Miscellaneous topics in Conway's Game of Life -- unfinished projects of all kinds and conditions

13 June 2018

The Answer to Life's Ultimate Question is 42 -- But the Cost of Living is Capped at 329...59...58...50...44... 43... 35

Code: Select all
#C universal constructor based on reverse caber tosser
#C Completed 10 June 2018
#C Original design by Adam P. Goucher
#C Original glider synthesis by Goldtiger997
x = 5379, y = 5173, rule = B3/S23
bo$2bo361bo$3o360bo$363b3o16$36bo$34bobo$35b2o$355bo$354bo$354b3o14$
29bo$30bo$28b3o2$335bo$335bobo$335b2o37$92bobo$93b2o$93bo2$356bo$72bo
283bobo$73b2o281b2o$72b2o2$337bo$336bo$336b3o891$1177bo$1178b2o$1177b
2o197$2925bo3b2o2bo$2925b2o3bo2bo$2926bo3bobo$2925bo5bo2$2926b2o$2925b
o2bo$2925bobo$2926bo65$1275bo$1276bo$1274b3o6$1265bo$1266b2o$1265b2o
15$1278bo$1279b2o$1278b2o$1291bo$1289bobo$1290b2o6$1287bobo$1277bobo8b
2o$1278b2o8bo$1278bo295$4459bo$4458bo$4458b3o$1848bo$1849bo$1847b3o14b
o$1865b2o$1864b2o$1717bo$1718b2o$1717b2o2$1865bobo2600bobo$1866b2o
2600b2o$1725bo140bo2602bo$1726bo$1724b3o11$1732bobo$1733b2o$1733bo13$
1749bo$1750b2o$1749b2o2$1761bobo$1762b2o$1762bo16$1765bobo$1766b2o$
1766bo4$1774bo$1772bobo$1773b2o23$1854bo$1855bo$1853b3o6$1794bo$1795b
2o$1794b2o32$1838bo$1839bo$1837b3o2$1851bo$1849bobo$1850b2o138$4513bob
o$4513b2o$4514bo4$4506bo$4506bobo$4506b2o38$1876bo2193bo$1874bobo2192b
o$1875b2o2192b3o412bo$4482b2o$4483b2o4$4063bobo$4063b2o$4064bo$2237bo$
2235bobo16bo$2236b2o17bo$2246bo6b3o$2247bo$2238bo6b3o$2239bo$2237b3o
23$4444bobo$4444b2o$4435bobo7bo$4435b2o$1822bo2613bo$1820bobo$1821b2o
2626bobo$4449b2o$4450bo13$1843bo$1844b2o$1843b2o466bo$2312b2o$2311b2o
4$1828bobo$1829b2o$1829bo$4095bo$4093b2o$4088bobo3b2o$4088b2o$1838bo
2250bo$1839b2o$1838b2o473bobo$2314b2o$2314bo2$4090bobo$4090b2o$4091bo
3$2222bo97bo$2223bo97bo$2221b3o95b3o$4092bobo$2234bobo1855b2o$2235b2o
1856bo$2235bo4$4069bo$4069bobo$4069b2o$2246bo$2247b2o$2246b2o2$4073bob
o$4073b2o$4074bo$4052bo$4050b2o$4051b2o5$4070bo13bo$2265bo1804bobo10bo
$2266b2o1802b2o11b3o$2265b2o6$2267bobo$2268b2o$2268bo4$2276bo$2266bo
10bo$2267bo7b3o$2265b3o55$2202bo$2203b2o$2202b2o$2215bo$2213bobo$2214b
2o6$2211bobo$2201bobo8b2o$2202b2o8bo$2202bo36$4205bo$4205bobo$4205b2o
4$4210bo$4209bo$4209b3o38$4154bobo$4154b2o$4155bo$4162bo$4162bobo$
4162b2o2$4153bo$4151b2o$2105bo2046b2o$2106bo$2104b3o11$4137bo$4137bobo
$4137b2o3$2103bobo$2104b2o$2104bo2040bo$4145bobo$4145b2o12$4122bo$
4121bo$4121b3o2$4117bo$4116bo$4116b3o$2123bobo$2124b2o$2124bo2001bo$
4126bobo$4126b2o16$2386bobo$2387b2o$2387bo13$3880bo$3879bo$3879b3o6$
3873bobo$3873b2o$3874bo$2493bo$2491bobo$2335bo156b2o$2336bo$2334b3o$
3861bo$2339bo1521bobo$2337bobo1521b2o$2338b2o$2484bo$2485b2o$2484b2o$
2355bo$2356bo$2354b3o14bo16bobo$2372b2o15b2o1441bo$2371b2o16bo1441bo$
