51bo7bo7b2obo251b
3o$269b2o17bo40bobo15bo2bo5b2o243bo3bo$270bo15bobo33b2o4bobo9b3o4b2obo
5b2o242bo5bo$287b2o33b2o3bo2bo8b2obo2b3o252b2obob2o$328bobo7bo3bo2b2o$
269b2o58bobo6bo2bo244b2o$269bo2bo58bo8b2o243bobo15bo$587bo14bobo$273bo
328bobo$336b2o265bo$271b2o63b3o241bo$270bo11b3o42b2o9b2obo238b2o21b2o$
284bo42bo5bo4bo2bo237bobo21b2o$283bo48bo5b2obo$267b2o3b2o54bo3bo3b3o7b
2o$267b2o3b2o56bo5b2o8b2o147b2o91bobo2bobo$268b5o204b2o16b2o87b2obo2bo
2bo2bob2o$269bobo205b2o109bobo2bobo2$269b3o58b2o9b2o210b3o$283bo46bobo
7bobo152b3o57bo$283b2o36b2o2b2o6bo8bo5bo136b2o8b3o56bo$282bobo36b2obo
2bo2bo2bo13bobo127bo7b2o7bo3bo83bo$325b2o6bo13b2obo126bo15bo5bo81b3o$
267b2o61bobo14b2ob2o3b2o119bobo7bo7bo3bo81b5o$268bo61b2o15b2obo4b2o
118b2ob2o5bobo7b3o81b2o3b2o$265b3o79bobo124bo5bo4bobo$265bo82bo128bo8b
o78bo$379bo94b2o3b2o84b2o$378bobo183bobo14b3o$370b2o5bo3b2o100b2obob2o
6bobo82b3o$254bo108bo5bo2bo4bo3b2o3b2o87b4o4bo5bo5bo2bo$252bobo107bobo
5b2o5bo3b2o3b2o87bo2b2o4bo3bo4bob2o$242b2o6b2o12b2o84b2o9bo3b2o11bobo
95bob2o5b3o69b2o23b2o$241bo3bo4b2o12b2o18bo15bo49b2o9bo3b2o3bo8bo116bo
61b2o22b2o$240bo5bo3b2o31b2o13bobo60bo3b2o2b2o106b2o14b2obo60bo$230b2o
8bo3bob2o4bobo28bobo5b2o4bobo17bo44bobo4bobo106bo16bo$230b2o8bo5bo7bo
36b2o3bo2bo16b2o45bo200bo2b2o4b2o2bo$241bo3bo51bobo15b2o4b2o240bo3b3o
2b3o3bo$242b2o54bobo13b3o4b2o2b2o145b2obob2o16b2o3b2o62bo2b2o4b2o2bo$
300bo4bobo7b2o4b2o2b2o51bo7bo85bo5bo9b2o6b5o$305b2o9b2o59b4o5bobo84bo
3bo10b2o6b2ob2o30b2o$306bo10bo54b2o2bo2b2o8b2o4b2o77b3o19b2ob2o29bobo$
247b2o11b2o110b2o2b2o11b2o4b2o100b3o32bo$245bo2bo12b2o106b2o10bo7b2o$
244bo7b2o6bo107b3o10bo4bobo171b3o$236b2o6bo6bo2bo45b2o8b2o35bo21b2o10b
o4bo172bo3bo$236b2o6bo7b2o46b2o8b2o4b3o28b3o13b2o7b2o184bo5bo$245bo2bo
58b2o6b5o30bo11bobo7b2o184bo5bo$247b2o57b3o5bo3bobo28b2o11bo135b2o61bo
$253bo53b2o6bo3b2o40b2o112b2o21b2o43b3o13bo3bo$253b2o55b2o41bo121b2o
