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## (27,1)c/72 caterpillar challenge

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

### Re: (27,1)c/72 caterpillar challenge

From x3 SW and SE rakes I made one third of the gliders in a climber. There are already some scary signal crossings in this pattern so I don't know if it can be extended to make the missing two thirds.

`x = 1378, y = 1375, rule = B3/S231377bo\$1375b2o\$1376b2o72\$bo\$2bo\$3o59\$1320bo\$1318b2o\$1319b2o72\$52bo\$53bo\$51b3o59\$1263bo\$1261b2o\$1262b2o72\$103bo\$104bo\$102b3o59\$1206bo\$1204b2o\$1205b2o72\$154bo\$155bo\$153b3o59\$1149bo\$1147b2o\$1148b2o72\$205bo\$206bo\$204b3o59\$1092bo\$1090b2o\$1091b2o72\$256bo\$257bo\$255b3o59\$1035bo\$1033b2o\$1034b2o34\$1024bo\$1023b3o\$1023bob2o\$1024b3o\$1024b2o5\$1023b3o\$1022bo2bo\$1025bo\$1025bo\$1022bobo14\$1027bo\$1026b3o\$1026bob2o\$1027b3o\$1027b2o5\$1026b3o\$1025bo2bo\$307bo720bo\$308bo719bo\$306b3o716bobo14\$1030bo\$1029b3o\$1029bob2o\$1030b3o\$1030b2o5\$1029b3o\$1028bo2bo\$1031bo\$1031bo\$1028bobo14\$1033bo\$1032b3o\$1032bob2o\$1033b3o\$1033b2o5\$1032b3o\$1031bo2bo\$1034bo\$1034bo\$1031bobo14\$1036bo\$1035b3o\$1035bob2o\$1036b3o\$1036b2o5\$1035b3o\$1034bo2bo\$1037bo\$1037bo\$1034bobo14\$1039bo\$1038b3o\$1038bob2o\$1039b3o\$1039b2o5\$1038b3o\$1037bo2bo\$1040bo\$1040bo\$1037bobo14\$1042bo\$1041b3o\$1041bob2o\$1042b3o\$1042b2o5\$1041b3o\$1040bo2bo\$1043bo\$1043bo\$1040bobo19\$963b3o\$963bo2bo\$361bo601bo\$360b3o600bo\$355bo3b2obo601bobo\$354b3o2b3o\$353b2obo3b2o\$353b3o\$354b2o608bo\$963b3o\$963bob2o\$964b3o\$964b2o15\$966b3o\$966bo2bo\$364bo601bo\$363b3o600bo\$358bo3b2obo601bobo\$357b3o2b3o\$356b2obo3b2o\$356b3o\$357b2o608bo\$966b3o\$966bob2o\$967b3o\$967b2o15\$969b3o\$969bo2bo\$367bo601bo\$366b3o600bo\$361bo3b2obo601bobo\$360b3o2b3o\$359b2obo3b2o\$359b3o\$360b2o608bo\$969b3o\$969bob2o\$970b3o\$970b2o15\$972b3o\$972bo2bo\$370bo601bo\$369b3o600bo\$364bo3b2obo601bobo\$363b3o2b3o\$362b2obo3b2o\$362b3o25b3o\$363b2o24bo2bo580bo\$384b3o5bo579b3o\$383bo2bo5bo579bob2o\$386bo2bobo581b3o\$386bo586b2o\$383bobo14\$975b3o\$975bo2bo\$373bo601bo\$372b3o600bo\$367bo3b2obo601bobo\$366b3o2b3o\$365b2obo3b2o641bo\$365b3o25b3o618b3o\$366b2o24bo2bo580bo36b2obo\$387b3o5bo579b3o35b3o\$386bo2bo5bo579bob2o34b3o\$389bo2bobo581b3o35b2o\$389bo586b2o\$386bobo633b3o\$1022bo2bo\$1022bo\$1022bo\$1023bobo10\$978b3o\$978bo2bo\$376bo601bo\$375b3o600bo\$370bo3b2obo601bobo\$369b3o2b3o\$368b2obo3b2o641bo\$368b3o25b3o618b3o\$369b2o24bo2bo580bo36b2obo\$390b3o5bo579b3o35b3o\$389bo2bo5bo579bob2o34b3o\$392bo2bobo581b3o35b2o\$392bo586b2o\$389bobo633b3o\$1025bo2bo\$1025bo\$1025bo\$1026bobo10\$954b3o24b3o\$953bo2bo24bo2bo\$379bo576bo24bo\$378b3o571bo3bo24bo\$373bo3b2obo575bo25bobo\$372b3o2b3o573bobo\$371b2obo3b2o583bo57bo\$371b3o25b3o560b3o55b3o\$372b2o24bo2bo559b2obo17bo36b2obo\$393b3o5bo559b3o17b3o35b3o\$392bo2bo5bo560b2o17bob2o34b3o\$395bo2bobo581b3o35b2o\$395bo586b2o\$392bobo633b3o\$1028bo2bo\$1028bo\$1028bo\$1029bobo10\$957b3o\$956bo2bo\$959bo\$955bo3bo\$959bo\$956bobo\$966bo57bo\$402b3o560b3o55b3o\$401bo2bo559b2obo54b2obo\$396b3o5bo559b3o55b3o\$395bo2bo5bo560b2o55b3o\$398bo2bobo619b2o\$398bo\$395bobo633b3o\$1031bo2bo\$1031bo\$1031bo\$1032bobo10\$960b3o\$959bo2bo\$962bo\$958bo3bo\$962bo\$959bobo\$969bo57bo\$405b3o560b3o55b3o\$404bo2bo559b2obo54b2obo\$399b3o5bo559b3o55b3o\$398bo2bo5bo560b2o55b3o\$401bo2bobo619b2o\$401bo\$398bobo633b3o\$1034bo2bo\$1034bo\$1034bo\$1035bobo10\$963b3o\$962bo2bo\$965bo\$961bo3bo\$965bo\$962bobo\$972bo57bo\$408b3o560b3o55b3o\$407bo2bo559b2obo54b2obo\$402b3o5bo559b3o55b3o\$401bo2bo5bo560b2o55b3o\$404bo2bobo619b2o\$404bo\$401bobo633b3o\$1037bo2bo\$1037bo\$1037bo\$1038bobo10\$966b3o\$965bo2bo\$968bo\$964bo3bo\$968bo\$965bobo\$975bo57bo\$974b3o55b3o\$973b2obo54b2obo\$973b3o55b3o\$974b2o55b3o\$1032b2o2\$1040b3o\$1040bo2bo\$1040bo\$1040bo\$1041bobo10\$969b3o\$968bo2bo\$971bo\$967bo3bo\$971bo\$968bobo\$978bo\$977b3o\$976b2obo\$976b3o\$977b2o17\$972b3o\$971bo2bo\$974bo\$970bo3bo\$974bo\$971bobo\$981bo\$980b3o\$979b2obo\$979b3o\$980b2o!`
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

### Re: (27,1)c/72 caterpillar challenge

That's a good start! The picture I had in mind involved some frozen tracks. An early duplicator split off the NE-traveling signal into NE and SE. The NE just travels a large distance as a delay mechanism, while the SE glider is repeatedly duplicated as in the original caterpillar to build a constellation with 2/3 density frozen tracks. The delayed glider is reflected back to provide the final 1/3, and the climber begins at the point where the streams cross.

Edit: No that doesn't make sense, there's no way to get the glider far enough NE not to just crash into the helix. Perhaps the final glider just comes from the nearby duplicators.

The crossings themselves should be fine by a 2d analog of the Chinese remainder theorem - just give it enough space and as long as there is a hole, there is a way to position the crossing that satisfies the modular arithmetic constraints and successfully passes through the hole. There is definitely a concern though for whether there even is a hole at points in my idea.
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

It's possible to build an x1 climber pair using only kickbacks (as shown below) but you need to build one of the right sided gliders last (there would be a collision if you built all of the right sided gliders first). In the pattern posted above the right sided glider is always built first so you would need splitters with different phase in the left hand helix or use extra spaceships to rephase manually.

`x = 3325, y = 2785, rule = B3/S233323b2o\$3322b2o\$3324bo2\$518b2o\$517bobo\$519bo21\$3266b2o\$3265b2o\$3267bo2\$569b2o\$568bobo\$570bo21\$3209b2o\$3208b2o\$3210bo2\$620b2o\$619bobo\$621bo21\$3152b2o\$3151b2o\$3153bo2\$671b2o\$670bobo\$672bo21\$3095b2o\$3094b2o\$3096bo2\$722b2o\$721bobo\$723bo21\$3038b2o\$3037b2o\$3039bo2\$773b2o\$772bobo\$774bo21\$2981b2o\$2980b2o\$2982bo2\$824b2o\$823bobo\$825bo12\$3247b2o\$3246b2o\$3248bo2\$442b2o\$441bobo\$443bo3\$2924b2o\$2923b2o\$2925bo2\$875b2o\$874bobo\$876bo12\$3190b2o\$3189b2o\$3191bo2\$493b2o\$492bobo\$494bo3\$2867b2o\$2866b2o\$2868bo2\$926b2o\$925bobo\$927bo12\$3133b2o\$3132b2o\$3134bo2\$544b2o\$543bobo\$545bo3\$2810b2o\$2809b2o\$2811bo2\$977b2o\$976bobo\$978bo12\$3076b2o\$3075b2o\$3077bo2\$595b2o\$594bobo\$596bo3\$2753b2o\$2752b2o\$2754bo2\$1028b2o\$1027bobo\$1029bo12\$3019b2o\$3018b2o\$3020bo2\$646b2o\$645bobo\$647bo3\$2696b2o\$2695b2o\$2697bo2\$1079b2o\$1078bobo\$1080bo12\$2962b2o\$2961b2o\$2963bo2\$697b2o\$696bobo\$698bo3\$2639b2o\$2638b2o\$2640bo2\$1130b2o\$1129bobo\$1131bo12\$2905b2o\$2904b2o\$2906bo2\$748b2o\$747bobo\$749bo3\$2582b2o\$2581b2o\$2583bo2\$1181b2o\$1180bobo\$1182bo3\$3171b2o\$3170b2o\$3172bo2\$366b2o\$365bobo\$367bo3\$2848b2o\$2847b2o\$2849bo2\$799b2o\$798bobo\$800bo3\$2525b2o\$2524b2o\$2526bo2\$1232b2o\$1231bobo\$1233bo3\$3114b2o\$3113b2o\$3115bo2\$417b2o\$416bobo\$418bo3\$2791b2o\$2790b2o\$2792bo2\$850b2o\$849bobo\$851bo3\$2468b2o\$2467b2o\$2469bo2\$1283b2o\$1282bobo\$1284bo3\$3057b2o\$3056b2o\$3058bo2\$468b2o\$467bobo\$469bo3\$2734b2o\$2733b2o\$2735bo2\$901b2o\$900bobo\$902bo3\$2411b2o\$2410b2o\$2412bo2\$1334b2o\$1333bobo\$1335bo3\$3000b2o\$2999b2o\$3001bo2\$519b2o\$518bobo\$520bo3\$2677b2o\$2676b2o\$2678bo2\$952b2o\$951bobo\$953bo3\$2354b2o\$2353b2o\$2355bo2\$1385b2o\$1384bobo\$1386bo3\$2943b2o\$2942b2o\$2944bo2\$570b2o\$569bobo\$571bo3\$2620b2o\$2619b2o\$2621bo2\$1003b2o\$1002bobo\$1004bo3\$2297b2o\$2296b2o\$2298bo2\$1436b2o\$1435bobo\$1437bo3\$2886b2o\$2885b2o\$2887bo2\$621b2o\$620bobo\$622bo3\$2563b2o\$2562b2o\$2564bo2\$1054b2o\$1053bobo\$1055bo3\$2240b2o\$2239b2o\$2241bo2\$1487b2o\$1486bobo\$1488bo3\$2829b2o\$2828b2o\$2830bo2\$672b2o\$671bobo\$673bo3\$2506b2o\$2505b2o\$2507bo2\$1105b2o\$1104bobo\$1106bo3\$2183b2o\$2182b2o\$2184bo2\$1538b2o\$1537bobo\$1539bo3\$2772b2o\$2771b2o\$2773bo2\$723b2o\$722bobo\$724bo3\$2449b2o\$2448b2o\$2450bo2\$1156b2o\$1155bobo\$1157bo3\$2126b2o\$2125b2o\$2127bo2\$1589b2o\$1588bobo\$1590bo3\$2715b2o\$2714b2o\$2716bo2\$774b2o\$773bobo\$775bo3\$2392b2o\$2391b2o\$2393bo2\$1207b2o\$1206bobo\$1208bo3\$2069b2o\$2068b2o\$2070bo2\$1640b2o\$1639bobo\$1641bo3\$2658b2o\$2657b2o\$2659bo2\$825b2o\$824bobo\$826bo3\$2335b2o\$2334b2o\$2336bo2\$1258b2o\$1257bobo\$1259bo3\$2012b2o\$2011b2o\$2013bo2\$1691b2o\$1690bobo\$1692bo3\$2601b2o\$2600b2o\$2602bo2\$876b2o\$875bobo\$877bo3\$2278b2o\$2277b2o\$2279bo2\$1309b2o\$1308bobo\$1310bo3\$1955b2o\$1954b2o\$1956bo2\$1742b2o\$1741bobo\$1743bo3\$2544b2o\$2543b2o\$2545bo2\$927b2o\$926bobo\$928bo3\$2221b2o\$2220b2o\$2222bo2\$1360b2o\$1359bobo\$1361bo3\$1898b2o\$1897b2o\$1899bo2\$1793b2o\$1792bobo\$1794bo3\$2487b2o\$2486b2o\$2488bo2\$978b2o\$977bobo\$979bo3\$2164b2o\$2163b2o\$2165bo2\$1411b2o\$1410bobo\$1412bo8\$1842bo\$1842bobo\$1842b2o2\$2430b2o\$2429b2o\$2431bo2\$1029b2o\$1028bobo\$1030bo3\$2107b2o\$2106b2o\$2108bo2\$1462b2o\$1461bobo\$1463bo12\$2373b2o\$2372b2o\$2374bo2\$1080b2o\$1079bobo\$1081bo3\$2050b2o\$2049b2o\$2051bo2\$1513b2o\$1512bobo\$1514bo12\$2316b2o\$2315b2o\$2317bo2\$1131b2o\$1130bobo\$1132bo3\$1993b2o\$1992b2o\$1994bo2\$1564b2o\$1563bobo\$1565bo12\$2259b2o\$2258b2o\$2260bo2\$1182b2o\$1181bobo\$1183bo3\$1936b2o\$1935b2o\$1937bo2\$1615b2o\$1614bobo\$1616bo12\$2202b2o\$2201b2o\$2203bo2\$1233b2o\$1232bobo\$1234bo3\$1879b2o\$1878b2o\$1880bo2\$1666b2o\$1665bobo\$1667bo8\$1785bo\$1785bobo\$1785b2o2\$2145b2o\$2144b2o\$2146bo2\$1284b2o\$1283bobo\$1285bo3\$1822b2o\$1821b2o\$1823bo2\$1717b2o\$1716bobo\$1718bo12\$2088b2o\$2087b2o\$2089bo2\$1335b2o\$1334bobo\$1336bo8\$1766bo\$1766bobo\$1766b2o11\$2031b2o\$2030b2o\$2032bo\$2956b2o\$1386b2o1568bobo\$1385bobo1568bo\$1387bo\$153bo\$153b2o\$152bobo18\$1974b2o\$1973b2o\$1975bo\$2899b2o\$1437b2o1460bobo\$1436bobo1460bo\$1438bo\$204bo\$204b2o\$203bobo18\$1917b2o\$1916b2o\$1918bo\$2842b2o\$1488b2o1352bobo\$1487bobo1352bo\$1489bo\$255bo\$255b2o\$254bobo14\$1728bo\$1728bobo\$1728b2o2\$1860b2o\$1859b2o\$1861bo\$2785b2o\$1539b2o1244bobo\$1538bobo1244bo\$1540bo\$306bo\$306b2o\$305bobo18\$1803b2o\$1802b2o\$1804bo\$2728b2o\$1590b2o1136bobo\$1589bobo1136bo\$1591bo\$357bo\$357b2o\$356bobo5\$1709bo\$1709bobo\$1709b2o11\$1746b2o\$1745b2o\$1747bo\$2671b2o\$1641b2o1028bobo\$1640bobo1028bo\$1642bo\$408bo\$408b2o\$407bobo21\$2614b2o\$2614bobo\$1690bo923bo\$1690bobo\$459bo1230b2o\$459b2o\$458bobo12\$2880b2o\$2880bobo\$2880bo2\$77bo\$77b2o\$76bobo3\$2557b2o\$2557bobo\$2557bo2\$510bo\$510b2o\$509bobo12\$2823b2o\$2823bobo\$1671bo1151bo\$1671bobo\$128bo1542b2o\$128b2o\$127bobo3\$2500b2o\$2500bobo\$2500bo2\$561bo\$561b2o\$560bobo12\$2766b2o\$2766bobo\$2766bo2\$179bo\$179b2o\$178bobo3\$2443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\$1039bo38\$1006bo\$1006bobo\$1006b2o3\$1019bobo\$1019b2o\$1020bo38\$987bo\$987bobo\$987b2o3\$1000bobo\$1000b2o\$1001bo38\$968bo\$968bobo\$968b2o3\$981bobo\$981b2o\$982bo!`

It doesn't look possible to make the 3-glider track with kickbacks only though.