3831b3o$2374bobo1467bo$2375b2o1467bobo$2375bo30bo1437b2o$2407b2o$2401b
o4b2o$2402bo$2400b3o18bo$2364bo57b2o$2365b2o54b2o$2364b2o2$3832bo$
3832bobo$3832b2o3$2311bo96bobo1455bo5bo$2312bo96b2o1454bo4b2o$2310b3o
96bo1455b3o3b2o2$2413bo$2326bobo85bo$2327b2o83b3o$2327bo3$2336bo$2337b
2o$2336b2o$2412bo1443bobo$2410bobo1443b2o$2411b2o1444bo4$2409bo$2407bo
bo$2408b2o5$2414bo$2415b2o$2414b2o$3887bo$3886bo$3869bo16b3o$3869bobo$
3869b2o7bo$3876b2o$3877b2o7bo$3884b2o$3885b2o62$3795bo$3793b2o$3794b2o
3$3798bobo$3798b2o$3799bo2$2145bo$2146bo$2144b3o4$3794bo$3794bobo$
3794b2o2$3789bo$3789bobo$2153bo1635b2o$2154b2o$2153b2o1644bo$3798bo$
3798b3o83$2750bo$2751bo$2742bo6b3o$2743bo$2734bo6b3o$2735bo$2733b3o35$
4006bo$4004b2o$4005b2o6$4008bo$4006b2o$4007b2o11$2572bo$2573bo$2571b3o
2$2577bo2216bo$2578bo2214bo$2576b3o2214b3o$3995bobo$2573bo1421b2o$
2568bo5b2o1420bo$2566bobo4b2o$2567b2o$3988bo$3987bo$3987b3o25$2856bobo
$2857b2o$2857bo2$2852bo$2853b2o$2852b2o3$3693bo$3693bobo$3693b2o3$
2857bo$2858bo$2856b3o2$2862bo$2863bo$2861b3o$3684bobo$3684b2o$2853bo
831bo$2851bobo$2852b2o128$3522bo$3521bo$3521b3o4$2581bo$2582bo$2580b3o
$2556bo$2557bo$2555b3o4$2580bo1181bobo$2559bo18bobo1181b2o$2557bobo19b
2o1182bo$2558b2o$2569bobo$2570b2o$2570bo212bobo$2784b2o$2784bo2$2779bo
$2780b2o$2779b2o3$4144bo$4144bobo$4144b2o11$2591bo$2589bobo$2590b2o5$
2601bo$2602b2o1187bo4bobo$2601b2o1188bobo2b2o$3791b2o4bo44$3441bo$
3441bobo$2629bo811b2o$2630b2o$2629b2o104$2797bo$2798bo$2796b3o4$2796bo
bo$2797b2o809bobo$2797bo810b2o8bo$3609bo6b2o$3617b2o21$3571bo$2759bo
811bobo$2760bo810b2o$2758b3o25$2767bo$2768bo$2766b3o41$3056bo$3054bobo
$3055b2o2$3061bo$3059bobo$3060b2o803bo$3863b2o$3051bo812b2o$3052bo$
3050b3o68$3774bo17bo$3772b2o17bo$3773b2o16b3o3$3781bobo12bo$3781b2o13b
obo$3782bo13b2o3$3777bobo$3777b2o$3778bo174$2677b2o$2676bobo$2678bo
813bo$3491b2o$3491bobo66$2747b2o$2748b2o$2747bo4$2737b3o$2739bo$2738bo
40$3692bo$3678b2o11b2o$3677b2o12bobo$3679bo266$2251b2o$2252b2o$2251bo
146b2o$2399b2o$2398bo2$2241b3o$2243bo135b3o12b2o$2227b2o13bo138bo13b2o
$2226bobo151bo13bo$2228bo$2384b2o17bo$2383bobo17b2o$2385bo16bobo$2227b
2o$2226bobo323b2o$2228bo194b3o127b2o1345bo$2425bo126bo1346b2o$2424bo
1474bobo2$4097b2o$2545b2o1550bobo$2544bobo21bo1528bo$2546bo21b2o$2567b
obo1322bo$3891b2o$2369b2o1520bobo211bo$2368bobo1733b2o$2370bo1733bobo
12$2372bo$2372b2o$2371bobo5$2343bo$2343b2o14bo$2342bobo14b2o5b3o$2358b
obo7bo$2367bo4$2344b2o$2343bobo$2345bo$3857b2o189b3o$3857bobo188bo$
3857bo191bo$3608b3o$2284bo511b2o810bo$2284b2o509bobo811bo$2283bobo511b
o$4076b3o$4076bo$2293b2o1782bo$2294b2o$2293bo2$2288b2o$2289b2o1562b2o$
2288bo1563b2o$3854bo$3857bo$3856b2o228bo$3856bobo13bo212b2o$3871b2o
