Tutorials/Glider syntheses

Glider synthesis is the process of colliding gliders – the smallest spaceship in Conway's Game of Life – in a specific way to construct a specific object. It is one of the few areas in the Game of Life that many discoveries can still be made without using scripts.

This is an example of a glider synthesis:

x=73, y = 28, rule = B3/S23 52bo$50bobo$51b2o4$51bobo$52b2o2bobo4bo$52bo3b2o5bobo$2bo54bo5b2o$ obo$b2o$49b2o$13bo35bo$3b2o6b2o37b3o12bo$4b2o6b2o38bo10b2o$3bo51b 2o7b2o$55b2o$8b2o$9b2o54b2o$8bo48b2o5b2o4b3o$58bo7bo3bo$12bo45bobo 10bo$12b2o45b2o$11bobo$16b3o$16bo$17bo! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

It is a 13 glider synthesis of Achim Flammenkamp's pseudo-barberpole, which, at the time of writing, is the cheapest synthesis known of that object. Note that this particular synthesis can be divided into two stages which can take place arbitrarily far apart; multi-stage synthesis are typically shown this way to make it easier to see what is happening in each step. The three still life syntheses are independent and could also be moved into separate stages, so this is really a four-stage synthesis. Simple well-separated still lifes tend to be trivial to construct, and often the order of construction doesn't matter, so several stages are sometimes left combined in cases like this.

Locating known glider syntheses

To locate a known glider synthesis, there are three main places you should look:

• The "Syntheses" page on Catagolue, showing the current synthesis data from Shinjuku
• Mark Niemiec's synthesis database,
• 2718281828's 3G collision database (see 3-glider collision database below)

As of May 2019, many of the syntheses in Niemiec's database are out of date, but the site does have some that aren't on Catagolue yet.

Also, there's a very important difference between the two databases. Shinjuku/Catagolue focuses on documenting the single synthesis of each object that takes the smallest number of gliders. By contrast, Niemiec's database collects many types of syntheses for a large number of objects, including more expensive ones. For example, there may be syntheses of two combined objects where each type of object is added to an already existing instance of the other type. Or there might be syntheses where all gliders come from one side of the object (useful in building the object near other existing objects), and so on.

Sometimes you will not find a synthesis for a particular object in either of these places. That could be because:

• There does exist a known synthesis, but it is hidden somewhere obscure. Your best bet is to ask on the ConwayLife.com forums.
• No syntheses are known because no-one has decided to synthesise that specific object before. These are usually pretty easy to make a synthesis for yourself.
• No syntheses are known because the object is very difficult to synthesise. An example of this would be Sir Robin.
• The object has been proven impossible to synthesise. Examples of this include all Gardens of Eden as well as solutions to the grandfather problem.

In the next section we will look at how to make your own syntheses.

Making your own glider syntheses

Using Catagolue to find glider syntheses

Before you start, you will need to download the second Python script posted by Brett Berger here. If you select an object (which can either be a true object or a constellation) in Golly and run this script, it will open the object's Catagolue page. You might instead want to use synthesistools.py in Shinjuku to do the following process more quickly. More details about this will be given in "Using search programs to assist in creating syntheses".

Let's say you want to find a synthesis for block on down candlefrobra, which, according to Mark Niemiec's website, takes 12 gliders:

x=10, y = 5, rule = B3/S23 4bo$2obob2obo$2obo3bobo$3bo4bo$3b2o! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Select the pattern in Golly and run the script mentioned above. It should bring you to this page on Catagolue. Scroll down to the part of the page with lots of differently coloured dots. These are all sample soups for the object. The black ones are asymmetric soups, which are the easiest to make syntheses from. (However, it should not be forgotten that you can still get good syntheses from symmetric soups -- especially if the object has the same type of symmetry as the soup.)