EDIT: Attaching an x3 rakes -> x1 climber trail pattern

gentrail.rle.gz
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

### Re: (27,1)c/72 caterpillar challenge

Just checked out your attachment - that's good news, especially if it turns out the climber pair is capable of building up the other 3 to make a full cluster. That puts the total number of spaceships to synthesize at 23 on the right, and 20 plus the helix on the left. The helix would have to be adapted to drop SE instead of NE gliders to work with this - I had requested NE earlier assuming all fanouts would happen on the right but I doubt it would be cheaper not to use kickbacks, and that necessarily requires some fanouts on the left helix.

`x = 2578, y = 2698, rule = 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08b3o18bo47bo47bob2o38b3o41b3o\$2108b3o18bo44bobo49b3o37b2obo41bo2bo\$2108b2o16bobo97b2o38b3o42bo\$2267b2o42bo\$2182bo129bobo\$2167b3o11b3o28bo66b3o\$2167bo2bo9b2obo27b3o17b3o44bo2bo48bo\$2167bo12b3o28bob2o15bo2bo47bo47b3o40bo\$2167bo3bo9b2o29b3o18bo47bo47bob2o38b3o\$2167bo44b3o18bo44bobo49b3o37b2obo\$2168bobo41b2o16bobo97b2o38b3o\$2106b3o262b2o\$1731bobo372bo2bo176bo\$1731b2o373bo164b3o11b3o28bo\$1732bo373bo164bo2bo9b2obo27b3o17b3o48b3o\$2107bobo161bo12b3o28bob2o15bo2bo47bo2bo\$1745bo525bo3bo9b2o29b3o18bo50bo\$1744bo380bo145bo44b3o18bo50bo\$1744b3o377b3o40bo104bobo41b2o16bobo48bobo\$2124bob2o38b3o41b3o\$2125b3o37b2obo41bo2bo\$2125b2o38b3o42bo164b3o\$2166b2o42bo164bo2bo\$1992bo218bobo161bo\$1991bo119bo66b3o194bo3bo\$1991b3o116b3o17b3o44bo2bo48bo145bo\$2110bob2o15bo2bo47bo47b3o40bo104bobo\$2111b3o18bo47bo47bob2o38b3o41b3o\$2111b3o18bo44bobo49b3o37b2obo41bo2bo\$2111b2o16bobo97b2o38b3o42bo\$2270b2o42bo\$2185bo129bobo\$2170b3o11b3o28bo66b3o\$2170bo2bo9b2obo27b3o17b3o44bo2bo48bo\$2170bo12b3o28bob2o15bo2bo47bo47b3o40bo\$2170bo3bo9b2o29b3o18bo47bo47bob2o38b3o\$2170bo44b3o18bo44bobo49b3o37b2obo\$2171bobo41b2o16bobo97b2o38b3o\$2109b3o262b2o\$2109bo2bo176bo\$2109bo164b3o11b3o28bo\$2109bo164bo2bo9b2obo27b3o17b3o\$2110bobo161bo12b3o28bob2o15bo2bo\$2274bo3bo9b2o29b3o18bo\$2128bo145bo44b3o18bo\$2127b3o40bo104bobo41b2o16bobo\$2127bob2o38b3o41b3o\$2128b3o37b2obo41bo2bo\$2128b2o38b3o42bo\$2169b2o42bo\$2214bobo\$2114bo66b3o\$2113b3o17b3o44bo2bo48bo\$2113bob2o15bo2bo47bo47b3o\$2114b3o18bo47bo47bob2o\$2114b3o18bo44bobo49b3o\$2114b2o16bobo97b2o\$1712bobo\$1712b2o474bo\$1713bo459b3o11b3o28bo\$2173bo2bo9b2obo27b3o17b3o\$1726bo446bo12b3o28bob2o15bo2bo\$1725bo447bo3bo9b2o29b3o18bo\$1725b3o445bo44b3o18bo\$2174bobo41b2o16bobo\$2112b3o\$2112bo2bo\$2112bo\$2112bo\$2113bobo2\$2131bo\$2130b3o40bo\$2130bob2o38b3o41b3o\$2131b3o37b2obo41bo2bo\$2131b2o38b3o42bo\$2172b2o42bo\$2217bobo\$2117bo66b3o\$2116b3o17b3o44bo2bo48bo\$2116bob2o15bo2bo47bo47b3o\$2117b3o18bo47bo47bob2o\$2117b3o18bo44bobo49b3o\$2117b2o16bobo97b2o2\$2191bo\$2176b3o11b3o28bo\$2176bo2bo9b2obo27b3o17b3o\$2176bo12b3o28bob2o15bo2bo\$2176bo3bo9b2o29b3o18bo\$2176bo44b3o18bo\$2177bobo41b2o16bobo\$2115b3o\$2115bo2bo\$2115bo\$2115bo\$2116bobo2\$2134bo\$2133b3o40bo\$2133bob2o38b3o41b3o\$2134b3o37b2obo41bo2bo\$1693bobo438b2o38b3o42bo\$1693b2o480b2o42bo\$1694bo525bobo\$2120bo66b3o\$1707bo411b3o17b3o44bo2bo48bo\$1706bo412bob2o15bo2bo47bo47b3o\$1706b3o411b3o18bo47bo47bob2o\$2120b3o18bo44bobo49b3o\$2120b2o16bobo97b2o2\$2194bo\$2179b3o11b3o28bo\$2179bo2bo9b2obo27b3o17b3o\$2179bo12b3o28bob2o15bo2bo\$2179bo3bo9b2o29b3o18bo\$2179bo44b3o18bo\$2180bobo41b2o16bobo\$2118b3o\$2118bo2bo\$2118bo\$2118bo\$2119bobo2\$2137bo\$2136b3o40bo\$2136bob2o38b3o\$2137b3o37b2obo\$2137b2o38b3o\$2178b2o2\$2123bo66b3o\$2122b3o17b3o44bo2bo\$2122bob2o15bo2bo47bo\$2123b3o18bo47bo\$2123b3o18bo44bobo\$2123b2o16bobo2\$2197bo\$2182b3o11b3o\$2182bo2bo9b2obo\$2182bo12b3o\$2182bo3bo9b2o\$2182bo\$2183bobo\$2121b3o\$1674bobo444bo2bo\$1674b2o445bo\$1675bo445bo\$2122bobo\$1688bo\$1687bo452bo\$1687b3o449b3o40bo\$2139bob2o38b3o\$2140b3o37b2obo\$2140b2o38b3o\$2181b2o\$1935bo\$1934bo191bo66b3o\$1934b3o188b3o17b3o44bo2bo\$2125bob2o15bo2bo47bo\$2126b3o18bo47bo\$2126b3o18bo44bobo\$2126b2o16bobo2\$2200bo\$2185b3o11b3o\$2185bo2bo9b2obo\$2185bo12b3o\$2185bo3bo9b2o\$2185bo\$2186bobo\$2124b3o\$2124bo2bo\$2124bo\$2124bo\$2125bobo2\$2143bo\$2142b3o40bo\$2142bob2o38b3o\$2143b3o37b2obo\$2143b2o38b3o\$2184b2o2\$2129bo66b3o\$2128b3o17b3o44bo2bo\$2128bob2o15bo2bo47bo\$2129b3o18bo47bo\$2129b3o18bo44bobo\$2129b2o16bobo\$1655bobo\$1655b2o546bo\$1656bo531b3o11b3o\$2188bo2bo9b2obo\$1669bo518bo12b3o\$1668bo519bo3bo9b2o\$1668b3o517bo\$2189bobo\$2127b3o\$2127bo2bo\$2127bo\$2127bo\$2128bobo2\$2146bo\$2145b3o40bo\$2145bob2o38b3o\$2146b3o37b2obo\$2146b2o38b3o\$2187b2o2\$2132bo66b3o\$2131b3o17b3o44bo2bo\$2131bob2o15bo2bo47bo\$2132b3o18bo47bo\$1644b3o12b3o470b3o18bo44bobo\$1645bo16bo469b2o16bobo\$1645b3o11bo2bo\$1660b2o544bo\$1660b2o529b3o11b3o\$1659bo2bo528bo2bo9b2obo\$1659bo531bo12b3o\$1661b2o528bo3bo9b2o\$2191bo\$2192bobo\$2130b3o\$2130bo2bo\$2130bo\$2130bo\$2131bobo2\$2149bo\$2148b3o\$2148bob2o\$2149b3o\$2149b2o3\$2135bo\$2134b3o17b3o\$2134bob2o15bo2bo\$2135b3o18bo\$2135b3o18bo\$2135b2o16bobo!`

The spaceship would have to be in the middle of these helices, meaning the 7 lines of x3 NE gliders shown at the top would have to be lengthened to accomodate whatever dimensions end up happening. Because the tracks get perpetually closer to the left helix, the width isn't determined by the spine width but by a combination of the spine width and ship length. It's all just numbers though.

In the event it isn't possible to build up the full ship from just 2 tracks, it is useful to note that the 3-track forerake can fit exactly one rephasing on the left two tracks. (Unfortunately not more, or it could feasibly be possible to bring a very distant track into position). Here's what that looks like if this helps. It's actually quite the remarkable squeeze.
`x = 124, y = 253, rule = B3/S2399bo\$99bobo\$99b2o3\$112bobo\$112b2o\$113bo16\$121bobo\$121b2o\$122bo20\$80bo\$80bobo\$80b2o3\$93bobo\$93b2o\$94bo16\$102bobo\$102b2o\$103bo20\$61bo\$61bobo\$61b2o3\$74bobo\$74b2o\$75bo16\$83bobo\$83b2o\$84bo20\$42bo\$42bobo\$42b2o3\$55bobo\$55b2o\$56bo16\$64bobo\$64b2o\$65bo4\$29b3o\$29bobo12b3o\$29bo2bo12bo\$30b3o12b3o\$30b3o\$28bo2bo\$31bo\$28bo2\$30bo\$29bo\$29b2o\$36bo\$35bobo6b2o\$35bobo6b2o\$36bo14bo\$50bobo\$33bo6b3o6b2obo\$31b3o13b2o2bo\$35b2o6bo3b5o4bo\$36bo2bo6bo4bo3bobo\$36b2o4bo3bob3o4bobo\$38bo2bo5b3o2bo3bo\$34b2ob2o9bo\$35bo13bo4bo\$49bo4bo\$53bo10\$19bo\$19bobo\$19b2o\$45bobo\$45b2o\$32bobo11bo\$32b2o\$33bo38\$o\$obo\$2o\$26bobo\$26b2o\$13bobo11bo\$13b2o\$14bo!`
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

I wrote:It doesn't look possible to make the 3-glider track with kickbacks only though.

Actually the 3-glider track is constructible with kickbacks. In fact, with some careful threading of the needle, all 5 tracks can be made with 15 pairs of rakes and 3 blinker trails. Is this worth considering or is there a nice way to go from either 2 or 3 tracks up to 5?

`x = 3996, y = 5563, rule = 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chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

### Re: (27,1)c/72 caterpillar challenge

That's a nice construction! I think that would cost around 150 *WSS to fanout from a single stream, making this helix about twice as complicated as that of the original caterpillar. I'm hoping to avoid breaking the "largest interesting construction" record, I don't know if I'm alone in this.

I would instead hope to find universality with only 2 tracks, at least to help build a 5-track cluster that can churn out recipes more quickly. It hasn't shown that much promise though, certainly a "nice way" is elusive, so the above is a good fallback to have.

The debris from a single climber is so active, I would be surprised if there wasn't some pair affording universal construction, even if it isn't a subset of the 5-track cluster. It might be good to run some more gencols searches for that. Original searches were only interested in clean paired reactions, or Nico's search that found a clean forerake on 3 that has proven very valuable. (Nico's might not have been a systematized search so much as joining two of the pairs and getting lucky, I really don't know..). Regardless, there are probably a good number of messy rakes on 2 tracks that can be manipulated into a dirty constructor. If the 150 *WSS helix is the mark to beat, and a 2-track construction was shown below to take around 60 *WSS if you include the helix, then we probably have a couple 100K vertical cells to play around with in going from 2->5.

Who knows, maybe there is a 2-track cluster that is as convenient to make our target constellations with as the 5-track cluster has been. I'm imagining all 2-track options being dirty though, so it's more likely it will build a 5-track constructor plus debris, and then the 5 will clean the debris and start the real work.

