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LifeWiki
The largest collection of online information about Conway's Game of Life and Life-like cellular automata. Contains over 2,000 articles.
Types of Animal Tracks Toddler Kids T-Shirt
Share discoveries, discuss patterns, and ask questions about cellular automata with fellow enthusiasts.
Golly
Golly is a free program that allows you to easily explore much larger patterns at higher speeds than any web-based applet ever could.

For several years the upper speed limit for diagonally-traveling self-constructing spaceships has been c/12, the speed of a Cordership. This is because self-constructing spaceships speeds are always limited to the maximum speed at which a target object can be moved by a given construction arm. We can build structures that come as close as we want to that maximum speed, simply by increasing the period of the spaceship and spending a longer time moving the target object at top speed. Only a constant amount of time is needed to construct a copy of the spaceship's circuitry, so with a long enough period, the construction time can be made to be as small a percentage of the elbow-push time as you want.

Until recently, the fastest Demonoids used a "Corderpush" method to move their elbows and target blocks: i.e., first a Cordership was constructed and allowed to travel a long distance, and eventually it was shot down by a following salvo of gliders to produce faraway target ash, which was then converted into a new copy of the spaceship's circuitry by a slow salvo.

In late July 2020, Goldtiger997 constructed a new type of Demonoid puffer with the record-breaking velocity of (4825784,4825784)c/45679544 -- slightly slower than c/10 diagonally. This is a speed that can't be attained by Corderpush technology. What was used instead was a new and very large seed for a c/5 diagonal spaceship, which like a Cordership can be followed by a slow salvo of gliders to stop it after it travels a long distance, producing target objects for construction without releasing any stray gliders.

Read the whole story at b3s23life.blogspot.com

 

July 26th, 2020

Glider synthesis technology for Conway's Life spaceships -- i.e., the techniques needed to construct spaceships by crashing gliders into each other -- continues to improve. This is due in large part to the impressive efforts of a new generation of Lifenthusiasts. The current list of glider-constructible spaceships includes loafer, dart, crab, x66, weekender, puffership, B29, Pushalong 1, copperhead, fireship, spider, 25P3H1V0.1, 25P3H1V0.2, 27P4H1V1, 30P5H2V0, 30P4H2V0.4, 31P8H4V0, 46P4H1V0, 56P6H1V0, 58P5H1V1, 60P5H2V0, and 70P2H1V0.1.

The full list of spaceships with known glider recipes can be found on the LifeWiki Glider Synthesis page. Considering that only one spaceship in the above list (60P5H2V0) had a known synthesis at the beginning of 2013, this is a lot of progress!

Here's a showcase animation created by Saka a few months ago to document the construction of 58P5H1V1, a 58-bit c/5 spaceship:

Read the whole story at b3s23life.blogspot.com

 

Newer Better Faster Smaller Stable Signal Circuits
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July 2nd, 2020

In 2020 so far there's been a major surge in interest in stable circuitry. For example, on January 26 Entity Valkyrie constructed a Funny Zoo Keeper Nursery Nurse Gift Idea Koala Pullover Hoodie, and on May 22 a 58P5H1V1 gun -- the first-ever guns to fire c/5 orthogonal spaceships and c/5 diagonal spaceships, respectively. In both cases, as is almost inevitable for new glider synthesis, cheaper recipes have since been found, making it possible to construct significantly smaller guns.

More recently, Entity Valkyrie also found the key cleanup mechanism for an incomplete color-changing glider lane shifter found by Martin Grant. The result was the Bandersnatch, so named because of its association with Snarks and Boojums in Lewis Carroll's poem The Hunting of the Snark (appropriately subtitled "an agony in eight fits".)

Code: Select all
#N Bandersnatch #O Entity Valkyrie and Martin Grant, 5 June 2020
#C Spartan 0-degree color-changing glider shifter
x = 50, y = 46, rule = B3/S23
o$b2o$2o16$45bo$44bobo$44bobo$43b2ob3o$31b2o16bo$31b2o10b2ob3o$43b2ob
o7$46b2o$37bo8b2o$36bobo$36bo2bo$37b2o$20b2o$19bobo$19bo24b2o$18b2o24b
2o5$35b2o$35b2o!
#C [[ THUMBNAIL THUMBSIZE 3 AUTOSTART WIDTH 640 HEIGHT 540 X 7 Y 10 THUMBSIZE 2 ZOOM 16 GPS 40 LOOP 200 ]]
The Bandersnatch is a significant discovery, and has already helped to solve quite a few glider adjustment problems. For example, it enabled Goldtiger997 to build a highway robber with 863-tick recovery time. (The current record is a larger staged-recovery design with 742-tick recovery time.) The Bandersnatch consists of just seven well-separated still lifes, which is Spartan by the modern definition, so it is bound to become very useful in self-constructing circuitry as well.

In April, Louis-François Handfield constructed a much more compact universal regulator than the previous best known mechanism.

Read the whole story at b3s23life.blogspot.com

 

January 17th, 2020

On 30 December 2019, almost a decade after constructing the Gemini spaceship, Andrew J. Wade made a sudden reappearance in a very different corner of the Life spaceship construction field. This time the new discovery was the "scholar", the second known elementary 2c/7 spaceship (after the weekender, which was found by David Eppstein very nearly two decades ago).

The new spaceship was discovered using a depth-first search program called life_slice_ship_search. Details can be found on this conwaylife.com forum thread.

Code: Select all
#C 2c/7 elementary spaceship #2, "scholar",
#C found by Andrew J. Wade with life_slice_ship_search, 30 Dec 2019.
x = 23, y = 82, rule = B3/S23
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bo2bo2$8b3ob3o$8bobobobo$9b5o$3b3o11b3o$3b3o11b3o$bo3bo11bo3bo$5bo11bo
$6bo9bo$bo3bo3bobobo3bo3bo$2b2o4bo5bo4b2o$3bo15bo$4b3o9b3o$5bo5bo5bo$
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2bo2bo11bo2bo$3b2o13b2o!
#C [[ GRID THEME 7 TRACKLOOP 7 0 -2/7 THUMBSIZE 2 HEIGHT 680 ZOOM 7 GPS 7 AUTOSTART ]]

Read the whole story at b3s23life.blogspot.com

 

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.

A Mix of Theory and Practice

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 BAGELISE Women#39;s Casual Color Block Cowl Neck Long Sleeve Dr 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.

Everything Fall Sandstone Personalized Car Coasters - Set of 2

 

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, 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
#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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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 several times, as indicated by the series of numbers in this article's title.
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!
UPDATE 19 September 2020: Design improvements by MathAndCode and Adam P. Goucher make possible a reduced reverse caber tosser design requiring only 17 gliders, almost a 50% reduction from the previous fixed cost of 32 gliders.

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 ikpx, a Champion Copper Plus Small Engine 512 Spark Plug (Carton of 1).

A detailed summary of the discovery process Synthetic Opal Center Filigree Style Septum Ear Hoop Piercing Je.

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