So click on the first asymmetric soup (the first black dot), and copy the RLE it provides into Golly. You should get this:

x=16, y = 16, rule = B3/S23 ob2o3bo2bo2bobo$ob5ob3o2bobo$obobo4b2obo2bo$3b2o5b3obo$2bobo8b3o$bo2bo 4b5obo$4b6obo2b2o$obo2b2o2b4o$o2bob4obo3b2o$5b3o2bo3bo$6bob2ob2o2bo$2b 2ob5obob2o$4o3b2obobo2bo$ob3ob2obo3b2o$3b3ob5o2b2o$bo3b2obob2obo! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Now run the soup until the candlefrobra appears (this should happen at generation 919). Use the goto.py script (which comes with Golly) to go 20 generations back. Watch each generation up to the candlefrobra's formation step-by-step to see which objects react to make the candlefrobra. Next, go back 20 generations, select the objects that reacted to make a candlefrobra, and paste them into a new layer.

Test to see if that pasted pattern works. If it doesn't work, go back to the layer with the soup, and select and paste a larger area. Once you've deleted any objects that don't participate in the reaction, you should get something like this:

x=11, y = 16, rule = B3/S23 9bo$8bobo$9b2o2$6bo$2o3bobo$2o2b2ob2o6$5bobo$4b3o$3b3o$3b2o! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

The reaction is pi + block + boat + traffic light --> candlefrobra + some junk. We know how to make all those reactants with gliders, so we can now make a synthesis! In fact, all of the reactants can be made in two gliders (those collisions can be found in two-glider-collisions.rle in Golly's pattern collection).

However, before you start, you may notice that not all of the blinkers in the traffic light react before making the candlefrobra. So maybe we don't need all of the blinkers. In fact, the only blinker we need is the top one. Try deleting the rest of the blinkers just before the traffic light first reacts. This isn't necessary, but to help your understanding, I've replaced the traffic light predecessor with one that only makes a blinker to get this:

x=11, y = 19, rule = B3/S23 9bo$8bobo$9b2o2$6bo$2o3bobo$2o2b2ob2o8$5b2o$2b3obo$2b2o$2b2obo$3bobo! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Now there is also no junk left over after the synthesis, only the candlefrobra.

Now you can start the synthesis. To do this, you should synthesise each of the reactants separately in such a way that they work when put together. You can find all the syntheses you need for this in two-glider-collisions.rle. Try to do this yourself. If you can't manage to make it work using only 2-glider collisions, look in Mark Niemiec's website to find more useful syntheses.

If you need a hint, these are the syntheses I would use (zoomed out in case you don't want the hint):

x=35, y = 29, rule = B3/S23 bo26bo$2bo14bo11b2ob2o$3o13bobo9b2o2bobo$4bo12b2o13bo$3bo$3b3o8bo$8b2o 3bobo$8b2o2b2ob2o2$25b2o$24bobo$26bo2$27b2o$27bobo$13b2o12bo$10b3obo$ 10b2o$10b2obo$11bobo6$bobo$2b2o2b2o$2bo2b2o$7bo! [[ ZOOM -16 THEME 6 THUMBNAIL THUMBSIZE 2 ]]

If you used the hint, note that you may need to rewind some of the syntheses to make it work.

How did you go? If you created a synthesis with less than 12 gliders then congratulations, you would have created a record-breaking synthesis! For reference, this is the synthesis I created which used 8 gliders:

x=17, y = 21, rule = B3/S23 9bobo$bo8b2o$2bo7bo3b3o$3o11bo$4bo10bo$3bo$3b3o2$7b2o$6bobo$8bo$2bo$ob o6b2o$b2o6bobo$9bo4$10b3o$10bo$11bo! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

In this example with the block on trans-candlefrobra, we were lucky to get a good reaction from the very first soup. Sometimes you will have to look through 20 or more soups before finding a suitable reaction.

If you want more practice for creating synthesis from a reaction, here is the reaction the current record holding synthesis of why not (8 gliders) was made with:

x=22, y = 14, rule = B3/S23 17bo$16b3o$15b2ob2o$19b2o$19b3o$19b2o$10b3o2b2ob2o$2o8bobo3b3o$b2o7b3o 4bo$o3$12b2o$12b2o! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Good luck!