The relevant search would have one climber fixed on a track and enumerate the possible second track locations. For each location, it would count the number of ways for the second climber to interact with the first such that the tracks both survive. The track separations with the most options would be the most promising. Of course, following climber pairs can spark the debris to give new reactions, since the repeat distance is usually low enough to allow it. Basically, the space of possibilities seems so huge I can't imagine it holding nothing which could be salvaged into a constructor.
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

I've found a number of forerakes on track pairs, but none of them are clean. This unlikely pair is the cleanest so far, a forerake with only two pieces of debris. The same pair provides 4 dirty rephasing reactions by stalling the left climber 36, 44, 56 or 64 generations. 5 unique options is good, but there'll be too much junk in the way unless we have something cleaner.
`x = 146, y = 344, rule = B3/S23137bobo\$137b2o\$138bo4\$143bo\$143bobo\$143b2o37\$118bobo\$118b2o\$119bo4\$124bo\$124bobo\$124b2o37\$99bobo\$99b2o\$100bo4\$105bo\$105bobo\$105b2o37\$80bobo\$80b2o\$81bo4\$86bo\$86bobo\$86b2o37\$61bobo\$61b2o\$62bo4\$67bo\$67bobo\$67b2o37\$42bobo\$42b2o\$43bo4\$48bo\$48bobo\$48b2o37\$23bobo\$23b2o\$24bo4\$29bo\$29bobo\$29b2o37\$4bobo\$4b2o\$5bo4\$10b2o\$10b2o\$10bobo\$11b2o2b2o\$17bo\$10bo2b2obo\$10bo\$3b3o5bo4bo\$3bo2bo6bo2b2o\$2bo3bo7bob2o\$2b3o2bo7b2o\$3b4o3\$obo14b2o\$2o15b2o\$bo4\$6bo\$6bobo\$6b2o!`
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

Another option. This pair became more promising the more I investigated it. The tracks are simple, no vertical or phase offset, just 19 cells horizontally. If the climbers are in the same phase or if the left climber is 4 generations delayed, the debris is a TL+blinker constellation. If the right climber is 4 generations delayed, the debris is a longboat + NE glider. All other options destroy either the right track or the right climber, so we only have these 3. I'll refer to them as A, B, and C, from left to right.
`x = 380, y = 168, rule = B3/S2370bobo16bobo122bobo16bobo122bobo16bobo\$70b2o17b2o123b2o17b2o123b2o17b2o\$71bo18bo124bo18bo124bo18bo43\$51bobo16bobo122bobo16bobo122bobo16bobo\$51b2o17b2o123b2o17b2o123b2o17b2o\$52bo18bo124bo18bo124bo18bo43\$32bobo16bobo122bobo16bobo122bobo16bobo\$32b2o17b2o123b2o17b2o123b2o17b2o\$33bo18bo124bo18bo124bo18bo43\$13bobo16bobo122bobo16bobo122bobo16bobo\$13b2o17b2o123b2o17b2o123b2o17b2o\$14bo18bo124bo18bo124bo18bo23\$21b3o122b3o16b3o122b3o\$22bo124bo18bo124bo\$b3o18b3o122b3o16b3o122b3o14b3o\$o3bo302bo3bo2\$5bo306bo\$5o302b5o\$bo306bo!`

Some neat constructions that may hint at universality:
C, C with high spacing has no interference, the second forerake passes through the longboats.
`x = 125, y = 268, rule = B3/S23104bo18bo\$103bo18bo\$103b3o16b3o43\$85bo18bo\$84bo18bo\$84b3o16b3o43\$66bo18bo\$65bo18bo\$65b3o16b3o43\$47bo18bo\$46bo18bo\$46b3o16b3o43\$28bo18bo\$27bo18bo\$27b3o16b3o4\$29b3o\$28bo2bo\$27bo4bo15bo\$29bo17b3o\$46bo2bo\$30b2o13b3o2b2o\$29bobo14bo2b3o\$29bobo15b2o2b2o\$50b3o\$35bo11b4obo\$33bo13b2o2b2o\$33b2o15b2o3\$24bo18bo\$23bo18bo\$23b3o16b3o43\$5bo18bo\$4bo18bo\$4b3o16b3o4\$6b3o\$5bo2bo\$4bo4bo15bo\$6bo17b3o\$23bo2bo\$7b2o13b3o2b2o\$6bobo14bo2b3o\$6bobo15b2o2b2o\$27b3o\$12bo11b4obo\$10bo13b2o2b2o\$10b2o15b2o3\$bo18bo\$o18bo\$3o16b3o!`

C, C, C with high spacing causes the third rake to cleanly delete the longboat left by the first. This means an infinite chain of well-spaced Cs will consist of two forerakes and no other debris.
`x = 284, y = 532, rule = B3/S23192bo18bo\$191bo18bo\$191b3o16b3o43\$173bo18bo\$172bo18bo\$172b3o16b3o43\$154bo18bo\$153bo18bo\$153b3o16b3o4\$155b3o\$154bo2bo\$153bo4bo15bo\$155bo17b3o\$172bo2bo\$156b2o13b3o2b2o\$155bobo14bo2b3o\$155bobo15b2o2b2o\$176b3o\$161bo11b4obo\$159bo13b2o2b2o\$159b2o15b2o3\$150bo18bo\$149bo18bo\$149b3o16b3o9\$181bo\$180bobo\$181bobo\$145bo36bobo\$144bo36bo3bo\$146bo33bo4bo\$144b3o33bo3bo\$146bobo22bo8bo2b2o\$146b2ob2o20bo9b3o\$145bo5bo19bo10bo\$146bo3bo\$147b3o\$148bo21\$179b3o\$131bo18bo16bo7b2ob2o2bo\$130bo18bo16bo5b2obobo4bo\$130b3o16b3o15b2o3b2obo\$168bo3bo8bo\$173bo7bo\$172bo5bob2o\$132b3o38bobo2bobo\$131bo2bo39bo4b2o\$130bo4bo15bo26bobo15b3o\$132bo17b3o25b2o18bo\$149bo2bo44bo\$133b2o13b3o2b2o\$132bobo14bo2b3o\$132bobo15b2o2b2o\$153b3o\$138bo11b4obo\$136bo13b2o2b2o\$136b2o15b2o58b3o\$215bo\$214bo\$127bo18bo\$126bo18bo\$126b3o16b3o4\$230b3o\$232bo\$231bo3\$158bo\$157bobo18bo\$158bobo16bobo\$122bo36bobo16bobo\$121bo36bo3bo16b2o66b3o\$123bo33bo4bo86bo\$121b3o33bo3bo86bo\$123bobo22bo8bo2b2o\$123b2ob2o20bo9b3o\$122bo5bo19bo10bo\$123bo3bo\$124b3o\$125bo\$264b3o\$266bo\$265bo7\$281b3o\$283bo\$282bo4\$177bo\$176bobo\$177bobo\$178b2o2\$156b3o\$108bo18bo16bo7b2ob2o2bo\$107bo18bo16bo5b2obobo4bo\$107b3o16b3o15b2o3b2obo\$145bo3bo8bo\$150bo7bo\$149bo5bob2o\$109b3o38bobo2bobo\$108bo2bo39bo4b2o\$107bo4bo15bo26bobo15b3o\$109bo17b3o25b2o18bo\$126bo2bo44bo\$110b2o13b3o2b2o\$109bobo14bo2b3o\$109bobo15b2o2b2o\$130b3o\$115bo11b4obo\$113bo13b2o2b2o\$113b2o15b2o58b3o\$192bo\$191bo\$104bo18bo\$103bo18bo53bo\$103b3o16b3o50bobo\$176bobo\$177b2o2\$207b3o\$209bo\$208bo3\$135bo\$134bobo18bo\$135bobo16bobo\$99bo36bobo16bobo\$98bo36bo3bo16b2o66b3o\$100bo33bo4bo86bo\$98b3o33bo3bo86bo\$100bobo22bo8bo2b2o\$100b2ob2o20bo9b3o\$99bo5bo19bo10bo\$100bo3bo\$101b3o\$102bo\$241b3o\$243bo\$242bo2\$175bo\$174bobo\$175bobo\$176b2o2\$258b3o\$260bo\$259bo4\$154bo\$153bobo\$154bobo\$155b2o2\$133b3o\$85bo18bo16bo7b2ob2o2bo\$84bo18bo16bo5b2obobo4bo\$84b3o16b3o15b2o3b2obo\$122bo3bo8bo\$127bo7bo\$126bo5bob2o\$86b3o38bobo2bobo\$85bo2bo39bo4b2o\$84bo4bo15bo26bobo15b3o\$86bo17b3o25b2o18bo\$103bo2bo44bo22bo\$87b2o13b3o2b2o64bobo\$86bobo14bo2b3o65bobo\$86bobo15b2o2b2o65b2o\$107b3o\$92bo11b4obo\$90bo13b2o2b2o\$90b2o15b2o58b3o\$169bo\$168bo\$81bo18bo\$80bo18bo53bo\$80b3o16b3o50bobo\$153bobo\$154b2o7\$112bo\$111bobo18bo\$112bobo16bobo\$76bo36bobo16bobo\$75bo36bo3bo16b2o\$77bo33bo4bo\$75b3o33bo3bo\$77bobo22bo8bo2b2o\$77b2ob2o20bo9b3o\$76bo5bo19bo10bo\$77bo3bo\$78b3o\$79bo5\$152bo\$151bobo\$152bobo\$153b2o8\$131bo\$130bobo\$131bobo\$132b2o2\$110b3o\$62bo18bo16bo7b2ob2o2bo\$61bo18bo16bo5b2obobo4bo\$61b3o16b3o15b2o3b2obo\$99bo3bo8bo\$104bo7bo\$103bo5bob2o\$63b3o38bobo2bobo\$62bo2bo39bo4b2o\$61bo4bo15bo26bobo15b3o\$63bo17b3o25b2o18bo\$80bo2bo44bo22bo\$64b2o13b3o2b2o64bobo\$63bobo14bo2b3o65bobo\$63bobo15b2o2b2o65b2o\$84b3o\$69bo11b4obo\$67bo13b2o2b2o\$67b2o15b2o58b3o\$146bo\$145bo\$58bo18bo\$57bo18bo53bo\$57b3o16b3o50bobo\$130bobo\$131b2o7\$89bo\$88bobo18bo\$89bobo16bobo\$53bo36bobo16bobo\$52bo36bo3bo16b2o\$54bo33bo4bo\$52b3o33bo3bo\$54bobo22bo8bo2b2o\$54b2ob2o20bo9b3o\$53bo5bo19bo10bo\$54bo3bo\$55b3o\$56bo5\$129bo\$128bobo\$129bobo\$130b2o8\$108bo\$107bobo\$108bobo\$109b2o2\$87b3o\$39bo18bo16bo7b2ob2o2bo\$38bo18bo16bo5b2obobo4bo\$38b3o16b3o15b2o3b2obo\$76bo3bo8bo\$81bo7bo\$80bo5bob2o\$81bobo2bobo\$82bo4b2o\$86bobo15b3o\$86b2o18bo\$105bo22bo\$127bobo\$128bobo\$129b2o4\$121b3o\$123bo\$122bo2\$107bo\$106bobo\$107bobo\$108b2o8\$86bo\$85bobo\$86bobo\$87b2o10\$20bo18bo\$19bo18bo\$19b3o16b3o\$106bo\$105bobo\$106bobo\$107b2o8\$85bo\$84bobo\$85bobo\$86b2o13\$105bo\$104bobo\$105bobo\$106b2o8\$84bo\$83bobo\$84bobo\$85b2o\$bo18bo\$o18bo\$3o16b3o10\$104bo\$103bobo\$104bobo\$105b2o8\$83bo\$82bobo\$83bobo\$84b2o!`

C, C with a lower spacing can cause sparks to interfere, preventing the longboats and second rake from forming. The debris is instead a boat+blinker+block constellation.
`x = 190, y = 269, rule = B3/S23105bo18bo\$103b2o17b2o\$104b2o17b2o43\$86bo18bo\$84b2o17b2o\$85b2o17b2o43\$67bo18bo\$65b2o17b2o\$66b2o17b2o43\$48bo18bo\$46b2o17b2o\$47b2o17b2o10\$46b3o\$45bo2bo\$45bo4bo\$44b2ob2obo13b3o\$44b2obo2bo12bo2bo\$46b4o13b2o2bo\$47b3o16b2o2\$44bo18bo\$42b2o17b2o\$43b2o17b2o12\$73b2o\$72bo\$71bo2bo\$35bo4bob2o27bo\$34bo2bo2bo4b2o25bob4o\$35bo2bo6b2o7bo18bob3o\$36bo4bo12bo\$38bo2bo19b3o\$39b2o12\$29bo\$28b3o\$27bo2b2o\$27bo3bo15bo\$29bobo14b3o\$45bo2b2o\$26b2ob2o14b3o\$28bo2\$73b2o\$35bo10bo26b2o\$34b3o8bobo16b2o\$33b5o7bobo15b2o2b3obo\$32bo5bo14bo6b2obo3b3ob2o\$31b2o2bo2b2o12b3o5bo9bo2bo\$30b3obobob3o10b5o5bo10bo\$31b2o2bo2b2o10b2o3b2o5bobo\$32bo5bo12b5o6bob2o\$33b5o14b3o9bo3bobo\$34bo2bo15bo14bo2bo\$37bo30bo2bo\$34bo2bo32bo\$35b2o16b2o\$53b2o30b2o\$86b2o\$85bo6\$21bo18bo\$19b2o17b2o62b2o\$20b2o17b2o62b2o\$102bo3\$49bo\$48b3o\$46b2obobo15bo\$46b3o17bob2ob2o\$45b4o3bo14b4o2bo45b2o\$44bo2b2obo20b2o47b2o\$43b3ob3o69bo\$36b2o9bo5b2o\$36b2o15b2o5\$136b2o\$137b2o\$136bo7\$153b2o\$46b2o106b2o\$46b2o105bo6\$41bo\$41bo128b2o\$41bo129b2o\$170bo3\$50bo\$49bobo\$49b2o\$2bo18bo\$2o17b2o166b2o\$b2o17b2o166b2o\$187bo!`

C, A and C, B with proper spacing can prevent the TL + blinker from forming, leaving just the debris from C.
`x = 133, y = 314, rule = B3/S23112bo18bo\$111bo18bo\$111b3o16b3o43\$93bo18bo\$92bo18bo\$92b3o16b3o43\$74bo18bo\$73bo18bo\$73b3o16b3o43\$55bo18bo\$54bo18bo\$54b3o16b3o43\$36bo18bo\$35bo18bo\$35b3o16b3o17\$28bo\$26b6o\$26b2o2b2o13b3o\$48bo\$30bo14bo2bo\$26b2o2bo15b2o\$26b2o3bo14b2o\$30bo14bo2bo\$28bobo14bo\$29bo17b2o7\$28bo\$28bo16b2o\$28b2o15b2o\$27bobo\$26bo2bo7b3o\$25bo4bo5bo3bo5b3o\$25bo2b3o10bo3bobo8bo\$25b2o5bo8bo3bo9b3o\$27b3o10b2o3b3o2bo2bo4bo\$30bo2bo2b4o9bo6bobo\$32bo5bo11bo5b2o\$33b2o16b3o19\$13bo18bo\$12bo18bo\$12b3o16b3o24b2o\$48bobo7b2o\$48b2o\$49bo\$46bo8b2o\$46bo8b2o\$46bo\$51b3o\$50bo3bo\$13bo18bo16bo5bo\$12b3o16b3o21bo\$11bo2b2o14bo2b2o15b2o3bo\$11bob2o15bob2o18b2o\$13b2ob2o14b2ob2o\$10bo5bo12bo5bo\$11bo4bo13bo4bo\$12bo2bo15bo2bo\$14bo18bo\$9bo18bo37b3o\$8bo18bo40bo\$8b3o16b3o37bo7\$83b3o\$85bo\$84bo2\$37b3obo\$35bo5bo\$35b2obo2bo\$34b2o2bo\$7bo25b6o\$3o2bobo2b3o17b3ob4o16bo45b3o\$b3o7b2o17b2o3b2o16bobo46bo\$3bo50bobo44bo\$5bobo47b2o\$5b2o5\$117b3o\$119bo\$118bo16\$53bo\$52bobo\$53bobo\$54b2o!`

The above means a C, A, C, A, C, A .. chain will have one forerake and no other debris. C, A, C, A ... C, A, C, C, C, C ... will place two forerakes with a variable separation and no other debris. However, the C chain does not permit any new forerakes without some debris.