68bo14b3o$241bobo8bobo55b2o41bo190bo16bo$241bo3bo106bo$231b2o12bo10b2o
$231b2o8bo4bo7bo2bo7bo41bo7bo183bo35bo25b2o$245bo7bo7b2o3bo39b4o5bobo
31b2o3b2o144bo34b2o24b2o$241bo3bo7bo6bo5bo34b2o2bo2b2o8b2o4b2o23bo5bo
142b3o33bobo$241bobo9bo7b5o35b2o2b2o11b2o4b2o$254bo2bo32b2o6b2o10bo7b
2o30bo3bo188b2o3bo2bo3b2o$256b2o32b2o5b3o10bo4bobo33b3o189b5o4b5o$298b
2o10bo4bo227b2o3bo2bo3b2o$301b2o184bo$301b2o184b3o$490bo17b3o$349b2o
138b2o19bo$350bo158bo$347b3o190bo$347bo144bo46b3o$492bo45b5o$491bobo
43b2o3b2o$490b2ob2o43b5o$489bo5bo26b2o14bo3bo$492bo30b2o14bobo$489b2o
3b2o26bo17bo$527b2o$527b2o$524b2o14b2o$512b2o9b3o14b2o$513b2o9b2o$512b
o4b2o8b2o5b2o$489b2o25bobo8b2o5bobo$490bo25bo19bo$487b3o25b2o19b2o$
487bo$397b2o$395bo3bo$394bo5bo101bo$381b2o10b2obo3bo8b2o90b2o$379bo3bo
10bo5bo8b2o90bobo$373b2o3bo5bo10bo3bo$373b2o2b2obo3bo12b2o$378bo5bo$
379bo3bo$381b2o$395b3o$395bo$396bo9bo121b2o$405bobo97b2o21b2o$393bobo
8bob2o10b2o85bo2bo$393bo2bo6b2ob2o10b2o70bo$396b2o6bob2o82b2o17bo19bo$
394bo3b2o5bobo81bobo36b3o$370bo25b2o8bo100b2o18bo3bo$370b3o13b2o5bo2bo
109bo22bo$373bo11bobo5bobo130bo5bo$372b2o11bo140bo5bo$384b2o117b2o3b2o
5b2o10bo3bo$503b2o3b2o5b2o11b3o$497b2o5b5o3bo$497bobo5bobo4b2o4bo5b2o$
374b3o122bo11bobo3b3o3b2o$499b2o4b3o8bo3bo4bo$374bobo141bo$373b5o81b2o
54bo5bo$372b2o3b2o80b2o21b2o31bo5bo$372b2o3b2o103b2o32bo3bo$508bo8b3o$
507bobo17bo$506bo3bo15b3o$507b3o16b3o$482bo22b2o3b2o$372b2o108bo41b2o
3b2o$373bo85bo7b2o12bobo40b2o3b2o$370b3o85b3o7b2o10b2ob2o$370bo86b5o5b
o11bo5bo$456b2o3b2o19bo35b2o7bo$474b2o3b2o3b2o32b2o6bobo$474b2o52b2o$
461b2o65b2o$463bo14b3o46b3o$460bo16b2obo45bobo$460bo2bo6bo6b2o29b2o16b
2o$459b2ob2o5b3o6b2o28b2o$460b2o6b5o6bobo$467b2o3b2o5bo2b2o2$458b2o3b
2o$458b2o3b2o$459b5o5b3o$460bobo6b3o$478b5o$460b3o14bob3obo$469b2o7bo
3bo$469b2o8b3o$480bo3$461b2o$461b2o16b2o$479b2o!