Using converters to make syntheses

Let’s say we want to make a synthesis for this 18-bit still-life:

x=11, y = 6, rule = B3/S23 9bo$8bobo$2o2b2obobo$o2bobobo$2b2obobo$6bo! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

So we run the pattern-to-catagolue script, and it brings us here But there (at the time of writing) are no catagolue soups! So what can we do? It is time to be introduced to the world of converters…

A converter is a collision of gliders with a still-life/oscillator, which turns it into a new still-life/oscillator. Here is an example of a converter. It turns a hook into a barge:

x=37, y = 11, rule = B3/S23 12bo$12bobo$5bo6b2o$3bobo$4b2o$bo26bo$b2o6b2o16bobo$obo7bo17bobo$9bo5b 2o12bo5b2o$10b3obobo13b3obobo$12b2o18b2o! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Converters are very useful for creating syntheses that are too large and/or rare to turn up on catagolue. For example, the duodecapole currently has no appearances on catagolue, but we can still create a synthesis from a barberpole-lengthening converter and an already known synthesis for the decapole like this:

x=113, y = 33, rule = B3/S23 26bo$27b2o15bo$26b2o16bobo$44b2o38bo$82bobo6bo$2bo80b2o4b2o5bo$obo83bo 3b2o2b2o$b2o83b2o7b2o$85bobo$26bobo$26b2o63b2o$27bo63bo$59bo32bobo$23b obo32bo$24b2o5bobo24b3o33bobo$24bo7b2o$32bo9bo53bobo$41b2o7bo$14b3o24b obo5b2o47bobo$16bo32bobo$15bo84bobo$47bo55bo$47b2o53b2o$46bobo$107bobo $72b2o24b2o7b2o$72bobo24b2o2b2o3bo$72bo25bo5b2o4b2o$103bo6bobo$29b2o 79bo$28bobo16b2o$30bo15b2o$48bo![[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Here are three places you will find converters:

• Martin Grant’s collection
• Bob Shemyakin’s collection
• Various places in the forums

So with this new knowledge, back to synthesising the 18-bit still life:

x=11, y = 6, rule = B3/S23 9bo$8bobo$2o2b2obobo$o2bobobo$2b2obobo$6bo! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

So what could we convert that from? We could convert it from the equivalent with a snake instead of a carrier, but I would convert it from the equivalent with a hook instead of a tub, because it is more likely to have more soups on catagolue, and the corresponding converter is cheaper:

x=20, y = 12, rule = B3/S23 10bo$8bobo$9b2o$15bo$13b2o$14b2o$17b2o$9b2o6bobo$b2o2b2obobo6bo$bo2bob obo$3b2obobo$7bo![[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Now, when we go to the catagolue page of the still-life with the hook, we find it has lots of soups (at the time of writing it is 43!)

So let’s try the first soup:

x=16, y = 16, rule = B3/S23 o4b2o5b2o$ob4o2bobo3bo$5bo6bob2o$bob3o6b2obo$obo2bobobo2bo$ob2o2bo3b4o bo$o2bobobobo3bobo$2b2ob4ob2o2b2o$bo3bobobobo$5o2b2obobo2bo$o6b3o2b2o$ 2o3bo3b2obo2bo$o3b3o4bo2bo$o3bobob3o2bo$b3ob3o2b2ob3o$ob4ob4obobo![[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

The soup reduces to this predecessor:

x=19, y = 25, rule = B3/S23 9b2o$8bo2bo$9bobo$10bo2$17b2o$17b2o2$13bo$12bobo$12bobo$13bo2$11bo$10b 3o$9b2ob2o$10b3o$11bo$5b2o$4bo2bo$4bobo$5bo2$2o$2o![[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