212bobo$2271b2o1598bobo$2260b3o9b2o$2262bo8bo12b2o$2261bo21bobo$2285bo
1595b2o$3880b2o$2750b2o1130bo$2288b3o460b2o6bo1135b3o$2290bo459bo8b2o
810bo323bo$2289bo468bobo809b2o324bo$3570bobo$4082bo$4081b2o$4081bobo$
2272b3o1295b3o$2274bo1295bo$2273bo1297bo2$2262b2o$2263b2o$2262bo60bo$
2270b2o51b2o$2269bobo50bobo6bo$2271bo59b2o$2330bobo$2338b3o$2340bo$
2339bo$2319b3o$2321bo$2320bo$2769bo1072b2o$2769b2o1070b2o$2768bobo
1072bo5$3848b2o$3848bobo$3848bo28$2207b3o$2209bo$2208bo4$2212b2o$2211b
obo$2213bo3$3858bo$3857b2o$3857bobo85$2573bo4b2o$2573b2o2bobo1184b2o$
2572bobo4bo1183b2o$3765bo6$2952b3o$2954bo$2953bo4$3775b2o$3775bobo$
3775bo5$2953b2o$2952bobo$2954bo832b2o$3786b2o214b2o$3788bo213bobo$
4002bo3$2587b3o$2589bo1416bo$2588bo1416b2o$4005bobo2$4015b2o$4014b2o$
4016bo$4012bo$4011b2o$2603bo1186b2o219bobo$2603b2o1185bobo$2602bobo
1185bo7$3788b3o$3788bo$3789bo40$2146b2o12bo$2147b2o11b2o$2146bo12bobo
73$4216bo$4206bo8b2o$4205b2o8bobo$4205bobo6$4203b2o$4203bobo$4203bo$
4215b2o$4214b2o$4216bo4$4143bo$4142b2o$4142bobo35$1848b2o$1847bobo$
1849bo15$4151b2o$4141b2o7b2o$4140b2o10bo$4142bo2$4132bo$1849b2o2280b2o
$1850b2o2279bobo$1849bo2$2109b3o18b2o$2111bo19b2o$2110bo19bo4$4156b3o$
4156bo$4157bo3$2105b3o$1760bo346bo$1760b2o344bo2052b2o$1759bobo2397bob
o$4159bo21$1728bo$1728b2o46b2o$1727bobo47b2o$1776bo5$1737b2o$1736bobo$
1738bo2660b2o$4398b2o$4400bo10$1791b2o$1790bobo$1792bo4$1784bo$1784b2o
$1783bobo156$4503b2o$4502b2o$4504bo7$1912b2o$1913b2o$1912bo40$1863b3o$
1865bo$1864bo$4428b2o$1864bo2562b2o$1864b2o2563bo$1863bobo2$1855b3o$
1857bo2571b2o$1856bo2572bobo$4418b3o8bo$4418bo$4419bo38$4460b2o$4440b
2o18bobo$4440bobo17bo$4440bo3$4453bo$4452b2o$4452bobo14$1824b2o$1823bo
bo$1825bo2621bo$4446b2o$4446bobo3$1832bo$1832b2o$1831bobo2$1825b2o$
1824bobo$1826bo2609bo$4435b2o24b3o$4435bobo23bo$4462bo2$1843b2o$1842bo
bo$1844bo4$1836b2o$1835bobo$1837bo$1825b3o$1827bo$1826bo$4428b3o$4428b
o$4429bo5$1840b3o$1842bo$1841bo$4443b3o$4443bo$4444bo25$2711b2o218b3o$
2712b2o217b3o$2711bo218bo2$2933b2o1833b2o$2926b3o3bo1835bobo$2925bob2o
4b2o1833bo$2925bo6bo$2926bobobo$1903b2o$1904b2o$1903bo2$4362b2o$4362bo
bo$4362bo5$1940b2o$1939bobo$1941bo7$1935b2o$1934bobo$1936bo$1920b2o$
1921b2o$1920bo2489b2o$4409b2o$4411bo385bo$4796b2o$4796bobo6$1917b3o$
1919bo$1911b2o5bo$1910bobo$1912bo$4403bo$4402b2o$4402bobo6$4408b3o125b
2o$4408bo127bobo$4409bo126bo47$2641b2o$2640bobo$2642bo29$1359b3o$1361b
o$1360bo11$4614b2o$4614bobo$4614bo49$1295b3o$1297bo$1296bo3$1270b2o$
1271b2o$1270bo$1283b3o$1285bo$1284bo4$1288b2o$1287bobo$1289bo$1262b2o$
1261bobo$1263bo4$1255bo$1255b2o$1254bobo289$5377b2o$5376b2o$5378bo!
#C [[ WIDTH 592 HEIGHT 500 X 5 Y -60 PAUSE 2 AUTOSTART ]]
#C [[ T 800 STEP 5 ]]
#C [[ T 2500 GPS 60 X 410 Y 456 Z 2 ]]
#C [[ T 2600 STEP 4 ]]
#C [[ T 2700 STEP 3 ]]