So by more piping, we can create extra growth rates. This prompted Dean Hickerson to say the following:

The quadratic filter is a great idea! I wish I'd thought of it.

Anyway, Gabriel Nivasch decided to create an exponential filter, with the property that:

• S(X | exponential_filter) = 2^S(X)

By piping copies of this, you can get slowness rates of Θ(2^2^...^n), or growth rates of Θ(log log ... log(t)).

For instance, he created a growth rate of log(log(t)) by piping a caber tosser into an exponential filter:

• S(caber_tosser | exponential_filter) = 2^S(caber_tosser) = λn.Θ(2^2^n).

Code: Select all

x = 738, y = 774, rule = S23/B3
397b4o3b2o$396bo6bo2bob3o$396b5o2bo2bo$403bo2bo$404bo$386b2o17bobo$
386b2o18bo3$422bo$422bo$422bo$418bo$378b2o37bo2b3o$378b2o38bo4bo$419bo
3bo$420b3o2$412bo$411b3o7bobo$410bo2bo7bobo$370b2o39b3o7bobo$370b2o39b
3o7bobo$409bob2obo6b2o$408b3o2bo$407b2ob4o$408b3obo10b4o3b2o$408b3o11b
o6bo2bob3o$379bobo26b2o12b5o2bo2bo$379b3o47bo2bo$380b2o48bo$412b2o17bo
bo$410bob2o18bo$378bo31b4o$378bobo30bo$378b3o$377bo$377b5o3$384bo6b3o
20bobo$384bob2o3b2o20bo3bo$384bobo5b2o18bo4bo7b3o$384bob3o23bo4bo6b4o
3b2o$384b2o26bo3bo6bo4bo3b2o$413bo2bo7b2ob2o$425b4o$427bo4$424b2o$424b
2o2$405bobo$405b3o$406b2o3$404bo11b2o$404bobo9b2o$404b3o$403bo$403b5o
4$408b2o$408b2o79$495bo$494bobo$494bobo$495bo2$490b2o7b2o$489bo2bo5bo
2bo$490b2o7b2o2$495bo$494bobo$494bobo$495bo13$440b3o$440bobo$440b3o$
440b3o$440b3o$440b3o$440bobo$440b3o8$441b2o$441bobo$441bo12$439b2o$
440b2o$421bo17bo$421b3o$424bo$423b2o4$463b3o$408b3o52bo$408b3o53bo$
409bo15b3o$409bo15bo2bo$409bo15bo$408bobo14bo$426bobo2$408bobo11bo$
409bo11bobo$409bo$409bo$408b3o6bo$404bo3b3o6b2o$403b4o9bobo$391b2o9b2o
bobo$391b2o8b3obo2bo$402b2obobo$403b4o$404bo2$387bo98b2o$386b3o97bobo$
486bo2$386b3o2$386bobo$386bobo$399b3o$386b3o12bo$400bo2$386b3o$382bo4b
o$381bobo10b2o$369b2o9bo3b2o9b2o$369b2o9bo3b2o8bo$380bo3b2o$381bobo24b
3o$382bo27bo$409bo2$364b3o$365bo142b3o$365bo142bo$364b3o142bo$186bo
238b3o$186b2o176b3o57bo2bo$185bobo176b3o60bo$377b2o48bo$364b3o11b2o44b
obo$365bo11bo$365bo$364b3o$360bo$359bobo$347b2o10b2obo9bo$347b2o10b2ob
2o8b2o$359b2obo8bobo$359bobo223b2o$127b2o231bo25b2o197bo2bo$127b2o214b
o41bobo183bobo15bo$343bo43bo181bo3bo2b3o10bo$342b3o224bo19bo$127bo434b
2o4bo4bo7b2o2bo2bo5b2o$126b3o402b2o29b2o5bo7bobo2bo2b2o7bobo$125bo3bo
212b3o186bobo35bo3bo5b3o14bo$127bo215bo187bo39bobo22b2o$124bo5bo212bo$