But before we start the synthesis, there are a few clever tricks we can do that will reduce the overall synthesis. The block only acts as cleanup, so perhaps it can be replaced with a glider:

x=23, y = 34, rule = B3/S23 13b2o$12bo2bo$13bobo$14bo2$21b2o$21b2o2$17bo$16bobo$16bobo$17bo2$15bo$ 14b3o$13b2ob2o$14b3o$15bo$9b2o$8bo2bo$8bobo$9bo10$2o$b2o$o! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

1 glider less. The loaf only partly reacts before being separated from the rest of the reaction, so maybe it can be substituted with a glider. Also, the glider that we replaced a block with actually is only acting as cleanup for the loaf’s reaction, so if we replace the loaf with a glider in the right way, the other glider can be removed. Unfortunately, the loaf can’t be replaced by 1 glider, but replacing it with 2 gliders still reduces the cost:

x=18, y = 34, rule = B3/S23 8b2o$7bo2bo$8bobo$9bo2$16b2o$16b2o2$12bo$11bobo$11bobo$12bo2$10bo$bo7b 3o$2bo5b2ob2o$3o6b3o$10bo14$16b2o$15b2o$17bo![[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

2 gliders less. But we can do even more! Often it is possible to synthesise two nearby objects at once, instead of separately, to achieve a cheaper cost in gliders. In this example, the beehive and the traffic light can be made together in a 3-glider synthesis, instead of using 4 gliders to synthesise them separately. (More details on how these are found in a later tutorial.)

x=9, y = 8, rule = B3/S23 4bo$4bobo$4b2o$2bo$obo$b2o4b2o$6b2o$8bo! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

3 gliders less! See if you can complete the synthesis of the 17-bit still-life from there…

…How did you go? This in the 11 glider synthesis I got:

x=64, y = 75, rule = B3/S23 39bobo$39b2o$40bo27$18bo$16bobo$17b2o$31bo$18b3o10bobo$18bo12b2o$19bo$ 23bobo$bo21b2o$2bo21bo$3o10bobo12b2o$14b2o12bobo$14bo13bo6$26b2o$26bob o$26bo16$61b2o$61bobo$61bo5$34b2o$33b2o$35bo![[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Now all we need to do to complete the synthesis the 18-bit still-life is to add the converter:

x=139, y = 75, rule = B3/S23 39bobo$39b2o$40bo27$18bo$16bobo$17b2o$31bo$18b3o10bobo$18bo12b2o$19bo 87bo$23bobo79bobo$bo21b2o81b2o$2bo21bo87bo$3o10bobo12b2o80b2o$14b2o12b obo80b2o$14bo13bo85b2o21bo$75b2o29b2o6bobo19bobo$67b2o2b2obobo21b2o2b 2obobo6bo13b2o2b2obobo$67bo2bobobo23bo2bobobo22bo2bobobo$69b2obobo25b 2obobo24b2obobo$73bo30bo29bo$26b2o$26bobo$26bo16$61b2o$61bobo$61bo5$ 34b2o$33b2o$35bo![[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

And we’re done! We successfully created a 14 glider synthesis of a still-life with no appearances on catagolue, by constructing it from another still-life which did have appearances on catagolue.

If you want more practice at using converters and catagolue to find syntheses, try finding a synthesis for this still-life:

x=9, y = 10, rule = B3/S23 2o$obo$3bo3bo$4bobobo$5b2obo$7bo$5b2o$5bo$6bo$5b2o! [[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Converters are used in many others ways than just assisting soup search result-based syntheses. They are used a lot in the syntheses of difficult objects like billiard tables and spaceships. For example, this is the weekender synthesis:

