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June 16th, 2018

Design Summary for Fixed-Cost Glider Construction

The previous post summarized the new 329-glider reverse caber tosser universal constructor design, but didn't go into detail about what exactly makes the design universal. Here are (most of) the fiddly details.

The idea of a fixed-cost glider recipe for any possible glider-constructible object has gone through several iterations in the past few years. The first completed construction was a decoder that used a double sliding-block memory, and repeatedly divided the stored number by two or three, returning the remainder for each cycle. That information could then be used to run a construction arm, but an explicit construction arm was never created for that design.

A newer "reverse caber tosser" design is an alternate storage mechanism for data feeding a universal constructor. The reverse caber tosser was designed by Adam P. Goucher, with Martin Grant finding the key glider-reflection reaction. A very large integer can be encoded in the position of a very faraway Cordership (instead of a block). If the distance to the Cordership is measured using circuitry designed to be as simple as possible, a complete decoder and universal constructor can be created by colliding exactly 329 gliders.

Read the whole story at b3s23life.blogspot.com

 

June 13th, 2018
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 current upper limit is 329 gliders. This may be reduced somewhat if a more efficient universal constructor is designed or an improved synthesis is found.

Read the whole story at b3s23life.blogspot.com

 

March 10th, 2018

On 6 March 2018 the first member of a new class of Conway's Life spaceships was discovered. This is Sir Robin, the first elementary spaceship that travels in an oblique direction. Its displacement is two cells horizontally and one cell vertically (or vice versa) every six generations, which is the fastest possible knightship speed. The name is a reference to Monty Python's "Brave Sir Robin", who bravely runs away as fast as possible.

Code: Select all
#C (2,1)c/6 knightship found by Adam P. Goucher,
#C based on a front end originally found by Josh Ball,
#C rediscovered and extended by Tomas Rokicki,
#C using a SAT solver-based search
x = 79, y = 31, rule = B3/S23
8bo$6bo2bo$4b2obo3bo$4bo2bo3bo$3o2bobo$o4bobobo$3bo2bo3bo$bobo6bo$2b2o
6bo2$4b2ob2o4bob4o11bo$4b2ob2ob2ob3o2b2obob2o4bobo$4b2o4bo3bobobo6b2o$
4b3o5bo4bobo6bob2o2b2o$6bo7bo5bo5bob3obo$6b2o2bobob4ob2o3bo3b2o2b2o$
11b2obobo10bo3b3o22bo$17bo2bo6bob3obo24bo$13b3o5bo3bo2bo3b2o9bo8b3o3bo
$18b4o3bo5bo2bo4bob2obo5b3o5bo$21bo3bo5bo3b2o2b2o3b2o3b2ob2obobo$23bob
o5bo4b2obo5bob2obo2bo2b2o6bobo$24b2o11bo2bo4b2obobob2o2b2o5b2o2bo2b2o$
32b2obobo3b2o2b2o3bob2o2b2o5b2o2bo2b3o$32b2obobo4bobo3bo2b3o2bob2obo3b
2obob4o3bo$37b2o4bo13bo4bo2b3o5b3obo$38bobo4bo11bobo2bo3bob2o4bo3bo$
41bobo2bo14b2o6bo3bo$39b2o2b2o15b2o3b3o4b2o$43b3o18bo3bob3o$65b2obo3bo!
#C [[ GRID THEME 7 TRACKLOOP 6 -1/3 -1/6 THUMBSIZE 2 HEIGHT 480 ZOOM 7 GPS 12 AUTOSTART ]]

The new knightship was found by Adam P. Goucher based on initial results by Tom Rokicki, after about a month of automated searching. The program that completed the knightship was icpx, a "multithreaded hybrid of LLS and gfind".

A detailed summary of the discovery process is now available.

Read the whole story at b3s23life.blogspot.com

 

June 4th, 2017

Rich’s p16 came in at 11th place in the 2016 Pattern of the Year awards. First place was never even a remote possibility, not in a year that produced the Caterloopillar and the Copperhead. (I actually thought the latter would win handily, but I guess that’s just my relative lack of interest in engineered spaceships showing.)

Read the whole story at mathematrec.wordpress.com

 

October 15th, 2016

A week or so ago, a better recipe was found for the last still life on Mark Niemiec's list of expensive 14-bit syntheses. Now all 14-bit still lifes can be constructed with less than 14 gliders -- less than 1 glider per bit, as the old saying goes.