124bo5bo212bo$125bo3bo213bo11b2o219b2o7bo$126b3o213b3o9bobo211bo7bo2bo
5bo$356bo210bo3b2o7bo2bobo$567bo5bo6bo2bo$342b3o223b5o7bo3bo$337bo5bo
232bo2bo$129bo207bobo3bo232b2o$325b2o11bobo$325b2o11bo2bo254bo$129bo
208bobo8b2o243bobo$127bobo207bobo10b2o217b2o24b2o$128b2o190bo16bo11bo
217bo3bo5bo2b3o$320b3o238b2o3bo5bo9bo3bo$323bo39b3o195b2o2b2obo3bo8bo
4bobo$322b2o41bo200bo5bo16b2o$122b2o3b2o235bo202bo3bo17b2o4b2o$136bo
156bo275b2o18b2o4b2o$123bo3bo9bo154bobo291bobo$124b3o8b3o144b2o7bob2o
258b3o30bo$124b3o154bobo6b2ob2o10b2o246bo$280bo6b3obob2o10b2o17b3o227b
o$143bo127b2o7bo2bo2bo2bo2bobo28bo3bo5bo91b3o186b2o$118bo8b2o12b3o127b
2o7bo6b2o4bo28bo5bo4b2o90bo2bo185b2o$118b3o6bo12bo140bobo38b2obob2o3bo
bo90bo$121bo6b3o9b2o140b2o141bo$120b2o8bo295bobo17b2o$294bobo28bo120b
2o$284bo10b2o27bobo$123bo159bobo9bo28bobo105b2o$121b2ob2o14bo135b2o4bo
b2o37b3o106bobo$140b3o133b2o3b2ob2o36b2o108bo185bo$120bo5bo16bo138bob
2o37bo3bo291bo$142b2o139bobo34b3o4b2o288b3o$120b2obob2o3b2o152bo35bo5b
obo$292b2o137bo$133bo158b2o47b2o88b3o10b2obob2o$126b2o212bobo82b3o6bo
4b3o$125bobo153bo60bo81bo2bo5b2o4bo4bo5bo$126bo15b2obob2o129b4o3bob2o
63bo74bo6b3o3bo$125b2o15bo5bo121b2o5b4o4bobob2o2b2o55b4o73bo7bobo7b2ob
2o$125b3o15bo3bo122b2o5bo2bo3b2obob2o2bobo48b2o3bobob2o14b2o53bobo7bo
3bo8bo128b2o$126b2o12bo3b3o130b4o3b2o8b3o47b2o2bo2bob3o11bo2bo63b5o
137bobo59bo$124bo14b2o137b4o3b2o8b3o6b2o43bobob2o11bo7b5o54b2o3b2o136b
o59b3o$139bobo139bo12b3o7b2o44b4o12bo6bo5bo54b5o6bo189bo$293bobo56bo5b
o7bo7b2o3bo38b2o15b3o6bobo188b2o$293b2o48b2o12bo9bo2bo7bo39b2o16bo6bo
3bo$125bo217bobo11b3o9b2o72b5o$124b3o216bo98b2o3b2o$123b5o163bo25bo
125b5o$122b2o3b2o14bo147b3o24b2o117bo6b3o$123b5o15bo150bo22b2o44bo70b
2o9bo$123bo3bo14bobo148b2o65b4o4bo48b3o5b3o6b3o196bo$124bobo14b2ob2o
213b4o5bo56bo2bo6b2o195b3o$125bo14bo5bo184b2o26bo2bo9b2o43bobo5bo9bo
17b2o176b5o$143bo145bo14b2o23bo2bo26b4o9b2o42b5o4bo8bobo16b2o167bo7b2o
3b2o$140b2o3b2o141bobo14b2o21bo31b4o51b2o3b2o4bobo5b2o184b2o$125b2o
144b2o14bo3b2o3b2o6bo23bo34bo51b2o3b2o199b2o$125b2o144bobo13bo3b2o3b2o
30bo303bo$144bo121b2o4b3o12bo3b2o28b2o6bo2bo5b2o95b2obob2o190bo$144bo
117b4o2bo4b3o12bobo29bobo8b2o5bobo17bo2bo8bo49b2o22b2o$145bo116b3ob2o
4b3o7bo6bo30bo19bo17bo10bobo48bob2o11bo5bo2b2o189b2o$181bo89bobo9b2o
34b2o19b2o12bo2bo3b2o5bo3b2o3b2o44bo211bo$182bo88b2o9b2o67b4o3b2obobo
4bo3b2o3b2o57b2ob2o195b3o$142b2o36b3o160b2o5b4o14bo3b2o44bob3o8bo6bo
15bo143b3o37bo$142b2o199b2o5bo2bo8b2o5bobo46bo11b2o21b3o142bo$350b4o