B, A with as tight of spacing as possible (tight enough that A, A or B, B or A, B won't work) can initiate a block-pull seqeunce, leaving an additional block and two blinkers. Subsequent B or A pairs with the correct spacing can continue the block pull to an arbitrary number of rephasings with no additional debris. C can be inserted into the block pull to turn it into a blinker pull with the same property and spacing. A or B can turn the blinker pull back into a block pull. I haven't found any clean termination for either, so the total cost here is 4 pieces of debris, for arbitrarily many rephasings.
`x = 218, y = 619, rule = B3/S23197bo18bo\$196bo18bo\$196b3o16b3o43\$178bo18bo\$177bo18bo\$177b3o16b3o43\$159bo18bo\$158bo18bo\$158b3o16b3o43\$140bo18bo\$139bo18bo\$139b3o16b3o12\$135bo\$134bo\$136bo\$134b3o\$136bobo\$136b2ob2o\$135bo5bo\$136bo3bo\$137b3o\$130bo7bo10bo\$129bobo16bobo\$128bo3bo14bo3bo\$129bo2bo15bo2bo\$129bo2bo15bo2bo\$130bobo16bobo9\$129b2o17b2o\$129b2o17b2o\$136bo18bo\$135bob2o15bob2o\$132b3o16b3o\$131b5o14b5o\$130bo2bo2b3o2bo7bo2bo2b3o2bo\$130bobo4bo2bobo6bobo4bo2bobo\$131bo3b2o3bobo7bo3b2o3bobo\$136bo4bo13bo4bo\$133b3o16b3o\$133b2o17b2o15\$137b3o\$137bo2bo\$117b2o17bo2b2o16b3o\$116bo2bo15bo2bo\$117bob2o15b2o17bo5bo\$117bo37bo5bo\$118bobo21bo12bo5bo\$117bo2b2o\$123bo19b2o12b3o\$123bo18bobo\$144b2o\$122b2o19bo\$122b2o\$123bo33bo\$157bo\$144b2o11bo\$124b2o18b2o\$124b2o5\$113bo18bo\$112bo18bo\$112b3o16b3o4\$157b2o\$157b2o5\$155b3o\$139b2o\$139b2o4\$156bo\$156bo\$156bo3\$122bo\$121bobo\$102bo17bo3bo\$102bo18bo2bo\$101bobo17bo2bo\$122bobo\$103b2o2\$103b2o2\$156b2o\$156b2o3\$121b2o\$101b2o18b2o\$101b2o25bo25b3o\$108bo18bob2o7b2o\$107bobo14b3o11b2o\$107bobo13b5o\$105bo2bo13bo2bo2b3o2bo\$104b4o5bo8bobo4bo2bobo\$103bo4bo3bobo8bo3b2o3bobo20bo\$103bobob2o3bobo13bo4bo21bo\$104b2o2b2o3bo11b3o27bo\$108bo16b2o\$106bob4o\$106b5o\$108b2o9\$155b2o\$155b2o4\$90bo18bo\$89bo18bo44b3o\$89b3o16b3o4\$123b2o\$123b2o29bo\$110bo43bo\$109b3o42bo\$108bo2bo\$90bo16b3o2b2o\$89b3o16bo2b3o\$88bo2b2o16b2o2b2o\$88bob2o20b3o\$90b2ob2o14b4obo\$87bo5bo15b2o2b2o\$88bo4bo18b2o\$89bo2bo\$91bo\$86bo18bo\$85bo18bo\$85b3o16b3o47b2o\$154b2o5\$152b3o6\$153bo\$153bo\$153bo\$84bo23b2o\$77b3o2bobo2b3o18b2o\$78b3o7b2o\$80bo\$82bobo\$82b2o7\$153b2o\$153b2o\$72b3o\$72bo2bo\$74b2o\$90b3o\$70bo2bo16bo2bo57b3o\$71b2o16bo3bo\$74b2o14bo2b2o\$73b3o16bo\$74bo15b2o\$71bo2bo14b3o\$72b2o15b3o60bo\$152bo\$78bobo71bo\$77bobobo14b3o8b2o\$95bo3bo7b2o\$75bo7bo11bo3bo\$84bo8b2o5b2o\$75b3o6bo7bo4bo4bo\$75b2o8bo6bo3bobo3bo\$75b2o2bo4bo7bo4bo4bo\$76bob3o2b2o8b2o5b2o\$76b2ob4o12b6o\$78b2o15b2o2b2o\$79bo18b3o\$97bobo\$97b2o53b2o\$152b2o5\$150b3o3\$63bo18bo\$62bo18bo\$62b3o16b3o\$151bo\$151bo\$151bo6\$91bo\$91bo\$91bo4\$60b2o\$60bob2o14bo72b2o\$62b2o14b2o71b2o\$60b2o18bo\$58b2o18b2o\$77bobo\$58bobo17bo\$59bo16bobo70b3o\$74bo\$74bobo4\$150bo\$150bo\$150bo2\$74b2o\$73bo2bo\$68b3obo3b2o\$68bo4b2o9b3o\$51b2o18bo13bob2obo\$50b3o2b2o11b2obo13b3obobo\$51bobob2o2b2o5bo17bo2b3obo\$52b2obo3b2o6b2o4bo2b3o5b2o4bo\$54b2o12bob2o3bob2o6bo\$73bob2o\$74bo\$150b2o\$150b2o5\$148b3o6\$149bo\$149bo\$149bo4\$41b3o\$41bo2bo\$40bo2b2o14b2o\$39bo2bo15bo2bo\$40b2o17bob2o\$59bo\$46bo13bobo12bo\$59bo2b2o11bo\$47b2o16bo9bo\$46bobo16bo83b2o\$48b2o99b2o\$47bo16b2o\$64b2o\$65bo2\$48b2o97b3o\$48b2o16b2o\$66b2o4\$148bo\$36bo18bo92bo\$35bo18bo93bo\$35b3o16b3o12\$148b2o\$60bo87b2o\$60bo\$60bo3\$146b3o5\$44bo\$44bo102bo\$43bobo101bo\$24bo122bo\$22b2ob2o18b2o\$22b2ob2o\$23bob3o17b2o\$22b3o6\$43b2o\$23b2o18b2o\$23b2o25bo\$30bo18bobo95b2o\$29bobo17bobo7bo87b2o\$29bobo15bo2bo8bo\$30bo15b4o5bo3bo\$45bo4bo3bobo\$26b3o5b2o9bobob2o3bobo\$26bob2o5b2o9b2o2b2o3bo89b3o\$26bob2o20bo\$29bo18bob4o\$30b3o15b5o\$28bo4bo16b2o\$32bo\$28bo117bo\$29bo116bo\$146bo10\$13bo18bo\$12bo18bo\$12b3o16b3o\$146b2o\$146b2o3\$45b2o\$45b2o\$144b3o2\$32bo\$31b3o\$30bo2b2o\$12bo17bob2o\$11b3o18b2ob2o108bo\$10bo2b2o14bo5bo109bo\$10b3obo15bo4bo109bo\$13b2o16bo2bo\$33bo\$9bo18bo\$8bo18bo\$8b3o16b3o8\$145b2o\$145b2o5\$143b3o\$b2o3bo\$o5b2o22b2o\$bobo2bo3b2o18b2o\$bobob2o3b2o\$2b2ob2o\$4bo139bo\$144bo\$144bo13\$144b2o\$144b2o5\$142b3o6\$143bo\$143bo\$143bo13\$143b2o\$143b2o5\$141b3o6\$142bo\$142bo\$142bo!`

My thought is perhaps some combination of the above will allow all debris to occupy a small footprint (ideally, exactly the size of the longboat's shadow) with respect to NE and SW rakes. Then the NE rakes could continually pass through the debris arising from continued operation and construct frozen tracks using whatever lanes remain available. The frozen tracks, by virtue of being SW gliders, also pass through the debris. Ultimately, a full cluster comes through, and once the cluster is all the way through the debris field, climbers running on it clean up the mess. That would successfully implement 2->5 without any helix help, saving us as many as 100 helix *WSS constructions down the line.

The longboat's shadow allows only 5 of the initial 13 even lanes to pass through to construction. I don't know if that is enough for universality. Can slow gliders constrained to a shooting range of lanes congruent mod 26 to 0, 2, 4, 6, or 8 produce frozen tracks?

Additional holes in the above - we can use C, A, C, A... to get a rake, and then place the longboat in the shadow of prior longboats. The issue comes from rephasing to get the next rake where it needs to be. So far, all arbitrary rephasings have some piece of debris dependent on when the rephasing ends, meaning there is debris tied to the rake. However, I haven't looked into ways to destroy the block + 2blinker constellation from beginning a block pull, and perhaps there is a solution in there that allows disentangling rephasing debris from the following rake.

There's probably something I am missing that either invalidates all of this or makes it easier than anticipated. But I definitely feel this is the most promising track pair thus far for starting off the ship, if the ship does start from only a pair.
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

What about doing construction with the NW rake you mentioned a while ago? As with SE rakes you can change lane just by delaying the climbers and once you have constructed a universal set of tracks on the left you can then start to clear away all of the debris from below. Something like this (but I think the 3 gliders tracks on the left are in an incorrect phase). It would need more spaceships in the helices in order to construct an initial slow salvo target but I think the idea is viable.

`x = 621, y = 1287, rule = B3/S23605bobo\$605b2o\$606bo2\$619bo\$618bo\$618b3o39\$586bobo\$586b2o\$587bo2\$600bo\$599bo\$599b3o39\$567bobo\$567b2o\$568bo2\$581bo\$580bo\$580b3o39\$548bobo\$548b2o\$549bo2\$562bo\$561bo\$561b3o39\$529bobo\$529b2o\$530bo2\$543bo\$542bo\$542b3o39\$510bobo\$510b2o\$511bo2\$524bo\$523bo\$523b3o39\$491bobo\$491b2o\$492bo2\$505bo\$504bo\$504b3o3\$124b2o\$124b2o3\$118b2o\$118b2o22\$123b2o\$123b2o3\$117b2o\$117b2o2\$163bo\$161b3o\$160bo311bobo\$160b2o310b2o\$473bo2\$486bo\$485bo\$485b3o6\$167bo\$166bobo\$166b2o4\$122b2o47b2o\$122b2o47b2o3\$116b2o\$116b2o2\$162bo\$160b3o\$159bo\$159b2o11\$166bo\$165bobo\$165b2o3\$193bo\$121b2o47b2o20bobo258bobo\$121b2o47b2o20b2o259b2o\$454bo2\$115b2o350bo\$115b2o349bo\$466b3o\$161bo\$159b3o\$158bo\$158b2o11\$165bo\$164bobo\$164b2o3\$192bo\$120b2o47b2o20bobo\$120b2o47b2o20b2o3\$114b2o\$114b2o2\$160bo\$158b3o\$157bo\$157b2o8\$434bobo\$434b2o\$435bo\$164bo\$163bobo282bo\$163b2o282bo\$447b3o2\$191bo\$119b2o47b2o20bobo\$119b2o47b2o20b2o2\$236bo\$113b2o120bobo\$113b2o120bo2bo\$236b2o\$159bo\$157b3o76b2o\$156bo78bobo\$156b2o77b2o11\$163bo\$162bobo\$162b2o3\$190bo\$118b2o47b2o20bobo\$118b2o47b2o20b2o2\$235bo\$112b2o120bobo\$112b2o120bo2bo\$235b2o\$158bo\$156b3o76b2o\$155bo78bobo178bobo\$155b2o77b2o179b2o\$416bo2\$429bo\$428bo\$428b3o6\$162bo\$161bobo\$161b2o3\$189bo\$117b2o47b2o20bobo\$117b2o47b2o20b2o2\$234bo\$111b2o120bobo\$111b2o120bo2bo\$234b2o\$157bo\$155b3o76b2o\$154bo78bobo\$154b2o77b2o11\$161bo\$160bobo\$160b2o3\$188bo\$116b2o47b2o20bobo206bobo\$116b2o47b2o20b2o207b2o\$397bo\$233bo\$110b2o120bobo175bo\$110b2o120bo2bo173bo\$233b2o174b3o\$156bo\$154b3o76b2o\$153bo78bobo\$153b2o77b2o11\$160bo\$159bobo\$159b2o3\$187bo\$115b2o47b2o20bobo\$115b2o47b2o20b2o2\$232bo\$109b2o120bobo\$109b2o120bo2bo\$232b2o\$155bo\$153b3o76b2o\$152bo78bobo\$152b2o77b2o8\$377bobo\$377b2o\$378bo\$159bo\$158bobo230bo\$158b2o230bo\$390b3o2\$186bo\$114b2o47b2o20bobo\$114b2o47b2o20b2o2\$231bo\$108b2o120bobo\$108b2o120bo2bo\$231b2o\$154bo\$152b3o76b2o\$151bo78bobo\$151b2o77b2o11\$158bo\$157bobo\$157b2o3\$185bo\$113b2o47b2o20bobo\$113b2o47b2o20b2o2\$230bo\$107b2o120bobo\$107b2o120bo2bo\$230b2o\$153bo\$151b3o76b2o\$150bo78bobo126bobo\$150b2o77b2o127b2o\$359bo2\$372bo\$371bo\$371b3o6\$157bo\$156bobo\$156b2o3\$184bo\$112b2o47b2o20bobo\$112b2o47b2o20b2o2\$229bo\$106b2o120bobo\$106b2o120bo2bo\$229b2o\$152bo\$150b3o76b2o\$149bo78bobo\$149b2o77b2o11\$156bo\$155bobo\$155b2o3\$183bo\$111b2o47b2o20bobo154bobo\$111b2o47b2o20b2o155b2o\$340bo\$228bo\$105b2o120bobo123bo\$105b2o120bo2bo121bo\$228b2o122b3o\$151bo\$149b3o76b2o\$148bo78bobo\$148b2o77b2o11\$155bo\$154bobo\$154b2o189bo\$343b6o\$343b2o2b2o\$182bo\$110b2o47b2o20bobo163bo\$110b2o47b2o20b2o160b2o2bo\$343b2o3bo\$227bo119bo\$104b2o120bobo116bobo\$104b2o120bo2bo116bo\$227b2o\$150bo\$148b3o76b2o\$147bo78bobo\$147b2o77b2o2\$345bo\$345bo\$323bo21b2o\$322b3o19bobo\$321b2o2bo17bo2bo7b3o\$321b5o16bo4bo5bo3bo\$320bo2b2o17bo2b3o10bo\$321b2o19b2o5bo8bo\$344b3o10b2o\$154bo192bo2bo2b4o\$153bobo172bo20bo5bo\$153b2o173b2o20b2o2\$329b2o\$181bo147bo\$109b2o47b2o20bobo\$109b2o47b2o20b2o2\$226bo102b2o\$103b2o120bobo101b2o\$103b2o120bo2bo\$226b2o\$149bo\$147b3o76b2o\$146bo78bobo\$146b2o77b2o\$316bobo\$316b2o\$317bo2\$330bo\$329bo27b2o\$329b3o25b2o\$334b3o9bobo\$346b2o\$347bo5bobo\$153bo196b2o\$152bobo200bo\$152b2o194b2o\$348b2o2bob2o\$349bo4b2o\$180bo167b2o3b3o\$108b2o47b2o20bobo167bo3bo\$108b2o47b2o20b2o169b3o\$350b3o\$225bo\$102b2o120bobo\$102b2o120bo2bo\$225b2o\$148bo\$146b3o76b2o114b2o\$145bo78bobo114bobo\$145b2o77b2o115bo6\$356b2o\$322b2o32b2o\$322bobo8b3o\$322bo\$358bo\$152bo194b2o9bo\$151bobo193b2o9bo\$151b2o\$354b3o3b3o2\$179bo123b2o45b2o6bo\$107b2o47b2o20bobo122bobo44b2o6bo\$107b2o47b2o20b2o123bo54bo\$297bobo\$224bo72b2o\$101b2o120bobo72bo\$101b2o120bo2bo\$224b2o85bo\$147bo162bo\$145b3o76b2o58b2o24b3o\$144bo78bobo58bobo\$144b2o77b2o59bo6\$355b2o\$265b2o88b2o\$265bobo64b3o\$265bo\$357bo\$151bo194b2o9bo\$150bobo193b2o9bo\$150b2o\$353b3o3b3o2\$178bo67b2o101b2o6bo\$106b2o47b2o20bobo66bobo100b2o6bo\$106b2o47b2o20b2o67bo110bo2\$223bo\$100b2o120bobo\$100b2o120bo2bo\$223b2o\$146bo\$144b3o76b2o2b2o\$143bo78bobo2bobo\$143b2o77b2o3bo4\$205bo\$204b2o\$204bobo147b2o\$354b2o\$331b3o2\$278bobo75bo\$150bo127b2o65b2o9bo\$149bobo127bo65b2o9bo\$149b2o35bo\$185b2o105bo59b3o3b3o\$185bobo103bo\$177bo113b3o54b2o6bo\$105b2o47b2o20bobo169b2o6bo\$105b2o47b2o20b2o178bo3\$99b2o\$99b2o66bo\$166b2o\$145bo20bobo\$143b3o\$142bo\$142b2o76bobo\$220b2o\$221bo4\$353b2o\$353b2o\$330b3o2\$355bo\$344b2o9bo\$145bo198b2o9bo\$146b2o\$147bo2bo200b3o3b3o\$148b2o\$148bo27bo170b2o6bo\$104b2o47b2o20bobo169b2o6bo\$104b2o41bo5b2o20b2o178bo\$148bo2\$98b2o\$98b2o2\$144bo\$142b3o\$141bo\$141b2o\$138bo120bobo\$137b2o120b2o\$137bobo120bo2\$273bo\$272bo79b2o\$272b3o77b2o\$329b3o2\$119bo234bo\$118b2o223b2o9bo\$118bobo222b2o9bo2\$350b3o3b3o2\$175bo170b2o6bo\$102bobo69bobo169b2o6bo\$174b2o25bobo150bo\$104bo96b2o\$101bo100bo\$103bo\$101b3o2\$143bo\$141b3o\$140bo\$140b2o13bobo\$156b2o\$156bo4\$351b2o\$351b2o\$328b3o2\$353bo\$342b2o9bo\$342b2o9bo2\$349b3o3b3o2\$174bo170b2o6bo\$173bobo169b2o6bo\$173b2o178bo\$240bobo\$240b2o\$241bo2\$254bo\$142bo110bo\$140b3o110b3o\$139bo\$139b2o6\$350b2o\$350b2o\$327b3o\$182bobo\$171bo10b2o168bo\$119bo49b6o8bo157b2o9bo\$120bo48b2o2b2o166b2o9bo\$118b3o\$170bo177b3o3b3o2\$344b2o6bo\$344b2o6bo\$352bo6\$141bo\$139b3o\$138bo\$138b2o6\$349b2o\$349b2o\$326b3o2\$221bobo127bo\$221b2o117b2o9bo\$222bo117b2o9bo2\$235bo111b3o3b3o\$234bo\$234b3o106b2o6bo\$343b2o6bo\$351bo6\$137bobo\$137bo\$137bo\$138bobo22bobo\$163b2o\$150bobo11bo\$150b2o\$151bo2\$348b2o\$348b2o\$325b3o2\$350bo\$339b2o9bo\$339b2o9bo2\$346b3o3b3o2\$342b2o6bo\$342b2o6bo\$350bo10\$202bobo\$202b2o\$203bo2\$216bo\$215bo131b2o\$215b3o129b2o\$324b3o2\$349bo\$338b2o9bo\$338b2o9bo2\$345b3o3b3o\$118bo\$118bobo220b2o6bo\$118b2o221b2o6bo\$144bobo202bo\$144b2o\$131bobo11bo\$131b2o\$132bo6\$144b3o\$144bo2bo\$143bo3bo\$148bo\$115b2o27b3ob2o\$115bobo12b3o15bo197b2o\$117bo12bo2bo9bo3b2o197b2o\$115bobo11bo3bo13bo175b3o\$114bo14b3o2bo\$114bobo13b4o214bo\$114bo25bobo194b2o9bo\$113bo26b2o195b2o9bo\$127bobo11bo\$127b2o215b3o3b3o\$128bo\$340b2o6bo\$340b2o6bo\$348bo\$183bobo\$183b2o\$184bo\$113b2o\$152bo44bo\$139b3o9b3o42bo\$108b2o29bo3b3o50b3o\$107b5o10bo28b2ob2o\$106b3o13bo2bob2o2bo7bo2bo5bo5b2o\$107b2o2bo2b2o8b2o3bo2b2o5bo2bo3bo2bob2ob2o\$108b3o3b2o8b2o6bo9b2o3b2o2b2obo\$125b7o6b3o2bo2bo6bo\$129b2o7b2o2bo\$138b3o\$345b2o\$345b2o\$322b3o2\$147bo199bo\$147b2o187b2o9bo\$146bobo187b2o9bo2\$343b3o3b3o2\$339b2o6bo\$339b2o6bo\$347bo\$164bo\$164b2o\$163bobo5\$95bo\$95bobo\$95b2o84bo\$121bobo57b2o\$121b2o57bobo\$108bobo11bo\$108b2o\$109bo234b2o\$344b2o\$321b3o2\$164bobo31bo147bo\$164b2o32b2o135b2o9bo\$165bo31bobo135b2o9bo2\$178bo163b3o3b3o\$177bo\$177b3o158b2o6bo\$338b2o6bo\$346bo\$215bo\$215b2o\$214bobo12\$343b2o\$343b2o\$320b3o2\$345bo\$334b2o9bo\$334b2o9bo2\$341b3o3b3o2\$337b2o6bo\$76bo260b2o6bo\$76bobo266bo\$76b2o\$102bobo\$102b2o\$89bobo11bo\$89b2o\$90bo4\$145bobo\$145b2o\$146bo2\$159bo\$158bo183b2o\$158b3o181b2o\$319b3o2\$344bo\$333b2o9bo\$333b2o9bo2\$340b3o3b3o2\$336b2o6bo\$336b2o6bo\$344bo15\$341b2o\$341b2o\$57bo260b3o\$57bobo\$57b2o284bo\$83bobo246b2o9bo\$83b2o247b2o9bo\$70bobo11bo\$70b2o267b3o3b3o\$71bo\$335b2o6bo\$335b2o6bo\$343bo\$126bobo\$126b2o\$127bo2\$140bo\$139bo\$139b3o8\$340b2o\$340b2o\$317b3o2\$342bo\$331b2o9bo\$331b2o9bo2\$338b3o3b3o2\$334b2o6bo\$334b2o6bo\$342bo8\$38bo\$38bobo\$38b2o\$64bobo\$64b2o\$51bobo11bo\$51b2o\$52bo4\$107bobo\$107b2o\$108bo2\$121bo\$120bo\$120b3o28\$19bo\$19bobo\$19b2o\$45bobo\$45b2o\$32bobo11bo\$32b2o\$33bo4\$88bobo\$88b2o\$89bo2\$102bo\$101bo\$101b3o28\$o\$obo\$2o\$26bobo\$26b2o\$13bobo11bo\$13b2o\$14bo4\$69bobo\$69b2o\$70bo2\$83bo\$82bo\$82b3o!`
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