Catagolue results continue to be very useful in finding new recipes.


Code: Select all
#C 12-glider synthesis for the last 14-bit still life,
#C snake bridge snake / 12.105, which had previously cost at least
#C one glider per bit.
#C Goldtiger997, 6 October 2016, optimized by Mark Niemiec on 7 October.
x = 79, y = 71, rule = LifeHistory
7.A$.A6.A$2.A3.3A$3A2$16.A$14.A.A$15.2A6$36.A$34.A.A$35.2A8$30.3A$32.
A$31.A4$31.3A$33.A11.2D.D$32.A12.D.2D$43.2D$39.2D.D$39.D.2D6$52.A$51.
2A$20.2A5.3A21.A.A$21.2A6.A$20.A7.A22$3.3A$5.A70.2A$4.A4.2A65.A.A$10.
2A64.A$9.A!
#C [[ AUTOFIT AUTOSTART GPS 25 LOOP 150 ]]

UPDATE: The next challenge along these lines was to similarly reduce 15-bit still life costs to below 1 glider per bit. The process started later in the same forum thread, and was completed on November 19, 2016, with the following 14-glider synthesis:

Code: Select all
#C 14-glider synthesis for the last 15-bit still life
#C which had previously cost at least one glider per bit.
#C Extrementhusiast, 19 November 2016
x = 48, y = 38, rule = B3/S23
17bobo$17b2o$18bo$4bobo$5b2o$5bo$18bo$18bobo$18b2o2$obo$b2o39b2o$bo40b
o3b2o$20b3o21bo2bo$20bo22b2obo$21bo6bo16bo$8b2o18bobo14bobo$7bobo18b2o
16b2o$9bo2$5b2o$4bobo$6bo9b2o$10b2o3bobo$11b2o4bo$10bo4$8b3o$7bo2bo$
10bo$6bo3bo$10bo$7bobo$32b3o$32bo$33bo!
#C [[ AUTOFIT AUTOSTART GPS 25 LOOP 150 ]]

UPDATE 2: The next project involved a similar reduction for 16-bit still life recipes. The official project kickoff was on December 16, 2016, when 443 of the 3,286 16-bit still lifes had no synthesis in less than 16 gliders in Chris Cain's database. It concluded successfully on May 24, 2017.

Read the whole story at b3s23life.blogspot.com

 

September 8th, 2016

Take a look at a pre-loaf and a pi:screen-shot-2016-09-07-at-11-37-22-pm

If you run them in B37c/S23, the pre-loaf stabilizes quickly, but the pi takes a while — and some space. It needs 110 generations to settle down.

If you run them in B37e/S23, though, the pre-loaf just becomes a loaf immediately and the pi stabilizes much more quickly, in only 23 generations, and without spreading out so much.

Read the whole story at mathematrec.wordpress.com

 

September 4th, 2016

That lame explanation seems even more lame when you consider this: The non totalistic rule B37c/S23 (meaning birth occurs if there are 3 live neighbors, or if there are 7 live neighbors with the dead neighbor in the corner of the neighborhood) is explosive, but B37e/S23 (birth occurs if there are 3 live neighbors, or if there are 7 live neighbors with the dead neighbor on the edge of the neighborhood) isn’t.

Read the whole story at mathematrec.wordpress.com

 

September 4th, 2016

Here’s an even more perplexing (to me, at least) instance of different CA behavior under similar-but-different rules. Consider this 32 x 32 soup:Screen Shot 2016-09-04 at 10.14.02 AM B36/S23 is a Life-like rule sometimes called HighLife. Many objects behave the same way as in Life; in particular, blocks, loaves, boats, and beehives are still lifes; blinkers are p2 oscillators; gliders are c/4 diagonal spaceships. So after 378 generations in B36/S23 when that soup looks like this, it’s stabilized:Screen Shot 2016-09-04 at 10.10.26 AM B38/S23 has no nickname I know of. Under that rule, the same soup stabilizes in 483 generations:Screen Shot 2016-09-04 at 10.10.52 AM And in B37/S23… here’s what it evolves to after 10,000 generations:Screen Shot 2016-09-04 at 10.11.08 AMPopulation 17,298 and growing, presumably forever.

Fairly typical. I’ve seen some soups take several thousand generations to stabilize in B38/S23, and I’ve seen a few — very few — stabilize in B37/S23. But most soups stabilize in 1000 generations or so in B36/S23 and B38/S23… and almost all soups explode in B37/S23.