16bo47bo11bobo19b5o142bo$277bobo7b2o62b4o85b2o9b2o3b2o$272bo4bo2bo6b2o
65bo85bo11b5o$273b2o5b2o159b3o8bo3bo142b2o$268b2o8bo3b2o159bo9bobo142b
o3bo$268b2o10b2o135b2o3b2o30bo142bo5bo$277bo2bo138b3o16b2o9b2o136b2o8b
o3bob2o10b2o$277bobo138bo3bo14b2o9bobo136b2o8bo5bo10bo3bo$419bobo10bo
6bo7b3o4b2o142bo3bo10bo5bo3b2o$420bo10bobo12b3o4bo2bo142b2o12bo3bob2o
2b2o$271bo9b2o141b2o3b2o3bo12b3o4b2o157bo5bo$270bobo7b4o140b2o3b2o3bo
13bobo163bo3bo$263b2o4bob2o5b3o2bo2bobo140b2o3bo14b2o156bobo5b2o$263b
2o3b2ob2o9b2o2bo2bo130b2o9bobo166b3o5b2o$269bob2o6bo9b2o6b2o121b2o10bo
169bo5bo$270bobo5bo8bo3b2o4b2o292bo9bo$271bo6bo10b2o299bobo$286bo2bo
288b2o10b2obo8bobo$286bobo289b2o10b2ob2o6bo2bo$590b2obo6b2o$377b2o3bo
2bo3b2o199bobo5b2o3bo$377b5o4b5o200bo8b2o$374bo2b2o3bo2bo3b2o210bo2bo
5b2o$373bobo226bobo5bobo$372bo3bo235bo$341bo30b5o235b2o$341b3o27b2o3b
2o$344bo27b5o$343b2o28b3o$374bo354bo$728bobo$728bobo$729bo2$630bo93b2o
7b2o$631b2o90bo2bo5bo2bo$630b2o92b2o7b2o$344b5o$343bob3obo24b2o353bo$
275b2o19b2o46bo3bo25b2o352bobo$276bo19bo48b3o380bobo$276bobo6bobo6bobo
49bo382bo$277b2o6bo2bo5b2o$288b2o$286bo3b2o51b2o$288b2o54bo$285bo2bo
52b3o$285bobo53bo9$316b2o19b2o$317bo19bo314bobo$317bobo6b2o7bobo315b2o
$318b3o5bobo6b2o316bo$320b3o6bo$320bo2bo2bo2bo$321b2o6bo$326bobo$326b
2o4$262bobo$262bo3bo$256b2o8bo132bo$246bobo6bo2bo3bo4bo4b2o123b3o$246b
o3bo5b2o8bo5b2o122bo$236b2o12bo11bo3bo129b2o$236b2o8bo4bo10bobo$250bo
6bo$246bo3bo5b2o$246bobo7bobo2$391b2o3b2o277bo$270b2o122bo281b2o$263bo
b2o3b3o118bo5bo277b2o$259bo2bo3bo5b2obo5b2o109b2ob2o$258b2o2bo4bo4bo2b
o5b2o110bobo$257b2o5b4o4b2obo118bo$256b3o7bo3b3o121bo$257b2o11b2o$249b
2o7b2o$248bobo8bo$248bo147b2o$247b2o147bo$397b3o$399bo10$697bobo$698b
2o$698bo6$377b2o$376b3o$373bob2o$373bo2bo$373bob2o$367b2o7b3o5b2o$366b
obo8b2o5bobo$366bo19bo$365b2o19b2o6$720bo9bo$659b2o6b2o52b2o5b3o$658bo
2bo4bo2bo50b2o5bo$657b6o2b6o56b2o$641b3o14bo2bo4bo2bo$643bo15b2o6b2o
11b2o43bo$642bo30bo5b2o43bobo$671b2ob2o5bo41bo3bo$723b5o$670bo5bo45b2o
3b2o$723b5o$670b2obob2o47b3o$725bo$374b2o$376bo$363b2o12bo$363b2o4bo7b
o8b2o$352b2o6b2o5b2o8bo8b2o$352b2o5b3o5bo2b2o4bo$360b2o6b5ob2o351b2o$
363b2o4bo302b2o53bo$363b2o307b2o54b3o$730bo2$365b2o9b2o315bo8bo$363bo
3bo7b3o315bobo6bobo$357b2o3bo5bo5b2o243b2o75b2o4b2o$357b2o2b2obo3bo3bo
2bo242bobo61b2o12b2o11bo$362bo5bo4b2o245bo61b2o12b2o11bobo$363bo3bo
325bobo16b2o4b2o$365b2o326bo18b2o4b2o$385bo326b2o$383bobo323bobo$384b
