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July 11th, 2019

On 19 June 2019 a surprising milestone was reached. Goldtiger997 made a final improvement to a 17-bit still-life synthesis -- ID xs17_03p6413z39c -- to bring the cost down to 33 gliders. (It's since been reduced further, to 29 gliders, and eventually down to only 9 gliders as part of the long-running "17-in-16" project.)

This made it possible to announce a surprising result: there's a strict upper bound for the cost in gliders for any strict still life, assuming it can be constructed by colliding gliders at all. If a glider-constructible still life contains N ON cells, then it can be constructed with less than 2N gliders.

For still lifes larger than 17 bits, this result is supplied by the strange and wonderful RCT method. The RCT (reverse caber tosser) is a pattern that is constructible with only 35 gliders, that reads the very faraway position of an approaching object to produce a stream of bits, which are then interpreted as a construction recipe fed to a universal construction arm. Cleanup of the RCT's mechanism would also have to be done to produce a full synthesis, which makes it tricky to create these 35-glider recipes in practice; no working examples have yet been completed.

Read the whole story at b3s23life.blogspot.com

November 11th, 2018

Time for a new post on self-constructing circuitry! I've been updating the same old post since 2014, but I think there's now some news that warrants a new article.For the last several years Adam P. Goucher has been incrementally working out the construction details for a "0E0P metacell". A metacell is a piece of Life circuitry that simulates the behavior of a single cell in Life, or in many cases some other CA rule, depending on how it's programmed.

"0E0P" is short for "[state] zero equals zero population", meaning that no support circuitry is needed: when one of these 0E0P metacells turns off, it self-destructs completely! This means that when the metacell needs to turn back on again, it must be re-constructed from the ground up by its neighbors.

One of the important effects of this design is that metacell patterns run at a sufficiently high step size, when viewed from very far away (e.g., at a size where an entire metacell takes up a single pixel in the display) will be indistinguishable from normal patterns that use the same rule -- except that the metacell patterns will run 2^36 times more slowly, of course.

A key breakthrough enabling the construction of the 0E0P metacell was a publicly available search program written by Goucher, capable of finding a single-channel construction recipe for any constellation of still lifes -- provided the still lifes aren't too close together, and that recipes are known for each of them in isolation. This search program was originally called "slmake" but is now renamed to "slsparse" due to its ability to analyze a large constellation and automatically separate it into several well-separated sub-constellations, or "metaclusters" (when that's possible).

Read the whole story at b3s23life.blogspot.com

June 16th, 2018

*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, some of which are already out of date now that a universal construction method has been found with as few as 35 gliders. See this conwaylife.com forum posting for a high-level walkthrough of how the 35-glider recipe might work.*

*The "reverse caber tosser" idea, with two gliders reflected back 180 degrees by a Cordership (or Corderpuffer, anyway) still remains intact -- and so does the three-glider PUSH/DFIRE salvo and the idea of using a block-laying switch engine as a source of elbow blocks. However, all of the PUSH/DFIRE salvos are now produced by glider-producing switch engines. These various switch engines are almost the only things that need to be constructed. In the 50-glider UC model, no stationary circuitry is needed at all. The 35-glider model needs a single block as a catalyst, to cleanly generate a return glider to retrieve the next bit from the approaching Corderpuffer.*

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. However, an explicit construction arm was never created for that design.

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

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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

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1749bo$1750b2o$1749b2o2$1761bobo$1762b2o$1762bo16$1765bobo$1766b2o$

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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

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$2266b2o1802b2o11b3o$2265b2o6$2267bobo$2268b2o$2268bo4$2276bo$2266bo

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$4137b2o3$2103bobo$2104b2o$2104bo2040bo$4145bobo$4145b2o12$4122bo$

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3873bobo$3873b2o$3874bo$2493bo$2491bobo$2335bo156b2o$2336bo$2334b3o$

3861bo$2339bo1521bobo$2337bobo1521b2o$2338b2o$2484bo$2485b2o$2484b2o$

2355bo$2356bo$2354b3o14bo16bobo$2372b2o15b2o1441bo$2371b2o16bo1441bo$

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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

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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 ]]

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

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:

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: 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: B38/S23 has no nickname I know of. Under that rule, the same soup stabilizes in 483 generations: And in B37/S23… here’s what it evolves to after 10,000 generations:Population 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