x=188, y = 177, rule = B3/S23 160bo$160bobo$7bo152b2o8bo$5bobo160b2o$6b2o161b2o9bo$179bo$179b3o$31bo $29bobo$30b2o$170bo$168b2o$169b2o$4bo174bo$5b2o156bobo11b2o$4b2o157b2o 13b2o$36bo127bo$34bobo$35b2o2$179bo$178bo$37bobo138b3o$38b2o$38bo4bo 122bo$44bo107bobo11bobo$42b3o107b2o12b2o$153bo3$136bobo$38bobo95b2o16b o$39b2o96bo15bo$18bo20bo113b3o7bobo$16bobo24bobo117b2o$17b2o25b2o89bob o26bo$44bo5bo84b2o$51b2o83bo$50b2o2$55bo77bo$37bo18bo75bo12bo$35bobo 16b3o75b3o10bobo$36b2o107b2o$128bo$127bo$43bobo81b3o7bobo$44b2o91b2o$ 44bo93bo$57bo60bo6bo$55bobo59bo7bobo$56b2o59b3o5b2o3$60bo61bo$61bo59bo $59b3o11bo47b3o$74bo$72b3o4$81bo$79bobo$80b2o2$75bo33bo$73bobo31b2o$ 74b2o3bo28b2o$80b2o$79b2o3$90bo$90bobo$79bo10b2o$77bobo39bo$78b2o37b2o $118b2o2$80bobo11bobo$81b2o11b2o$81bo13bo8$77b3o$79bo$78bo$92b3o$82bob o3b2o2bo$74bo8b2o4b2o2bo$74b2o7bo4bo$73bobo2$64b2o$63bobo17b2o5b3o$65b o18b2o6bo$83bo7bo$98b3o$98bo$99bo13b3o$113bo$114bo2$55b3o67b3o$57bo52b 2o13bo$56bo53bobo13bo$110bo3$52b2o75b2o$53b2o23b3o27b2o18b2o$52bo27bo 26b2o21bo$79bo29bo3$46bo89bo$40bo5b2o87b2o5bo$40b2o3bobo87bobo3b2o$39b obo99bobo16$158b2o$157b2o$159bo2$172b2o$171b2o$154b2o17bo$153b2o$155bo 6$9b2o$10b2o$9bo173b3o$183bo$184bo2$9bo164bo$9b2o162b2o$8bobo162bobo$ 30bo$bo28b2o$b2o26bobo$obo$185b2o$185bobo$185bo$11b2o$10bobo$12bo162b 2o$175bobo$163b3o9bo$163bo$164bo![[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Using search programs to assist in creating syntheses (incomplete)

3-glider collision database

For this part of the tutorial, you will need to use Python scripts with Golly.

Below is a 25-glider synthesis of lightweight emulator:

x=163, y = 51, rule = B3/S23 71bo$47bobo19bobo$48b2o20b2o$48bo30bo$79bobo$79b2o18bo$99bobo$63bo6bo 28b2o$49bo12bo5b2o$50b2o10b3o4b2o$49b2o2$92bobo$92b2o$3bobo87bo$3b2o 146b2o2b2o2b2o$4bo70b2o74bo2b4o2bo$bo73b2o75b8o$b2o146b3o8b3o$obo146bo 2bo6bo2bo$150b2o8b2o$93b2o$93bobo$93bo10bo$103b2o$46bobo54bobo$47b2o$ 47bo10bo$56bobo$57b2o$150b2o8b2o$3bobo143bo2bo6bo2bo$3b2o144b3o8b3o$4b o70b2o75b8o$bo73b2o69b2o3bo2b4o2bo$b2o142bobo3b2o2b2o2b2o$obo55bo88bo$ 58b2o$57bobo2$101b2o$81b2o4b3o10b2o$82b2o5bo12bo$51b2o28bo6bo$50bobo$ 52bo18b2o$70bobo$72bo30bo$80b2o20b2o$80bobo19bobo$80bo![[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Notice that in the first step, two blocks are created using a total of four gliders. This may be the most obvious way to synthesize them, but is it the cheapest?

This is where 2718281828's 3G collision database comes in. It contains ~460,000 different three-glider collisions and the objects/constellations they produce, and includes a Python script created by Goldtiger997 to search through the database. Download the three files and place them somewhere convenient, preferably your Scripts/Python folder. In Golly, paste the desired constellation into a new layer and run synthesise-constellation.py. If there are any collisions in the database that produce the same objects in the same positions relative to each other, they will all be displayed.