2o323bo$360bo8b2o$358bobo6bo2bo323b2o$351b2o4bobo7bo3bo2b2o306bobo10b
2o$351b2o3bo2bo7bo2b2o2b3o305bo2bo8bo$357bobo16b2obo293b2o10b2o11b2o$
358bobo4b3o8bo2bo5b2o286b2o8bo3b2o8bobo$360bo15b2obo5b2o291b2o5b2o9bo$
374b3o300bo4bo2bo10bo2bo$374b2o306bobo11bo$697bobo5b2o$698b2o5bobo$
376b2o329bo$376b2o329b2o8bo$718bo$716b3o$596b3o$377bo220bo$376bobo218b
o129b2o$375bo3bo347b2o4b3o$376b3o334bo10b2o6b5o$374b2o3b2o332bobo7b3o
5bo3bobo$702b2o12b2o6b2o6bo3b2o$702b2o12b2o9b2o$716b2o9b2o$713bobo$
713bo11bo$723bobo$379b3o342b2o$381bo336b2o$380bo337b2o$374b2o331b2o6b
2o6b2o$375bo331b2o5b3o5bo2bo$372b3o340b2o6b2o$372bo345b2o$718b2o$724b
3o$380bo345bo$363b2o15b2o192b2o149bo$123bo238bo3bo12bobo191bobo137bo$
123b3o220b2o13bo5bo3b2o202bo136b2o$126bo212b3o4b2o13bo3bob2o2b2o37bo
290b2o8b2o4b2o5bo$125b2o211b5o6b2o10bo5bo41b2o290b2o7b3o4b2o3bobo$337b
obo3bo5b3o10bo3bo31b2o8b2o11b2o288b2o4b2o2bobo$337b2o3bo6b2o12b2o33b2o
7b3o7bo3b3o288b2o6bo2bo11b2o$346b2o9bobo48b2o5b4o4b2obo286bo7bobo11b2o
$346b2o10b2o49b2o2bo4bo4bo2bo5b2o288bobo$358bo51bo2bo3bo5b2obo5b2o290b
o$414bob2o3b3o$421b2o$353bobo6b2o$125b2o3b2o221bo3bo4b2o37bo$357bo42b
2o$126bo3bo212b2o8bo4bo41bobo14bo$127b3o213b2o12bo59bobo$127b3o223bo3b
o52b2o8b2o$353bobo53bo2bo7b2o4b2o$409b3o8b2o4b2o$125b2o283b2o5bobo$
126bo219bo61bobo6bo$123b3o218b4o6b2o2b2o47b2o$123bo214b2o3bobob2o5b4ob
o2bobo44bo141b3o$338b2o2bo2bob3o5b2obo3bo3bo52b2o132bo$343bobob2o4bo
12bo5b2o43bo3bo130bo$344b4o14bo4bo4b2o34bo7bo5bo8b2o$346bo19bo41bobo4b
2obo3bo8b2o$362bo3bo30b2o12b2o3bo5bo$165b2o195bobo32b2o12b2o4bo3bo$
165b2o4b3o237b2o6b2o$162b2o6b5o233bobo$149b2o7b2ob3o5bo3bobo232bo$149b
2o11b2o6bo3b2o$138b2o6b2o17b2o$138b2o5b3o5b2o10b2o$146b2o9b2o$149b2o$
149b2o3$163b2o9b2o$163bobo7bobo$157bo5bo8bo6b2o2b2o$156bobo13bo2bo2bo
2bob2o$155bob2o13bo6b2o348b2o$154b2ob2o14bobo352bobo$155bob2o15b2o354b
o$151b2o3bobo$150bobo4bo$150bo$149b2o5$26bo$26bobo$9bo17bobo$9b2o16bo
2bo3b2o$4b2o4b2o15bobo4b2o$2o2b2o4b3o13bobo22b2o$2o2b2o4b2o7bobo4bo24b
3o$9b2o9b2o28bo3b2o$9bo10bo30b2o3bo$3b2o23b2o21b2o3bo61b2o88b2o88b2o
88b2o88b2o$3b2o22b4o13b2o7b2o19b2o41b4o43b2o41b4o43b2o41b4o43b2o41b4o
43b2o41b4o$3b2o22b2ob2o10b2ob2o6b3o16b2ob2o40b2ob2o40b2ob2o40b2ob2o40b
2ob2o40b2ob2o40b2ob2o40b2ob2o40b2ob2o40b2ob2o$3bo25b2o11b4o7b3o16b4o
43b2o41b4o43b2o41b4o43b2o41b4o43b2o41b4o43b2o25b3o$2bobo38b2o9bo18b2o
88b2o88b2o88b2o88b2o73bo9b2o$2bobo10b3o36b2o451bo10bobo$3bo13bo33bob3o
464bo$16bo27b2o474b2o$44bo6bo$2o3b2o16b3o9b2o5bobo$obobobo16bo9bo2bo5b