### Re: (27,1)c/72 caterpillar challenge

NW and SE constructions have the potential to be much nicer because the lane can be changed without the need for rephasings. A large number of track pairs provide NW rakes, even a singleton climber. I guess I had just thrown NW rakes away for being on the "wrong" side, and hadn't found a viable SE option.

Now that I see your construction above, it being on the "wrong" side doesn't seem problematic at all, really. It actually looks ideal! No need to worry about debris shadows, full monochromatic/monoparity construction options. A ton of debris to eventually clean, but it's doable. The helix could provide the x1 glider tracks for a single climber, and one additional x1 NE stream, which the climber's NW rake collides with for an initial target. It must be well spaced enough to allow the full construction effort to take place before things collide. This is actually cheaper than making a track pair. Since NW constructions have no need for a rephasing, and the debris is always on the opposite side of the climber, this seems fully capable of executing a 1->5.

I'm kind of curious at this point whether a singleton should try to build seeds for the entire left helix. I don't know how quickly it can pull off constructions, and the period tripling mechanism would have to be rethought. The additional debris would probably be too costly to clean, so my gut feeling is its job should still only be 1->5.
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

What is the most effective way to lay a x1 target stream far to the left of a singleton trail? We could create a glider trail using 3 sets of x3 kickbacks, or a block trail with another collection of x3 collisions, but those both mean the same cost as if we were building two trails. That is quite a few helix ships, and I feel like better can be done.

We get to use as many x1 NW rakes as we want from the climber. There are no NW G + N LWSS reactions that rebound a glider to the NE or SE and are repeatable. LWSS reactions that drop still lives are out for this side of the trail, since the helix will plow right into them. No matter what, if we are using a NW rake we need a NE, SE or SW x1 signal to crash into.

We could potentially work this front end at x2 instead of x3, using only the rakes from the climber and a handful of x2 ships to get ourselves started. It would consist of some reaction to convert some number of x1 NW streams colliding with a N *WSS salvo into an x2 NE stream, done twice to get x1 targets. Some gliders would have to be heisenburned somewhere to actually get it to work, since the climber can only provide x1 NW rakes but x1 N LWSS aren't usable. I think it could definitely require fewer helix ships to do things this way at least.

Here's a crappy mockup:
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

biggiemac wrote:We could potentially work this front end at x2 instead of x3, using only the rakes from the climber and a handful of x2 ships to get ourselves started.

Interesting idea. When I was trying to come up with an example pattern I ran into problems with the second x1 NW stream colliding with the target site already constructed by the first NW stream. I came up with a workaround as below. Hopefully there exist simple *WSS salvos that can turn our phase-and-color-restricted NW gliders into the desired NE gliders but I have not got around to searching for them yet.

`x = 574, y = 314, rule = B3/S23561b3o\$561bo\$b2o559bo\$obo\$2bo5\$542b3o\$542bo\$543bo7\$523b3o\$523bo\$35b2o487bo\$34bobo\$36bo5\$504b3o\$504bo\$505bo7\$485b3o\$485bo\$69b2o415bo\$68bobo\$70bo5\$466b3o\$466bo\$467bo7\$447b3o\$447bo\$103b2o343bo\$102bobo\$104bo5\$428b3o\$428bo\$429bo7\$409b3o\$409bo\$137b2o271bo\$136bobo\$138bo5\$390b3o\$390bo\$391bo7\$371b3o\$371bo\$171b2o199bo\$170bobo\$172bo5\$352b3o\$352bo\$353bo7\$333b3o\$333bo\$205b2o127bo\$204bobo\$206bo4\$571b3o\$314b3o254bo\$314bo257bo\$315bo5\$4b2o\$5b2o545b3o\$4bo290b3o254bo\$295bo257bo\$239b2o55bo\$238bobo\$240bo4\$533b3o\$276b3o254bo\$276bo257bo\$277bo5\$38b2o\$39b2o473b3o\$38bo475bo\$515bo4\$264bo\$264bo\$264bo\$495b3o\$238b3o254bo\$238bo257bo\$239bo5\$72b2o\$73b2o401b3o\$72bo403bo\$477bo7\$457b3o\$200b3o254bo\$200bo257bo\$201bo5\$106b2o\$107b2o329b3o\$106bo331bo\$439bo7\$419b3o\$162b3o254bo\$162bo257bo\$163bo5\$140b2o\$141b2o257b3o\$140bo259bo\$401bo4\$262bo\$262bo\$262bo\$381b3o\$124b3o254bo\$124bo257bo\$125bo5\$174b2o\$175b2o185b3o\$174bo187bo\$363bo7\$343b3o\$86b3o254bo\$86bo257bo\$87bo5\$208b2o\$209b2o113b3o\$208bo115bo\$325bo7\$305b3o\$48b3o254bo\$48bo257bo\$49bo5\$242b2o\$243b2o41b3o\$242bo43bo\$287bo4\$260bo\$260bo\$260bo\$267b3o\$267bo\$268bo21\$260b2o\$259bo2bo\$259bo2bo\$260b2o24\$259b2o\$258bo2bo\$258bo2bo\$259b2o!`

EDIT: Silly me. The two glider collision giving a blinker is transparent to one of the input lanes, therefore the following is a simpler alternative:

`x = 293, y = 109, rule = B3/S2312b2o\$11bobo\$13bo\$281b3o\$281bo\$282bo7\$262b3o\$262bo\$263bo4\$46b2o\$45bobo\$47bo\$243b3o\$243bo\$244bo7\$224b3o\$224bo\$225bo4\$80b2o\$b2o76bobo\$obo78bo\$2bo202b3o\$205bo84b3o\$206bo83bo\$291bo6\$186b3o\$186bo84b3o\$187bo83bo\$272bo3\$114b2o\$35b2o76bobo\$34bobo78bo\$36bo130b3o\$167bo84b3o\$168bo83bo\$253bo6\$148b3o\$148bo84b3o\$149bo83bo\$234bo4\$69b2o\$68bobo\$70bo\$214b3o\$214bo\$215bo\$141bo\$141bo\$141bo4\$195b3o\$195bo\$196bo4\$103b2o\$102bobo\$104bo\$176b3o\$176bo\$177bo7\$157b3o\$157bo\$158bo\$140bo\$140bo\$140bo!`
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

### Re: (27,1)c/72 caterpillar challenge

Some repeatable 2 *WSS salvos that rebound a glider.

`x = 1893, y = 92, rule = B3/S2380b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o108b2o98b2o98b2o98b2o\$80bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo107bobo97bobo97bobo97bobo\$80bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo109bo99bo99bo99bo16\$42b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o108b2o98b2o98b2o98b2o\$42bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo107bobo97bobo97bobo97bobo\$42bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo109bo99bo99bo99bo12\$899bo\$898b3o\$897b2obo\$897b3o\$4b2o98b2o91b3o4b2o98b2o98b2o98b2o98b2o98b2o98b2o92b2o4b2o98b2o98b2o98b2o98b2o94bo3b2o108b2o98b2o98b2o98b2o\$4bobo97bobo89bo2bo4bobo91b3o3bobo97bobo97bobo91bo5bobo92bo4bobo97bobo97bobo91b3o3bobo97bobo97bobo97bobo92b3o2bobo107bobo97bobo97bobo97bobo\$4bo95bo3bo94bo4bo92bo2bo3bo99bo99bo92b3o4bo93b3o3bo99bo99bo93bo2bo2bo99bo93b3o3bo99bo94bob2obo105bo3bo99bo99bo99bo\$99b3o93bo3bo100bo196b3o96b2obo97b2obo99b3o195bo199bo2bo198b3o106b3o\$bo6b3o88bob2o96bo96bo3bo106bo88bo2bo6bo89b3o7bo90b3o100bo2bo97b3o94bo3bo97b3o95bo107bo93b2o107bob2o6bo91b3o197b3o\$3o4bo2bo89b3o93bobo101bo105b3o90bo5b3o89b2o6b3o89b3o100bo100bo2bo93bo101bo2bo94bo3bo102b3o202b3o5b3o89bo2bo101b3o92bo2bo\$ob2o6bo89b3o102bo91bobo99bo5b2obo90bo4b2obo96b2obo90b2o100bo3bo96bo97bobo98bo97bo106bob2o97bo103b2o5b2obo92bo100bo2bo95bo\$b3o2bo3bo89b2o102b3o191b3o4b3o88bobo5b3o97b3o193bo100bo3bo194bo3bo94bobo104b3o96b3o109b3o93bo103bo95bo\$b3o2bo3bo193bob2o189b2obo4b3o96b3o97b3o194bobo97bo198bo205b2o97bob2o108b3o90bobo104bo92bobo\$b2o7bo194b3o92b3o94b3o6b2o97b2o98b2o295bobo92b3o101bobo302b3o108b3o194bobo\$7bobo96b3o96b2o92bo2bo94b3o596bo2bo198bo207b2o110b2o\$106bo2bo192bo95b2o300b3o296bo197b3o\$106bo195bo397bo2bo95b3o197bo196b2obo414bo199bo\$106bo3bo188bobo398bo98bo2bo193bobo98b3o96b3o104b3o307b3o197b3o\$106bo593bo98bo101bo194bo2bo97b2o103bo2bo306b2obo196b2obo\$107bobo591bobo95bo100b3o196bo205bo306b3o104bo92b3o\$800bobo96b2obo196bo201bo3bo307b2o103b3o91b3o\$899b3o194bobo206bo412bob2o90b3o\$199b3o26bo671b2o400bobo97bo316b3o91b2o\$38b3o157bo2bo26b2o70b3o297bo100bo298b3o25b2o371b3o315b2o\$40bo61bo98bo25bobo69bo2bo296b3o98b3o297bo2bo23bobo170b3o25bo172bob2o107bo36b2o\$39bo61b3o93bo3bo100bo127b2o67b3o96b2obo32b2o63b2obo99b3o195bo28bo170bo2bo24b2o172b3o106b3o36b2o\$3bo6b3o88bob2o96bo96bo3bo106bo21b2o65bo2bo6bo89b3o7bo26b2o62b3o100bo2bo97b3o94bo3bo97b3o95bo26bobo78bo93b2o107bob2o6bo27bo63b3o22b2o173b3o22b2o\$2b3o4bo2bo89b3o93bobo101bo31b3o71b3o19bo70bo5b3o27bo61b2o6b3o24bo64b3o100bo100bo2bo30bo62bo101bo2bo94bo3bo102b3o26bo175b3o5b3o89bo2bo21bobo77b3o92bo2bo21bobo\$2bob2o6bo89b3o29b2o71bo91bobo34bo64bo5b2obo90bo4b2obo27b2o67b2obo90b2o28bo71bo3bo96bo33b2o62bobo98bo97bo106bob2o25b2o70bo103b2o5b2obo92bo23bo76bo2bo95bo23bo\$3b3o2bo3bo89b2o31b2o69b3o126bo64b3o4b3o88bobo5b3o27bobo67b3o121b2o70bo100bo3bo28bobo163bo3bo23b3o68bobo104b3o24bobo69b3o23b2o84b3o93bo103bo95bo\$3b3o2bo3bo121bo71bob2o189b2obo4b3o96b3o97b3o120bobo71bobo27b2o68bo198bo29bo175b2o97bob2o23b2o83b3o90bobo104bo92bobo\$3b2o7bo194b3o92b3o94b3o6b2o97b2o98b2o223bobo69bobo92b3o101bobo25bo276b3o22bo85b3o194bobo\$9bobo96b3o96b2o92bo2bo94b3o432bo163bo2bo198bo207b2o110b2o225b2o\$108bo2bo192bo95b2o300b3o296bo197b3o546b2o\$108bo195bo397bo2bo95b3o197bo196b2obo414bo130bo68bo\$108bo3bo188bobo398bo98bo2bo193bobo98b3o96b3o104b3o307b3o197b3o\$108bo593bo98bo101bo194bo2bo97b2o103bo2bo306b2obo196b2obo\$109bobo591bobo95bo100b3o196bo205bo306b3o104bo92b3o\$802bobo96b2obo196bo201bo3bo307b2o103b3o91b3o\$901b3o194bobo206bo412bob2o90b3o\$201b3o698b2o400bobo97bo316b3o91b2o\$200bo2bo98b3o297bo100bo298b3o398b3o315b2o\$104bo98bo97bo2bo296b3o98b3o297bo2bo196b3o198bob2o107bo\$103b3o93bo3bo100bo196b3o96b2obo97b2obo99b3o195bo199bo2bo198b3o106b3o\$5bo6b3o88bob2o96bo96bo3bo106bo88bo2bo6bo89b3o7bo90b3o100bo2bo97b3o94bo3bo97b3o95bo107bo93b2o107bob2o6bo91b3o197b3o\$4b3o4bo2bo89b3o93bobo101bo105b3o90bo5b3o89b2o6b3o89b3o100bo100bo2bo93bo101bo2bo94bo3bo102b3o202b3o5b3o89bo2bo101b3o92bo2bo\$4bob2o6bo89b3o102bo91bobo99bo5b2obo90bo4b2obo96b2obo90b2o100bo3bo96bo97bobo98bo97bo106bob2o97bo103b2o5b2obo92bo100bo2bo95bo\$5b3o2bo3bo89b2o102b3o191b3o4b3o88bobo5b3o97b3o193bo100bo3bo194bo3bo94bobo104b3o96b3o109b3o93bo103bo95bo\$5b3o2bo3bo193bob2o189b2obo4b3o96b3o97b3o194bobo97bo198bo205b2o97bob2o108b3o90bobo104bo92bobo\$5b2o7bo194b3o92b3o94b3o6b2o97b2o98b2o295bobo92b3o101bobo302b3o108b3o194bobo\$11bobo96b3o96b2o92bo2bo94b3o596bo2bo198bo207b2o110b2o\$110bo2bo192bo95b2o300b3o296bo197b3o\$110bo195bo397bo2bo95b3o197bo196b2obo414bo199bo\$110bo3bo188bobo398bo98bo2bo193bobo98b3o96b3o104b3o307b3o197b3o\$110bo593bo98bo296bo2bo97b2o103bo2bo306b2obo196b2obo\$111bobo591bobo95bo299bo205bo306b3o104bo92b3o\$804bobo296bo201bo3bo307b2o103b3o91b3o\$1100bobo206bo412bob2o90b3o\$1306bobo414b3o91b2o\$1723b2o!`