Let's try this with our two-block constellation. After running the script, we get this:

x=268, y = 36, rule = B3/S23 2bo61bo35bo67bo44bo36bo$obo61bobo34b2o63b2o46b2o35b2o$b2o61b2o34b2o65b 2o44b2o35b2o2$218bo36bo$216b2o35b2o$217b2o35b2o17$111bo39bo$112bo39bo$ 13bo37bo58b3o37b3o$14bo37bo$12b3o35b3o62bo39bo$113b2o38b2o$114b2o38b2o $13b2o36b2o$13bobo35bobo$13bo37bo$201bo64bo$201b2o62b2o$200bobo62bobo![[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

All six of these collisions work in essentially the same way, by colliding a glider with a pi-heptomino. Since the two blocks are the first step of our lightweight emulator synthesis, we don't have to worry about other nearby objects interfering, so any of these will be suitable. In other cases, you may have to try several of these collisions before finding one that works for the synthesis you're working on.

Now that we have a three-glider collision of the two blocks, our lightweight emulator synthesis has been reduced to 24 gliders, which is currently the cheapest known as of the time of writing:

x=167, y = 47, rule = B3/S23 87bo$66bo21b2o$64bobo20b2o$65b2o26bo$91b2o$92b2o19bo$111b2o$82bo 29b2o$67bo7bobo3bo$68bo6b2o4b3o$66b3o7bo2$105bo58bo$105bobo43b2o2b 2o2b2o3bobo$90b2o13b2o44bo2b4o2bo3b2o$90b2o60b8o$149b3o8b3o$106b2o 41bo2bo6bo2bo$105b2o43b2o8b2o$107bo8b2o$116bobo$116bo$o$b2o3bo$2o 3b2o$5bobo57bo$63bobo$64b2o8bo$75b2o73b2o8b2o$74b2o73bo2bo6bo2bo$ 149b3o8b3o$90b2o60b8o$75b2o13b2o59bo2b4o2bo$74bobo74b2o2b2o2b2o$ 76bo$31b2o$30b2o73bo7b3o$32bo65b3o4b2o6bo$100bo3bobo7bo$68b2o29bo$ 69b2o$68bo19b2o$89b2o$88bo26b2o$93b2o20bobo$92b2o21bo$94bo![[ THEME 6 GRID THUMBNAIL THUMBSIZE 2 ]]

Submitting syntheses to Catagolue

Once you've completed a new record-breaking synthesis for a still life, oscillator, or spaceship, you can add it to the object's Catagolue page by pasting the RLE into the submission box at the bottom of the "Syntheses" page. There are some important things to note about how to format the pattern in order for it to be interpreted correctly:

• The rule must be either B3/S23 or LifeHistory (in the latter case only states 0 and 1 are allowed).
• The pattern must not exceed a bounding box of 9999×9999, a population of 100,000, or a file size of 400 kilobytes.
• Each individual step, including the gliders, must be separated by at least 20 empty rows/columns.
• Every glider must begin interacting before generation 200, and each step should overall stabilize by generation 4000.
• The initial pattern in each step must match the resulting pattern of the previous step (though rotations/reflections are allowed).
• Although the synthesis RLEs on Mark Niemiec's website have the final object displayed next to the synthesis for each individual step, these are technically redundant and should be removed from the pattern when submitting to Catagolue.

When you submit, your RLE is added to a queue to be processed by the automatic update process, which runs every 8 hours. If you're not sure whether your synthesis is on Catagolue yet, you can check the "Jobs" page on the Catagolue repository, particularly the jobs named shinjuku, to see the console output for the update process. Djikstra's algorithm is used to calculate the shortest path to the desired object using the known components, so you may find that earlier steps of your synthesis have been replaced by an already-known cheaper way of producing the same intermediate object.