2o$b5o12bo5bo7bo447b2o$2b3o3b2o6b4o12bo448b2o$3bo3bobo5bobob2o11bo89bo
bo355bo$9bo4bo2bob3o11bo2bo6b2o75bo3bo$14b2obob2o14b2o7b2o74bo$12b3ob
4o23bo75bo4bo8b2o$11bobo4bo101bo12b2o$11bo18b2o88bo3bo376bo2bob2obo2bo
$10b2o16bo2bo84bo5bobo375b2o2bo4bo2b2o$19b2o6bo7b3o3bo73b3o372b2o9bo2b
ob2obo2bo$4b3o12b2o6bo6bo3b5o53bo17bobobo372b2o3b3o$3b2ob2o19bo7bo3b2o
b2o9b2o39bobo17bobobo371bo5b3o$3b2ob2o20bo2bo3bo3b2ob3o8b2o37b2o21b3o
377bo3bo$3b5o22b2o5b4ob2o48b2o22bo377bo5bo$2b2o3b2o30b4o49b2o390b2o9bo
3bo$41bo46b2o4bobo8b2o376bobo10b3o$14b2o71bobo6bo8bobo8bo368bo$14bo2bo
69bo19bo7b3o$5b6o7bo6b2o59b2o19b2o5bobobo$4bo6bo6bo6b2o87bobobo$4bo4b
2o7bo96b3o$5b2o7bo2bo98bo$14b2o442bo$458b2o$457bobo$497b2o$497b2o3$
480bo2bob2obo2bo$480b4ob2ob4o$469b2o9bo2bob2obo2bo$468bobo5bo$470bo4b
3o$474bo3bo$473bob3obo$474b5o$461b3o$398b2o63bo$380b2o16b2o62bo$380b2o
16b2o$399bo$398bobo$398bobo$380bo7b2o9bo$379b3o6b2o45b2o$378bo3bo53b2o
$377bob3obo12b2o3b2o32bo40b2o$378b5o8bo4bobobobo73b2o$390bo6b5o$390bo
7b3o$399bo59bo2bo4bo2bo$457b3o2b6o2b3o$386b2o3b2o55bo10bo2bo4bo2bo$
377b2o2bo7bo58b2o5bo$379bobo4bo5bo54bobo4bobo$381b2o4b2ob2o61bo3bo$
382b2o4bobo63b3o$380bob2o5bo6bobo53b2o3b2o$380b3o6bo6b2o41b2o$397bo40b
obo$440bo$375b2o3b2o$378bo12b2o7b3o$375bo5bo9b2o6bo3bo$376b2ob2o17bo5b
o$377bobo19bo3bo$378bo21b3o10bo$378bo21b3o10b2o$412bobo40b2o$455b2o2$
401b2o36b2o6b2o$378b2o21b2o34bo4bo2bo4bo$378b2o57bo4bo2bo4bo$437bo4bo
2bo4bo$381bo44b3o10b2o6b2o$381b3o44bo4b3o$384bo42bo5b3o$383b2o47bo3bo$
402bobo$403b2o26b2o3b2o$403bo12b3o$418bo$417bo$383b2o3b2o$383bobobobo$
384b5o$385b3o$386bo32bo$390b2o27b2o$391b2o21b2o4b2o12b2o$390bo23b2o4b
3o11b2o$414b2o4b2o$411b2o6b2o7b2o$383b2o25bobo6bo8bobo$384bo25bo19bo$
381b3o25b2o19b2o$381bo6$394b2o$393bobo$395bo5$422b2o$399b2o21b2o$399b
2o$407b3o$407bo$408bo3$362b2o$362b2o21b2o$385b2o12b3o13b2o$398bo3bo12b
3o$391b2o4bo5bo8b2o6b2o3b2o$391bobo3b2obob2o7bo3bo6b3o$385bo7bo17bo3bo
5bo3bo$361b3o20b3o6b2o17b2o8bobo$371b3o9bo3bo15bo19bo$361bobo9bo8bob3o
bo13b2o$360b5o7bo10b5o32b3o$359b2o3b2o35bob2o15b3o$359b2o3b2o34bo2b2o$
377b2o21b4o5b2o3b2o$377b2o32b3o$364b2o14b3o27bo3bo3b2o3b2o$364bob2o4b
3o5bo18b2o3b2o5bobo5b5o$367bo13bo20bo9bo7b3o$372bobo24bo5bo15bo$362bob
3o4b5o24b2ob2o$362bo7b2o3b2o24bobo$362bo7b2o3b2o25bo9b2o$402bo9b2o2$
373bo8b3o$374b2o5bo3bo$361b2o3b2o12bo5bo33b2o$363b3o10bo3b2obob2o15b2o
16b2o$362bo3bo35b2o$363bobo6bo2bo$364bo7b2o9bo$382bobo$382bobo$383bo$
364b2o$364b2o16b2o$382b2o!