Does that make any sense to you? Explain it to me, then.

Read the whole story at mathematrec.wordpress.com

 

September 2nd, 2016

It surprises me how hard it can be to guess what kind of behavior a given CA rule will produce. There are some things that are fairly obvious. For instance, under a rule that doesn’t include births with fewer than 4 live neighbors, no pattern will never expand past its bounding box. (Any empty cell outside the bounding box will have no more than 3 live neighbors, so no births will occur there.)

But beyond a few observations like that, it’s hard to predict. At least for me.

Consider the rule B34/S456, for a semi random example. Start with a 32 by 32 soup at 50% density:gen0 Then let it run for 1000 generations. It expands to a blob 208 by 208 in size, population 21,132:b34s456But change the B34/S456 rule to B3/S456 or B4/S456 — removing one number or the other from the birth rule — and either way, the same initial configuration dies.

Read the whole story at mathematrec.wordpress.com

 

July 17th, 2016

Here’s another big spaceship evolving from a soup. The rule here is B358/S23, and the soup has D2_+1 symmetry.Screen Shot 2016-07-17 at 7.06.44 AM

x = 143, y = 41, rule = B358/S23
47b2o$49bo$51b2o$45bo7bo32bo$b2o21bo20bob3o36bo35b3o$o2bo19bobo24bo3bo
30bobo34bo14b2o$bobo18bo3bo14bobo5b2o32bo5bo32bo4bo12b2o$5bob3o12bo3bo
17b3obo2b4o2bo24bo7bo17bobo12bo12b2obo2bo$7bo2bo12bobo15bo3b2ob2o3bo3b
o25bobobobo18bobo14bo2bo4bo3bob2obo$3b5ob2o13bo15bo2b3o11b2o25bo3bo35b
2o2bo4bo3bo2b3o$2bo2bo36bo3b2o3b2o4bobo19b2o34b2o6bo4bo4bo$2bo2b2o5b2o
30bob2o8bo2bo19b2o4bobo20bobo4b2o6bo4b2o4bo2bo$6bo6b2o2bo22b3ob2o2bo7b
o27b2ob2o19bobo13bo4bo6bo$4bob2o4b2o2bo3bo23b2o2bo7bobo26b3o37bo$2bobo
12bobobo24bobobo6bo28bo39bo$2bobo4bo7bob4o25b2o$4bo3bo3b2o4b2obo26b2o$
8b3ob2o3b2obo$18bo4$18bo$8b3ob2o3b2obo$4bo3bo3b2o4b2obo26b2o$2bobo4bo
7bob4o25b2o$2bobo12bobobo24bobobo6bo28bo39bo$4bob2o4b2o2bo3bo23b2o2bo
7bobo26b3o37bo$6bo6b2o2bo22b3ob2o2bo7bo27b2ob2o19bobo13bo4bo6bo$2bo2b
2o5b2o30bob2o8bo2bo19b2o4bobo20bobo4b2o6bo4b2o4bo2bo$2bo2bo36bo3b2o3b
2o4bobo19b2o34b2o6bo4bo4bo$3b5ob2o13bo15bo2b3o11b2o25bo3bo35b2o2bo4bo
3bo2b3o$7bo2bo12bobo15bo3b2ob2o3bo3bo25bobobobo18bobo14bo2bo4bo3bob2ob
o$5bob3o12bo3bo17b3obo2b4o2bo24bo7bo17bobo12bo12b2obo2bo$bobo18bo3bo
14bobo5b2o32bo5bo32bo4bo12b2o$o2bo19bobo24bo3bo30bobo34bo14b2o$b2o21bo
20bob3o36bo35b3o$45bo7bo32bo$51b2o$49bo$47b2o!

It goes left to right (right to left in the original soup) at speed 36c/72.

Again, the way this comes about is through development of a small seed. In this case at generation 83 you get a couple of these objectsScreen Shot 2016-07-17 at 12.09.26 PMwhich in four generations recur, inverted, but with some debris.Screen Shot 2016-07-17 at 12.09.44 PMBy itself, this seed becomes a 36c/72 puffer.Screen Shot 2016-07-17 at 12.09.02 PMBut two of them, mirror images at just the right separation, have their smoke trails interact in such a way as to extinguish them, and the result is a spaceship. If you start with this pairScreen Shot 2016-07-17 at 12.24.37 PM

Read the whole story at mathematrec.wordpress.com