#C [[ T 2800 STEP 2 ]]
#C [[ T 2900 STEP 1 ]]
#C [[ T 3000 STEP 2 ]]
#C [[ T 3100 STEP 3 ]]
#C [[ T 3200 STEP 4 ]]
#C [[ T 3300 STEP 5 ]]
#C [[ T 7850 GPS 60 STEP 50 X 555 Y 628 Z -1.5 ]]
#C [[ T 28000 X 225 Y 300 Z -4 ]]
#C [[ PAUSE 5 LOOP 28050 ]]
There has been speculation for at least a couple of years** about the simplest possible form of universal constructor, where an arbitrarily complex construction recipe is encoded in the position of a single faraway object. The position of the object is measured by the simplest possible decoder mechanism, resulting in a series of bits that can then be interpreted to produce a slow salvo.
It has already been shown that slow salvos can construct any pattern that is constructible by gliders. So with the correct placement of the faraway object, the complete pattern is capable of building any possible glider-constructible pattern of any size. The same pattern is also capable of building a self-destruct mechanism that completely removes all trace of the universal constructor, after its work is done -- leaving only the constructed pattern and nothing else. A counterintuitive consequence is that any glider-constructible object, no matter what size, can be built with a specific fixed number of gliders.
And now the actual number has been calculated, and it's surprisingly small. The initial upper limit was 329 gliders, based on the pattern shown above. This has since been reduced to only 59 and then 58 gliders, with a proposal to simplify further and bring the total down to 43.
See the follow-up article for a full summary of the tasks that the universal constructor has to accomplish to be enable the 329-glider recipe to to construct any arbitrary pattern. The plans for the 58-, 43-, and 35-glider recipes are similar, but greatly simplified by the fact that the streams of gliders can all be generated by faraway glider-producing switch engines instead of local glider guns and reflectors. With the 58-glider recipe, no stationary circuitry is needed at all; a single block is needed as a catalyst in the 43- and 35-glider recipes.
** It seems likely that someone came up with this idea long before 2015 -- i.e., the inevitability of a fixed-cost construction with N gliders, for any possible glider-constructible object. Really it's more or less implied by the sliding-block memory units described in Winning Ways. But I don't know of anywhere that the fixed upper-limit cost of construction was mentioned explicitly. It would be interesting to see what early estimates of that upper limit might have been... it seems likely they were significantly higher than three digits, let alone two!

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