I didn't look at ones where the first collision was with a HWSS. Perhaps these will be enough. There are 2 options where a LWSS is just used as a heisenburp, meaning it could continue upwards. Maybe the lower half could use one of those options, and the surviving LWSS could filter out the upper half, making a total of 5 x2 *WSS streams needed to construct the x1 target trail. If not, it's going to be 6 streams, still far better than the 12+ x3 streams needed if the target is constructed via the fanouts.
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

A problem that I have been running into is that NE gliders cannot cross x1 NW streams. Therefore something like below is the best way I can think of getting two x2 NE streams. Am I missing something?

`x = 761, y = 875, rule = B3/S23354b2o\$354bobo\$354bo7\$335b2o\$335bobo\$335bo7\$316b2o\$316bobo\$316bo441b2o\$758bobo\$758bo5\$297b2o\$297bobo\$297bo441b2o\$739bobo\$739bo5\$278b2o\$278bobo\$278bo441b2o\$720bobo\$720bo5\$259b2o\$259bobo\$259bo441b2o\$701bobo\$701bo5\$240b2o\$240bobo\$240bo441b2o\$682bobo\$682bo5\$221b2o\$221bobo\$221bo441b2o\$663bobo\$663bo5\$202b2o\$202bobo\$202bo441b2o\$644bobo\$644bo5\$183b2o\$183bobo\$183bo441b2o\$625bobo\$625bo5\$164b2o\$164bobo\$164bo441b2o\$606bobo\$606bo5\$145b2o\$145bobo\$145bo441b2o\$587bobo\$587bo5\$126b2o\$126bobo\$126bo441b2o\$568bobo\$568bo5\$107b2o\$107bobo\$107bo441b2o\$549bobo\$549bo5\$88b2o\$88bobo\$88bo441b2o\$530bobo\$530bo5\$69b2o\$69bobo\$69bo441b2o\$511bobo\$511bo5\$50b2o\$50bobo\$50bo441b2o\$492bobo\$492bo5\$31b2o\$31bobo\$31bo441b2o\$473bobo\$473bo7\$454b2o\$454bobo\$454bo7\$435b2o\$435bobo\$5b3o427bo\$5bo2bo\$5bo\$5bo\$6bobo\$14bo\$13b3o\$12b2obo\$12b3o\$13b2o3\$2bo\$b3o\$2obo\$3o\$b2o2\$7b3o\$7bo2bo\$7bo\$7bo\$8bobo\$16bo\$15b3o\$14b2obo\$14b3o\$15b2o3\$4bo\$3b3o\$2b2obo\$2b3o\$3b2o2\$9b3o\$9bo2bo\$9bo\$9bo\$10bobo\$18bo\$17b3o\$16b2obo\$16b3o\$17b2o3\$6bo\$5b3o\$4b2obo\$4b3o\$5b2o2\$11b3o\$11bo2bo\$11bo\$11bo\$12bobo\$20bo\$19b3o\$18b2obo\$18b3o\$19b2o3\$8bo\$7b3o\$6b2obo\$6b3o\$7b2o2\$13b3o\$13bo2bo\$13bo\$13bo\$14bobo\$22bo\$21b3o\$20b2obo\$20b3o\$21b2o3\$10bo\$9b3o\$8b2obo\$8b3o\$9b2o2\$15b3o\$15bo2bo\$15bo\$15bo\$16bobo\$24bo\$23b3o\$22b2obo\$22b3o\$23b2o3\$12bo\$11b3o\$10b2obo\$10b3o\$11b2o2\$17b3o\$17bo2bo\$17bo\$17bo\$18bobo\$26bo\$25b3o\$24b2obo\$24b3o\$25b2o3\$14bo\$13b3o\$12b2obo\$12b3o\$13b2o2\$19b3o\$19bo2bo\$19bo\$19bo\$20bobo\$28bo\$27b3o\$26b2obo\$26b3o\$27b2o3\$16bo\$15b3o\$14b2obo\$14b3o\$15b2o2\$21b3o\$21bo2bo\$21bo\$21bo\$22bobo\$30bo\$29b3o\$28b2obo\$28b3o\$29b2o3\$18bo\$17b3o\$16b2obo\$16b3o\$17b2o185\$83b3o\$83bo2bo\$83bo\$83bo\$84bobo2\$89b3o\$89bo2bo\$89bo\$89bo\$90bobo8\$85b3o\$85bo2bo\$85bo\$85bo\$86bobo2\$91b3o\$91bo2bo\$91bo\$91bo\$92bobo8\$87b3o\$87bo2bo\$87bo\$87bo\$88bobo2\$93b3o\$93bo2bo\$93bo\$93bo\$94bobo8\$89b3o\$89bo2bo\$89bo\$89bo\$90bobo2\$95b3o\$95bo2bo\$95bo\$95bo\$96bobo8\$91b3o\$91bo2bo\$91bo\$91bo\$92bobo2\$97b3o\$97bo2bo\$97bo\$97bo\$98bobo8\$93b3o\$93bo2bo\$93bo\$93bo\$94bobo2\$99b3o\$99bo2bo\$99bo\$99bo\$100bobo96\$218b3o\$217bo2bo\$220bo\$216bo3bo\$220bo\$217bobo5\$217b3o\$216bo2bo\$219bo\$219bo\$216bobo4\$220b3o\$219bo2bo\$222bo\$218bo3bo\$222bo\$219bobo5\$219b3o\$218bo2bo\$221bo\$221bo\$218bobo4\$222b3o\$221bo2bo\$224bo\$220bo3bo\$224bo\$221bobo5\$221b3o\$220bo2bo\$223bo\$223bo\$220bobo4\$224b3o\$223bo2bo\$226bo\$222bo3bo\$226bo\$223bobo5\$223b3o\$222bo2bo\$225bo\$225bo\$222bobo4\$226b3o\$225bo2bo\$228bo\$224bo3bo\$228bo\$225bobo5\$225b3o\$224bo2bo\$227bo\$227bo\$224bobo4\$228b3o\$227bo2bo\$230bo\$226bo3bo\$230bo\$227bobo5\$227b3o\$226bo2bo\$229bo\$229bo\$226bobo4\$230b3o\$229bo2bo\$232bo\$228bo3bo\$232bo\$229bobo5\$229b3o\$228bo2bo\$231bo\$231bo\$228bobo4\$232b3o\$231bo2bo\$234bo\$230bo3bo\$234bo\$231bobo5\$231b3o\$230bo2bo\$233bo\$233bo\$230bobo4\$234b3o\$233bo2bo\$236bo\$232bo3bo\$236bo\$233bobo5\$233b3o\$232bo2bo\$235bo\$235bo\$232bobo!`
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

### Re: (27,1)c/72 caterpillar challenge

Yep, I've also been a bit bummed NW and NE streams cannot pass through each other at x1. One can do things with a zig-zag, recycling the x2 stream after it makes the first blinker.
`x = 288, y = 413, rule = LifeHistory206.3A\$206.A\$207.A7\$187.3A\$187.A\$188.A7\$168.3A\$168.A\$169.A7\$149.3A\$149.A\$150.A7\$130.3A\$130.A\$131.A7\$111.3A\$111.A\$112.A7\$92.3A\$92.A\$93.A7\$73.3A\$73.A\$74.A7\$54.3A\$54.A\$55.A7\$35.3A\$35.A\$36.A7\$16.3A\$16.A\$17.A\$13.3A\$12.A2.A\$15.A\$11.A3.A\$15.A\$12.A.A4\$10.3A\$10.A2.A\$10.A\$10.A\$11.A.A2\$278.3A\$278.A\$279.A\$15.3A\$14.A2.A\$17.A\$.3A9.A3.A26.2A\$A2.A13.A25.A.A\$3.A10.A.A28.A\$3.A255.3A\$A.A256.A\$260.A\$12.3A\$12.A2.A\$12.A\$12.A\$13.A.A2\$240.3A\$240.A\$241.A\$17.3A\$16.A2.A\$19.A\$3.3A9.A3.A58.2A\$2.A2.A13.A57.A.A\$5.A10.A.A60.A\$5.A215.3A\$2.A.A216.A\$222.A\$14.3A\$14.A2.A\$14.A\$14.A\$15.A.A2\$202.3A\$202.A\$203.A\$19.3A\$18.A2.A\$21.A\$5.3A9.A3.A90.2A\$4.A2.A13.A89.A.A\$7.A10.A.A92.A\$7.A175.3A\$4.A.A176.A\$184.A\$16.3A\$16.A2.A\$16.A\$16.A\$17.A.A2\$164.3A\$164.A\$165.A\$21.3A\$20.A2.A\$23.A\$7.3A9.A3.A\$6.A2.A13.A\$9.A10.A.A122.2A\$9.A135.3A.A135.3A\$6.A.A138.2A.A134.A\$150.A135.A\$18.3A128.A\$18.A2.A126.A\$18.A126.3A\$18.A\$19.A.A2\$126.3A137.3A\$126.A139.A\$127.A139.A\$23.3A\$22.A2.A\$25.A\$9.3A9.A3.A\$8.A2.A13.A\$11.A10.A.A\$11.A235.3A\$8.A.A236.A\$248.A\$20.3A\$20.A2.A\$20.A\$20.A\$21.A.A2\$89.2A137.3A\$89.2A137.A\$229.A\$25.3A58.A\$24.A2.A57.A.2A.A\$27.A56.A5.A\$11.3A9.A3.A62.A\$10.A2.A13.A57.A.A\$13.A10.A.A\$13.A195.3A\$10.A.A196.A\$83.3A124.A\$22.3A58.A2.A\$22.A2.A57.A\$22.A60.A\$22.A61.A.A\$23.A.A2\$190.3A\$190.A\$88.3A100.A\$27.3A57.A2.A\$26.A2.A60.A55.A\$29.A56.A3.A55.A\$13.3A9.A3.A60.A27.2A26.A\$12.A2.A13.A57.A.A27.A.A\$15.A10.A.A90.A\$15.A155.3A\$12.A.A156.A\$85.3A84.A\$24.3A58.A2.A\$24.A2.A57.A\$24.A60.A\$24.A61.A.A\$25.A.A2\$152.3A\$152.A\$90.3A60.A\$29.3A57.A2.A\$28.A2.A60.A\$31.A56.A3.A\$15.3A9.A3.A60.A\$14.A2.A13.A57.A.A\$17.A10.A.A\$17.A\$14.A.A\$87.3A\$26.3A58.A2.A\$26.A2.A57.A\$26.A60.A\$26.A61.A.A\$27.A.A2\$114.3A\$114.A\$92.3A20.A\$31.3A57.A2.A\$30.A2.A60.A\$33.A56.A3.A\$17.3A9.A3.A60.A\$16.A2.A13.A57.A.A\$19.A10.A.A\$19.A\$16.A.A\$89.3A14.3A\$28.3A58.A2.A12.A2.A\$28.A2.A57.A18.A\$28.A60.A18.A\$28.A61.A.A12.A.A\$29.A.A4\$94.3A\$33.3A57.A2.A\$32.A2.A60.A\$35.A56.A3.A\$19.3A9.A3.A60.A\$18.A2.A13.A57.A.A\$21.A10.A.A\$21.A\$18.A.A\$91.3A14.3A\$30.3A58.A2.A12.A2.A\$30.A2.A57.A18.A\$30.A60.A18.A\$30.A61.A.A12.A.A\$31.A.A4\$96.3A\$35.3A57.A2.A\$34.A2.A60.A\$37.A56.A3.A\$21.3A9.A3.A60.A\$20.A2.A13.A57.A.A\$23.A10.A.A\$23.A\$20.A.A\$93.3A14.3A\$32.3A58.A2.A12.A2.A\$32.A2.A57.A18.A\$32.A60.A18.A\$32.A61.A.A12.A.A\$33.A.A4\$98.3A\$37.3A57.A2.A\$36.A2.A60.A\$39.A56.A3.A\$23.3A9.A3.A60.A\$22.A2.A13.A57.A.A\$25.A10.A.A\$25.A\$22.A.A\$95.3A14.3A\$34.3A58.A2.A12.A2.A\$34.A2.A57.A18.A\$34.A60.A18.A\$34.A61.A.A12.A.A\$35.A.A4\$100.3A\$39.3A57.A2.A\$38.A2.A60.A\$41.A56.A3.A\$25.3A9.A3.A60.A\$24.A2.A13.A57.A.A\$27.A10.A.A\$27.A\$24.A.A\$97.3A14.3A\$36.3A58.A2.A12.A2.A\$36.A2.A57.A18.A\$36.A60.A18.A\$36.A61.A.A12.A.A\$37.A.A4\$102.3A\$41.3A57.A2.A\$40.A2.A60.A\$43.A56.A3.A\$27.3A9.A3.A60.A\$26.A2.A13.A57.A.A\$29.A10.A.A\$29.A\$26.A.A\$99.3A14.3A\$38.3A58.A2.A12.A2.A\$38.A2.A57.A18.A\$38.A60.A18.A\$38.A61.A.A12.A.A\$39.A.A4\$104.3A\$43.3A57.A2.A\$42.A2.A60.A\$45.A56.A3.A\$29.3A9.A3.A60.A\$28.A2.A13.A57.A.A\$31.A10.A.A\$31.A\$28.A.A\$101.3A14.3A\$40.3A58.A2.A12.A2.A\$40.A2.A57.A18.A\$40.A60.A18.A\$40.A61.A.A12.A.A\$41.A.A4\$106.3A\$45.3A57.A2.A\$44.A2.A60.A\$47.A56.A3.A\$31.3A9.A3.A60.A\$30.A2.A13.A57.A.A\$33.A10.A.A\$33.A\$30.A.A\$103.3A14.3A\$42.3A58.A2.A12.A2.A\$42.A2.A57.A18.A\$42.A60.A18.A\$42.A61.A.A12.A.A\$43.A.A4\$108.3A\$47.3A57.A2.A\$46.A2.A60.A\$49.A56.A3.A\$33.3A9.A3.A60.A\$32.A2.A13.A57.A.A\$35.A10.A.A\$35.A\$32.A.A\$105.3A\$44.3A58.A2.A\$44.A2.A57.A\$44.A60.A\$44.A61.A.A\$45.A.A!`

I'm just hoping that doesn't end up costing more space than it saves. It will probably require the dirty singleton constructor to build the x2 *WSS streams, rather than the clean one, so that they can be packed tightly enough.