Gabriel Nivasch, Dean Hickerson and Dan Hoey then wondered about the possibility of slower growth rates, but none made the conceptual leap necessary to do so:

There are even slower-growing functions--log**, log***, etc.

Alexey has finally resolved this 9-year-old open problem by constructing what I shall name a recursive filter. It does the following:

• S(X | recursive_filter) = g, where g(n) := f(f(f(...f(1)))), where the number of 'f's is equal to n, and f := S(X).

If you want to, you can express this with lambda calculus:

• S(X | recursive_filter)(n) = n(S(X))(1) where we treat n as a Church numeral.

Anyway, an explicit example is the log* pattern he posted:

• S(caber_tosser | recursive_filter)(n) = λn.(2 ^^ n).

We can get extra arrows by piping extra recursive filters:

• S(caber_tosser | recursive_filter | recursive_filter)(n) = λn.(2 ^^^ n).

Indeed, for every primitive-recursive function f, we can now obtain a slowness rate S(X) which asymptotically dominates f. That is what Alexey has done.


So, simsim314, I shall politely request that you do not belittle work that solves a decade-old engineering problem in such a beautiful and elegant manner. You have made many great contributions to Life research (I'm in awe of CatForce, for instance), but that does not give you the right to insult others when they do the same. I think you owe Alexey an apology.

[simsim314]

Alexey has finally resolved this 9-year-old open problem by constructing what I shall name a recursive filter...in such a beautiful and elegant manner.

Putting it this way...well I really didn't knew people did tried to solve it, or there was some quest for it. Well then it's great discovery! Congrats to Alexey, and sorry for the mistake.

It would be nice if someone would update the wiki on this issue with more historical background on the topic.

EDIT

I shall politely request that you do not belittle work

I certainly had no intention to belittle anyone's work. But it's extremely hard to get high quality information on this topic. Even Dean Hickerson's collection has no wiki articles for many of his major discoveries.

[calcyman]

Putting it this way...well I really didn't knew people did tried to solve it, or there was some quest for it. Well then it's great discovery! Congrats to Alexey, and sorry for the mistake.

Good. I appreciate that you were trying to maintain high notability standards on the LifeWiki (which seems to be necessary, given the amount of recent vandalism); thanks for clarifying your intentions. I'm sorry that I came across as rather harsh, but I didn't want the discovery to go under-appreciated.

By the way, I would also like to co-congratulate Kiran for proposing the idea in the first place (with the post beginning with 'what if actual turtles are used?). Essentially, this post replaced the original blueprint (for an exponential filter) with a new one (for a recursive filter). This is quite serendipitous, as exponential filters already existed (thanks to Gabriel Nivasch), whereas recursive filters did not.

It would be nice if someone would update the wiki on this issue with more historical background on the topic.

Yes, indeed. For example, Dean Hickerson also gave an explicit method to construct a pattern with population growth O(t^r), for any rational r in the interval [1, 2].

[simsim314]

Dean Hickerson also gave an explicit method to construct a pattern with population growth O(t^r), for any rational r in the interval [1, 2].

Gabriel Nivasch did that in 2006. He constructed patterns with growth rate O(t^(1/2^n)) for all n

Those patterns are not only not in the wiki, but also not publicly available, on both Dean Hickerson and Gabriel Nivasch sites. Could you post them and any other major breakthroughs in this field of research?

[Kiran]

This is quite serendipitous, as exponential filters already existed (thanks to Gabriel Nivasch), whereas recursive filters did not.

I did not know that, I simply figured a recursive filter would be easier to build.

How slow can you grow?

Why was this not posted months earlier?

4. Sqrt(log(t)) That comes in online archives large patterns in golly.

I think this is diametric growth and probably a logarithmic sawtooth.
I don't know for sure because my browser cannot open the file.

With two of them, each glider shoots out at approximately 2 tetrated to the generation that the previous one shot out.

If two part 2 patterns and a part 3 is used you get a super-linear pattern which does not appear to grow at all!

[calcyman]

How slow can you grow?

Why was this not posted months earlier?

Because I wrote it from scratch yesterday, in an attempt to explain the value of Alexey's discovery...?

[Kazyan]

Oh my. To think I thought this was mathematically impossible...congratulations to Kiran and Alexey!