This whole ship is resistant to top-down construction, since everything must be spaced at the top such that it aligns perfectly at the bottom. And when modular restrictions come into play, the chinese remainder theorem helps us out but not without giving some pretty big numbers, given that 17 and 19 are both in play. The above isn't actually possible, since the NW streams have a specific horizontal restriction. Consecutive NW rakes must have offset (-4, 2x). I am working out a version of the above pattern that respects this, and I'll add lifehistory comments designating the amount by which pieces can be shifted.
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

That looks promising. I didn't find that reflector in my search so here is what I came up with instead. I realised that the NW rakes need to have a fixed sequence of horizontal spacing but I didn't want to hurt my head with that just yet!

`x = 1445, y = 1026, rule = B3/S23354b2o\$354bobo\$354bo7\$335b2o\$335bobo\$335bo7\$316b2o\$316bobo\$316bo441b2o\$758bobo\$758bo5\$297b2o\$297bobo1030b2o\$297bo441b2o589bobo\$739bobo588bo\$739bo5\$278b2o\$278bobo1030b2o\$278bo441b2o589bobo\$720bobo588bo\$720bo5\$259b2o\$259bobo1030b2o\$259bo441b2o589bobo\$701bobo588bo\$701bo5\$240b2o\$240bobo1030b2o\$240bo441b2o589bobo\$682bobo588bo\$682bo5\$221b2o\$221bobo1030b2o\$221bo441b2o589bobo\$663bobo588bo\$663bo5\$202b2o\$202bobo1030b2o\$202bo441b2o589bobo\$644bobo588bo\$644bo5\$183b2o\$183bobo1030b2o\$183bo441b2o589bobo\$625bobo588bo\$625bo5\$164b2o\$164bobo1030b2o\$164bo441b2o589bobo\$606bobo588bo\$606bo5\$145b2o\$145bobo1030b2o\$145bo441b2o589bobo\$587bobo588bo\$587bo5\$126b2o\$126bobo1030b2o\$126bo441b2o589bobo\$568bobo588bo\$568bo5\$107b2o\$107bobo1030b2o\$107bo441b2o589bobo\$549bobo588bo\$549bo5\$88b2o\$88bobo1030b2o\$88bo441b2o589bobo\$530bobo588bo\$530bo5\$69b2o\$69bobo1030b2o\$69bo441b2o589bobo\$511bobo588bo\$511bo5\$50b2o\$50bobo1030b2o\$50bo441b2o589bobo\$492bobo588bo\$492bo5\$31b2o\$31bobo1030b2o\$31bo441b2o589bobo\$473bobo588bo\$473bo6\$1045b2o\$454b2o589bobo\$454bobo588bo\$454bo6\$1026b2o414b2o\$435b2o589bobo413bobo\$435bobo588bo415bo\$5b3o427bo\$5bo2bo\$5bo\$5bo\$6bobo\$14bo\$13b3o991b2o414b2o\$12b2obo991bobo413bobo\$12b3o992bo415bo\$13b2o3\$2bo\$b3o\$2obo\$3o1401b2o\$b2o1401bobo\$1404bo\$7b3o\$7bo2bo\$7bo\$7bo\$8bobo\$16bo\$15b3o1367b2o\$14b2obo1367bobo\$14b3o1368bo\$15b2o3\$4bo\$3b3o\$2b2obo\$2b3o1361b2o\$3b2o1361bobo\$1366bo\$9b3o\$9bo2bo\$9bo\$9bo\$10bobo\$18bo\$17b3o1327b2o\$16b2obo1327bobo\$16b3o1328bo\$17b2o3\$6bo\$5b3o\$4b2obo\$4b3o1321b2o\$5b2o1321bobo\$1328bo\$11b3o\$11bo2bo\$11bo\$11bo\$12bobo\$20bo\$19b3o1287b2o\$18b2obo1287bobo\$18b3o1288bo\$19b2o3\$8bo\$7b3o\$6b2obo\$6b3o1281b2o\$7b2o1281bobo\$1290bo\$13b3o\$13bo2bo\$13bo\$13bo\$14bobo\$22bo\$21b3o1247b2o\$20b2obo1247bobo\$20b3o1248bo\$21b2o3\$10bo\$9b3o\$8b2obo\$8b3o1241b2o\$9b2o1241bobo\$1252bo\$15b3o\$15bo2bo\$15bo\$15bo\$16bobo\$24bo\$23b3o1207b2o\$22b2obo1207bobo\$22b3o1208bo\$23b2o3\$12bo\$11b3o\$10b2obo\$10b3o1201b2o\$11b2o1201bobo\$1214bo\$17b3o\$17bo2bo\$17bo\$17bo\$18bobo\$26bo\$25b3o1167b2o\$24b2obo1167bobo\$24b3o1168bo\$25b2o3\$14bo\$13b3o\$12b2obo\$12b3o1161b2o\$13b2o1161bobo\$1176bo\$19b3o\$19bo2bo\$19bo\$19bo\$20bobo\$28bo\$27b3o1127b2o\$26b2obo1127bobo\$26b3o1128bo\$27b2o3\$16bo\$15b3o\$14b2obo\$14b3o1121b2o\$15b2o1121bobo\$1138bo\$21b3o\$21bo2bo\$21bo\$21bo\$22bobo\$30bo\$29b3o1087b2o\$28b2obo1087bobo\$28b3o1088bo\$29b2o3\$18bo\$17b3o\$16b2obo\$16b3o\$17b2o187\$82b3o\$82bo2bo\$82bo\$82bo\$83bobo\$91bo\$90b3o\$89b2obo\$89b3o\$90b2o9\$84b3o\$84bo2bo\$84bo\$84bo\$85bobo\$93bo\$92b3o\$91b2obo\$91b3o\$92b2o9\$86b3o\$86bo2bo\$86bo\$86bo\$87bobo\$95bo\$94b3o\$93b2obo\$93b3o\$94b2o9\$88b3o\$88bo2bo\$88bo\$88bo\$89bobo\$97bo\$96b3o\$95b2obo\$95b3o\$96b2o9\$90b3o\$90bo2bo\$90bo\$90bo\$91bobo\$99bo\$98b3o\$97b2obo\$97b3o\$98b2o9\$92b3o\$92bo2bo\$92bo\$92bo\$93bobo\$101bo\$100b3o\$99b2obo\$99b3o\$100b2o9\$94b3o\$94bo2bo\$94bo\$94bo\$95bobo\$103bo\$102b3o\$101b2obo\$101b3o\$102b2o9\$96b3o\$96bo2bo\$96bo\$96bo\$97bobo\$105bo\$104b3o\$103b2obo\$103b3o\$104b2o9\$98b3o\$98bo2bo\$98bo\$98bo\$99bobo\$107bo\$106b3o\$105b2obo\$105b3o\$106b2o9\$100b3o\$100bo2bo\$100bo\$100bo\$101bobo\$109bo\$108b3o\$107b2obo\$107b3o\$108b2o174\$218b3o\$218bo2bo\$218bo\$218bo3bo\$218bo\$219bobo5\$217b3o\$217bo2bo\$217bo\$217bo\$218bobo4\$220b3o\$220bo2bo\$220bo\$220bo3bo\$220bo\$221bobo5\$219b3o\$219bo2bo\$219bo\$219bo\$220bobo4\$222b3o\$222bo2bo\$222bo\$222bo3bo\$222bo\$223bobo5\$221b3o\$221bo2bo\$221bo\$221bo\$222bobo4\$224b3o\$224bo2bo\$224bo\$224bo3bo\$224bo\$225bobo5\$223b3o\$223bo2bo\$223bo\$223bo\$224bobo4\$226b3o\$226bo2bo\$226bo\$226bo3bo\$226bo\$227bobo5\$225b3o\$225bo2bo\$225bo\$225bo\$226bobo4\$228b3o\$228bo2bo\$228bo\$228bo3bo\$228bo\$229bobo5\$227b3o\$227bo2bo\$227bo\$227bo\$228bobo4\$230b3o\$230bo2bo\$230bo\$230bo3bo\$230bo\$231bobo5\$229b3o\$229bo2bo\$229bo\$229bo\$230bobo4\$232b3o\$232bo2bo\$232bo\$232bo3bo\$232bo\$233bobo5\$231b3o\$231bo2bo\$231bo\$231bo\$232bobo4\$234b3o\$234bo2bo\$234bo\$234bo3bo\$234bo\$235bobo5\$233b3o\$233bo2bo\$233bo\$233bo\$234bobo!`
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

### Re: (27,1)c/72 caterpillar challenge

Here's the modular arithmetic all worked out for the transparent blinker trail. I'm not sure if there is a value of M where the spare glider heisenburns in the *WSS streams, I didn't bother to work out whether it was invariant.
`x = 1222, y = 1380, rule = 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Edited for clarity : now NW rakes list vertical movement, NE rakes horizontal. To move a NW rake 2 cells down, delay its climber 4 generations. To move a NE rake right by 2 cells, advance the helix by 4 generations.
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

I wrote:I'm not sure if there is a value of M where the spare glider heisenburns in the *WSS streams, I didn't bother to work out whether it was invariant.

Moving the last glider stream down 504 cells brings it 56 cells closer horizontally to the *WSS stream, since the *WSS are offset (2, 18) and (56, 504) = 28 * (2, 18). The NW x2 gliders are offset (-38, 18), meaning the horizontal separation in a snapshot is invariant mod 2 - (-38) = 40. The gcd of 40 and 56 is 8, meaning we only have 40/8 = 5 reachable separations through varying M. None of these provide a heisenburn for the glider, although if we could change the horizontal separation by 6 cells instead of 8 it would. It's a bit unfortunate, since I initially thought there were 19 reachable separations instead of 5, before I caught my error.

It's really hard to guess beforehand which primes one will encounter when working with a caterpillar design!

chris_c wrote:Here is what I came up with instead (7 *WSS with an intermediate block, one spare glider to clean)

I do like this design, especially since there is no costly extra zigzag. The *WSS streams have to continue downwards all the way until they are constructed, which could put them as far left as the helix. The rebounding glider streams would then have to make a circuit the full width of the ship front, which won't be trivial and will eat up a lot of space. My design does this circuit twice, yours only once with the cost 2 *WSS higher. Not sure which is better.

I still want it to be possible to do all the construction for these x2 streams using the singleton track, allowing the *WSS to be much further right and making the zigzags less costly. That would require some elegant x2 feedback loop. If that turns out to be reasonable, my design would probably win out. If not, I imagine we should go with yours.
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

biggiemac wrote:It's really hard to guess beforehand which primes one will encounter when working with a caterpillar design!

Agreed! Your latest arithmetic regarding the possibility of heisenburns is particularly scary. I didn't want to go near that problem.

biggiemac wrote:I still want it to be possible to do all the construction for these x2 streams using the singleton track, allowing the *WSS to be much further right and making the zigzags less costly. That would require some elegant x2 feedback loop. If that turns out to be reasonable, my design would probably win out. If not, I imagine we should go with yours.

I hope that your version can be made to work best because it is very elegant. Here is a version with zig-zaging but only 5 LWSS. I haven't worked out the modular arithmetic for the repeated -4 offsets (sorry).

`x = 574, y = 626, rule = B3/S23440b2o\$440bobo\$440bo7\$421b2o\$421bobo\$421bo7\$402b2o\$402bobo\$402bo7\$383b2o\$383bobo\$383bo7\$364b2o\$364bobo\$364bo7\$345b2o\$345bobo\$345bo7\$326b2o\$326bobo\$326bo7\$307b2o\$307bobo\$307bo7\$288b2o\$288bobo\$288bo7\$269b2o\$269bobo\$269bo7\$250b2o\$250bobo\$250bo7\$231b2o\$231bobo\$231bo7\$212b2o\$212bobo\$212bo7\$193b2o\$193bobo\$193bo7\$174b2o\$174bobo\$174bo7\$155b2o\$155bobo\$155bo7\$136b2o\$136bobo\$136bo6\$560b2o\$117b2o441bobo\$117bobo440bo\$117bo6\$541b2o\$98b2o441bobo\$98bobo440bo\$98bo6\$522b2o\$79b2o441bobo\$79bobo440bo\$79bo6\$503b2o\$60b2o441bobo\$60bobo440bo\$60bo6\$484b2o\$41b2o441bobo\$41bobo440bo\$41bo6\$465b2o\$22b2o441bobo\$22bobo440bo\$22bo6\$446b2o\$446bobo\$446bo5\$2bo\$b3o\$2obo10b2o411b2o\$3o10bobo411bobo\$b2o12bo411bo2\$7b3o\$7bo2bo\$7bo\$7bo\$8bobo\$16bo391b2o\$15b3o390bobo\$14b2obo390bo\$14b3o\$15b2o3\$4bo\$3b3o\$2b2obo42b2o339b2o\$2b3o42bobo339bobo\$3b2o44bo339bo2\$9b3o\$9bo2bo\$9bo\$9bo\$10bobo\$18bo351b2o\$17b3o350bobo\$16b2obo350bo\$16b3o\$17b2o3\$6bo\$5b3o\$4b2obo74b2o267b2o\$4b3o74bobo267bobo\$5b2o76bo267bo2\$11b3o\$11bo2bo\$11bo\$11bo\$12bobo\$20bo311b2o\$19b3o310bobo\$18b2obo310bo\$18b3o\$19b2o3\$8bo\$7b3o\$6b2obo106b2o195b2o\$6b3o106bobo195bobo\$7b2o108bo195bo2\$13b3o\$13bo2bo\$13bo\$13bo\$14bobo\$22bo271b2o\$21b3o270bobo274b2o\$20b2obo270bo276bobo\$20b3o548bo\$21b2o3\$10bo\$9b3o\$8b2obo138b2o123b2o\$8b3o138bobo123bobo274b2o\$9b2o140bo123bo276bobo\$552bo\$15b3o\$15bo2bo\$15bo\$15bo\$16bobo\$24bo231b2o\$23b3o230bobo274b2o\$22b2obo230bo276bobo\$22b3o508bo\$23b2o3\$12bo\$11b3o\$10b2obo170b2o51b2o\$10b3o170bobo51bobo274b2o\$11b2o172bo51bo276bobo\$514bo\$17b3o\$17bo2bo\$17bo\$17bo\$18bobo\$26bo191b2o\$25b3o190bobo274b2o\$24b2obo190bo276bobo\$24b3o468bo\$25b2o3\$14bo\$13b3o\$12b2obo\$12b3o461b2o\$13b2o461bobo\$476bo\$19b3o\$19bo2bo\$19bo\$19bo\$20bobo\$28bo151b2o\$27b3o150bobo274b2o\$26b2obo150bo26b2ob2o245bobo\$26b3o178b2ob2o245bo\$27b2o3\$16bo\$15b3o\$14b2obo\$14b3o421b2o\$15b2o421bobo\$438bo\$21b3o\$21bo2bo\$21bo\$21bo\$22bobo\$30bo111b2o\$29b3o110bobo274b2o\$28b2obo110bo276bobo\$28b3o388bo\$29b2o3\$18bo\$17b3o\$16b2obo\$16b3o381b2o\$17b2o381bobo\$400bo\$23b3o\$23bo2bo\$23bo\$23bo\$24bobo\$32bo71b2o\$31b3o70bobo274b2o\$30b2obo70bo276bobo\$30b3o348bo\$31b2o3\$20bo\$19b3o\$18b2obo\$18b3o341b2o\$19b2o341bobo\$362bo\$25b3o\$25bo2bo\$25bo\$25bo\$26bobo\$34bo\$33b3o307b2o\$32b2obo36b3o130b2ob2o133bobo\$32b3o39bo130b2ob2o133bo\$33b2o38bo3\$22bo\$21b3o\$20b2obo\$20b3o301b2o\$21b2o301bobo\$324bo\$27b3o38b3o\$27bo2bo37bo2bo\$27bo40bo\$27bo40bo\$28bobo38bobo\$36bo\$35b3o36b3o228b2o\$34b2obo36bo2bo28b3o196bobo\$34b3o37bo33bo196bo\$35b2o37bo32bo\$75bobo2\$24bo\$23b3o\$22b2obo\$22b3o261b2o\$23b2o261bobo\$286bo\$29b3o38b3o\$29bo2bo37bo2bo\$29bo40bo\$29bo40bo\$30bobo38bobo\$38bo\$37b3o36b3o188b2o\$36b2obo36bo2bo60b3o124bobo\$36b3o37bo65bo124bo\$37b2o37bo64bo\$77bobo2\$26bo\$25b3o\$24b2obo\$24b3o221b2o\$25b2o221bobo\$248bo\$31b3o38b3o\$31bo2bo37bo2bo\$31bo40bo\$31bo40bo\$32bobo38bobo\$40bo\$39b3o36b3o148b2o\$38b2obo36bo2bo92b3o26b2ob2o21bobo\$38b3o37bo97bo26b2ob2o21bo\$39b2o37bo96bo\$79bobo2\$28bo\$27b3o\$26b2obo\$26b3o181b2o\$27b2o181bobo\$210bo\$33b3o38b3o\$33bo2bo37bo2bo\$33bo40bo\$33bo40bo\$34bobo38bobo\$42bo\$41b3o36b3o\$40b2obo36bo2bo\$40b3o37bo\$41b2o37bo\$81bobo2\$30bo172bo\$29b3o170bobo\$28b2obo170bobo\$28b3o172bo\$29b2o\$198b2o7b2o\$35b3o38b3o118bo2bo5bo2bo\$35bo2bo37bo2bo118b2o7b2o\$35bo40bo\$35bo40bo126bo\$36bobo38bobo122bobo\$44bo157bobo\$43b3o36b3o118bo\$42b2obo36bo2bo\$42b3o37bo\$43b2o37bo\$83bobo2\$32bo\$31b3o\$30b2obo\$30b3o\$31b2o2\$37b3o38b3o\$37bo2bo37bo2bo\$37bo40bo\$37bo40bo123bo\$38bobo38bobo119bobo\$46bo154bobo\$45b3o36b3o115bo\$44b2obo36bo2bo\$44b3o37bo112b2o7b2o\$45b2o37bo111bo2bo5bo2bo\$85bobo109b2o7b2o2\$34bo167bo\$33b3o165bobo\$32b2obo165bobo\$32b3o167bo\$33b2o2\$39b3o38b3o\$39bo2bo37bo2bo\$39bo40bo\$39bo40bo\$40bobo38bobo\$48bo\$47b3o36b3o\$46b2obo36bo2bo\$46b3o37bo\$47b2o37bo\$87bobo2\$36bo164bo\$35b3o162bobo\$34b2obo162bobo\$34b3o164bo\$35b2o\$196b2o7b2o\$41b3o38b3o110bo2bo5bo2bo\$41bo2bo37bo2bo110b2o7b2o\$41bo40bo\$41bo40bo118bo\$42bobo38bobo114bobo\$50bo149bobo\$49b3o36b3o110bo\$48b2obo36bo2bo\$48b3o37bo\$49b2o37bo\$89bobo2\$38bo\$37b3o\$36b2obo\$36b3o\$37b2o2\$43b3o38b3o\$43bo2bo37bo2bo\$43bo40bo\$43bo40bo\$44bobo38bobo\$52bo\$51b3o36b3o\$50b2obo36bo2bo\$50b3o37bo\$51b2o37bo\$91bobo2\$40bo\$39b3o\$38b2obo\$38b3o\$39b2o2\$45b3o38b3o\$45bo2bo37bo2bo\$45bo40bo\$45bo40bo\$46bobo38bobo\$54bo\$53b3o36b3o\$52b2obo36bo2bo\$52b3o37bo\$53b2o37bo\$93bobo2\$42bo\$41b3o\$40b2obo\$40b3o\$41b2o2\$47b3o38b3o\$47bo2bo37bo2bo\$47bo40bo\$47bo40bo\$48bobo38bobo\$56bo\$55b3o36b3o\$54b2obo36bo2bo\$54b3o37bo\$55b2o37bo\$95bobo2\$44bo\$43b3o\$42b2obo\$42b3o\$43b2o2\$49b3o38b3o\$49bo2bo37bo2bo\$49bo40bo\$49bo40bo\$50bobo38bobo\$58bo\$57b3o36b3o\$56b2obo36bo2bo\$56b3o37bo\$57b2o37bo\$97bobo2\$46bo\$45b3o\$44b2obo\$44b3o\$45b2o2\$51b3o38b3o\$51bo2bo37bo2bo\$51bo40bo\$51bo40bo\$52bobo38bobo\$60bo\$59b3o36b3o\$58b2obo36bo2bo\$58b3o37bo\$59b2o37bo\$99bobo!`

For the record here are the other ways I found for potentially doing the same kind of trick:

`x = 261, y = 102, rule = B3/S235b2o3b2o\$4bobo3bobo\$6bo3bo5\$186b2o\$186bobo\$180bo5bo\$16b2o89bo72b2o60b2o\$16bobo88b2o70bobo60bobo\$16bo89bobo133bo\$113b2o121b3o\$113bobo122bo\$113bo123bo2\$194b2o\$194bobo\$194bo\$258b2o\$258bobo\$258bo5\$b2o\$2b2o4b2o118b2o\$bo6bobo117bobo\$8bo119bo8\$182b2o\$181bobo\$183bo54b2o\$190b2o47b2o7b3o\$190bobo45bo9bo\$190bo58bo\$122b2o\$122bobo\$10b2o110bo\$b3o6bobo101b2o\$3bo6bo102bobo\$2bo112bo15\$3o\$2bo6b2o101b3o\$bo7bobo102bo\$9bo103bo6b2o\$120bobo\$120bo11\$121b2o\$121bobo\$121bo\$112b3o\$114bo\$113bo10\$124b2o\$124bobo\$124bo2\$118bo\$118b2o\$117bobo!`

Another thing that could be annoying is that the LWSS recipe I posted a few pages back doesn't work with the 2 cell offset although the method in general (R-pent + glider + blinker) would still work at x2. I'm not sure how you propose to build the *WSS so I'm not sure if this is relevant.
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

### Re: (27,1)c/72 caterpillar challenge

chris_c wrote:Here is a version with zig-zaging but only 5 LWSS.

Nice! To make the extra zig zag less costly, all the singleton needs to build is the *WSS salvo that rebounds the second glider. In your design, that is two LWSS with the same shape and color (yay). The other 3 LWSS all have different shape/color combinations from the rightmost pair, so it will require 4 distinct recipes if we want to build all 5.

I think what we should look for in these recipes is something clean that also releases a NE glider, where again a signal encodes whether the LWSS is produced or not. The NE glider is caught to make the next construction target, giving the required space.

But if this is what we are going for, we might want our first two initial targets to have some x2 component, instead of building doubling reactions from scratch. There has to be an elegant way to accomplish that. Are there reaction pairs similar to the [G + (G|bi-block) -> HF] where instead of the results being identical, one is a (workable at x1) subset of the other?
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

biggiemac wrote:Are there reaction pairs similar to the [G + (G|bi-block) -> HF] where instead of the results being identical, one is a (workable at x1) subset of the other?

I'm not sure what you mean by "workable at x1" but all the way back when I wrote:

I wrote:When I was trying to come up with an example pattern I ran into problems with the second x1 NW stream colliding with the target site already constructed by the first NW stream

I was referring to this. Is it useful?

`x = 147, y = 160, rule = B3/S2346b3o2\$44bo5bo\$44bo5bo\$44bo5bo2\$46b3o48\$44b3o2\$42bo5bo\$42bo5bo\$42bo5bo2\$44b3o33\$59b2o\$59bobo\$59bo5\$144b2o\$144bobo\$40b2o102bo\$40bobo\$40bo5\$125b2o\$125bobo\$21b2o102bo\$21bobo\$21bo5\$106b2o\$106bobo\$2b2o102bo\$2bobo\$2bo5\$b3o83b2o\$o2bo83bobo\$3bo83bo\$3bo\$obo6\$5bo\$4b3o\$4bob2o\$5b3o\$5b2o4\$3b3o\$2bo2bo\$5bo\$5bo\$2bobo6\$7bo\$6b3o\$6bob2o\$7b3o\$7b2o!`
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

### Re: (27,1)c/72 caterpillar challenge

I meant something where the x2 part was well isolated from a x1 part, such that the trail can be treated as x1 for the purposes of construction. The best example would be something like this:
`x = 190, y = 131, rule = LifeHistory55.A\$54.A.A\$54.A.A\$55.A2\$50.2A7.2A\$49.A2.A5.A2.A\$50.2A7.2A2\$55.A\$54.A.A\$54.A.A\$55.A27\$64.2D\$64.2D2\$2A\$.2A\$A2\$134.2A\$134.A.A\$134.A6\$53.A\$52.A.A60.2A\$52.A.A60.A.A\$53.A61.A2\$48.2A7.2A\$34.2A11.A2.A5.A2.A\$35.2A11.2A7.2A\$34.A\$53.A\$52.A.A41.2A\$52.A.A41.A.A\$53.A42.A7\$77.2A\$77.A.A\$77.A26\$187.2A\$187.A.A\$187.A7\$168.2A\$168.A.A\$168.A7\$149.2A\$149.A.A\$149.A7\$130.2A\$130.A.A\$130.A!`

Except where the block in red was present after the second rake went by. That way construction can begin using the right blocks, and the left blocks can filter for fire/no fire. I found nothing starting from HF -> 2 blocks using only 2 rakes, but perhaps there is something that converges to a x1 trail with a third rake.

Is there a way after some number of construction rakes to isolate the x1 part and x2 part of the TL you posted?

Edit: Another option, except this particular example doesn't work because the left half of the blockade would stop the incoming NE glider. The glider in yellow is there to kill it off to at least show the concept I am looking for.
`x = 211, y = 125, rule = LifeHistory96.A\$95.A.A\$95.A.A\$96.A22\$111.2D\$111.2D6\$69.E\$70.E\$68.3E4\$155.2A\$155.A.A\$155.A7\$136.2A\$136.A.A\$136.A5\$94.A\$93.A.A\$93.A.A21.2A\$94.A22.A.A\$117.A7\$98.2A\$98.A.A\$98.A16\$.2A\$A.A\$2.A10\$208.2A\$208.A.A\$208.A4\$35.2A\$34.A.A\$36.A\$189.2A\$189.A.A\$189.A7\$170.2A\$170.A.A\$170.A7\$151.2A\$151.A.A\$151.A!`
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

biggiemac wrote:Is there a way after some number of construction rakes to isolate the x1 part and x2 part of the TL you posted?

Seems like there would be, probably not too many rakes away, unless there are severe constraints on the rakes that I haven't been paying attention to. Which is quite likely. But would something like this work?

`x = 150, y = 82, rule = B3/S232b3o57b3o2\$o5bo53bo5bo\$o5bo53bo5bo\$o5bo53bo5bo2\$2b3o30\$40b3o57b3o\$40bo59bo\$41bo59bo41\$87b3o57b3o\$87bo59bo\$88bo59bo!`

Some time ago I discovered that I could explore this kind of parallel cleanup problem pretty well by pasting something like

`x = 67, y = 7, rule = B3/S232b3o57b3o2\$o5bo53bo5bo\$o5bo53bo5bo\$o5bo53bo5bo2\$2b3o!`

into the Seeds of Destruction Game, and then playing around with different phases of glider pairs, pasted in with the "seed" option:

`x = 63, y = 3, rule = B3/S233o57b3o\$o59bo\$bo59bo!`

Of course a script would find a lot more options a lot quicker, but then I wouldn't get to personally cause as many entertaining explosions...!

dvgrn
Moderator

Posts: 5624
Joined: May 17th, 2009, 11:00 pm

### Re: (27,1)c/72 caterpillar challenge

The constraints on the rakes aren't really that bad, they just have to be monochromatic and have the same shape (p4).

The cleanup you posted doesn't accomplish what I am interested in - there has to be a surviving x1 part, ideally pretty far to the right of the x2 part. Far enough to the right that construction can be done pretending the x2 part doesn't even exist. That's why I was most interested in widely-separated patterns with blocks, like the HF block splitter or a blockade. If we use one NE stream to help replicate the right block, and let the left block(s) be, that helps start off the x2 feedback loop.

Edit: Something like this could be sufficient. (All gliders used are the right color and parity)
`x = 105, y = 47, rule = B3/S232b3o57b3o2\$o5bo53bo5bo\$o5bo53bo5bo\$o5bo53bo5bo2\$2b3o9b3o57b3o\$14bo59bo\$15bo59bo16\$30b3o57b3o\$30bo59bo\$31bo59bo8\$32b3o57b3o\$32bo59bo\$33bo59bo8\$42b3o57b3o\$42bo59bo\$43bo59bo!`
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

### Re: (27,1)c/72 caterpillar challenge

I suppose, I've only been suggesting to have a constellation trail with something x2 on the left and everything x1 on the right because I am assuming that gives the best route to successfully making some of the x2 *WSS streams using the singleton constructor.

However, if we dream big and take dvgrn's parallel construction idea to heart, there's no reason we can't at least ask if something like the following exists:

Two slightly different constellations (like the TL and the TL missing a blinker from above), for which some monochromatic monoparity NW salvo exists giving
1) An edge-shooting LWSS or MWSS from one of the constellations with no other debris besides a NE glider
2) A NE glider only from the other constellation (not necessarily identical to that from 1, but that'd be cool)

The salvos are completely parallel, and the initial difference encodes whether it's option 1 or option 2. Given how outlandish that sounds, I feel like the best way to achieve this without tons of brute force is for the two to converge as quickly as possible, but retain some difference clear from the construction path that ultimately prevents the edgy *WSS from forming in (2). Then it's just standard construction instead of parallel.

Since the *WSS is triggered by a single NW glider, the R + blinker + G option will be hard to orchestrate. I'm trying to scrape the forums for *WSS seeds edgy enough. The "Champion" from the 31c/240 project is activated from the wrong direction. (A turner is possible but if there is a better option it'd be nice).
Physics: sophistication from simplicity.

biggiemac

Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

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