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:
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.
- 1 Locating known glider syntheses
- 2 Making your own glider syntheses
- 2.1 Using Catagolue to find glider syntheses
- 2.2 Using converters to make syntheses
- 2.3 Using search programs to assist in creating syntheses (incomplete)
- 2.4 assisted cleanup
- 3 Submitting syntheses to Catagolue
- 4 Notes
- 5 References
- 6 External links
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As of May 2019, many of the syntheses in Niemiec's database are out of date, but the site does have some that aren't on Catagolue yet.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 any 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 a Python script posted by Brett Berger here. (If you are using Golly 4.0 or above, you will need the version linked at the bottom of the post.) 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 synthtools.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:
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.)
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:
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:
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):
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:
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 (7 gliders) was made with:
Using converters to make syntheses
Let’s say we want to make a synthesis for this 18-bit still-life:
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…
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:
Here are three places you will find converters:
- Martin Grant’s collection (also includes some components taken from Shinjuku)
- Bob Shemyakin’s collection (less comprehensive, but has the advantage that components are sorted by both glider cost and change in population)
- Various places in the forums
So with this new knowledge, back to synthesising the 18-bit still life:
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:
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:
The soup reduces to this predecessor:
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:
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:
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.)
3 gliders less! See if you can complete the synthesis of the 17-bit still-life from there…
…How did you go? This is the 11 glider synthesis I got:
Now all we need to do to complete the synthesis of the 18-bit still-life is to add the converter:
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:
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 current best weekender synthesis as of August 2019 (79 gliders):
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:
Notice that in the first step, two blocks are created using a total of four gliders. This may be the most obvious way to synthesise 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:
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:
Note: As of April 2020, a new version of this script is available which contains a subset of four-glider collisions in addition to the two- and three-glider collisions. The installation instructions are the same; just make sure to copy both the 3G and 4G files. If your three-glider search gives no results, try this search instead. The collisions are also laid out in a grid instead of a line in this version.
synthesise-patt.py - synthesising active objects
synthesise-patt.py uses the same database as synthesise-constellation, but is instead used to synthesise unstable objects and is therefore more useful when multiple things are happening during a given synthesis step. It can be found here. Like before, place the three files in your Scripts\Python folder.
In generation 25, we can see the following unstable object, created from a blinker and two gliders, for 4 gliders total:
Let's see if there's a way to make this object with only 3 gliders, and therefore the bridge snake component in 6 gliders. Place it into a new layer and run the script; if it's running correctly you should see something like "X collisions found, Y collisions tried" in the top left of Golly. After a few seconds, you should see a list of all syntheses whose population counts over time match that of the given object. For this object in particular, you should see these six syntheses:
Now comes the fun part: determining which, if any, of these is suitable for our bridge snake component. In most cases, collisions where gliders come from only two directions perpendicular to each other tend to be the most likely to work, but in this case I found that the third one from the left seemed promising:
Mirroring this horizontally, we can see that it seems to fit in well with the snake, as all three gliders come from the other three directions:
Now we can paste in the other three gliders, and rewind them a few generations so they show up at the correct time, and our 6G component is complete:
When choosing a generation on which to run the script, it's often a good idea to pause just before the object begins to interact with other stuff, so you get as many potentially useful collisions as possible. However, if you run the script and it gives you several hundred collisions producing irrelevant objects, you may want to consider rewinding a few generations so that the script searches for a more specific population sequence and is therefore more likely to give the pattern you want.
As practice, try to complete this component:
A four-glider solution can be found here.
find-octohash-Python3.py - finding active objects in 1G collisions
Another database that can be useful when a specific active reaction is needed is the octohash database. The name "octohash" denotes a hash function that returns the exact same hash value for any of the eight orientations of a pattern -- i.e, the octohash of any rotation or reflection of a pattern will always be the same as the octohash of the original pattern. lifelib has a similar function available called "octodigest", but the octohash database is designed to work with Golly and Python, without any dependency on lifelib.
The database is just a series of simple text files containing ten printable ASCII characters for each generation of each glider collision with each constellation. Python can search through these text files very quickly to find matching hashes. The hashing function first finds the canonical orientation of the current phase of the collision. Then it runs the RLE through a SHA1 hash function, throws away everything except the first seven bytes, and encodes the resulting integer in base 90 using the ASCII characters from 37 to 126 -- mostly. Backslashes, apostrophes, and commas are replaced with "!", "#", and "$" respectively, to make the text strings a little less likely to cause any escape-character or quote-character issues, in any programming language that may be used to work with these octohash strings.
This turns out to be a good enough hash function that no hash collisions showed up in the entire set of 12x12 constellation / glider interactions.
The current octohash database catalogues every generation of every possible collision between a single glider and all possible small constellations of common objects. Constellations may contain up to two well-separated objects -- no pseudo still lifes -- and must fit inside a 12x12 bounding box. The objects used in the enumeration were block, boat, beehive, tub, pond, ship, loaf, eater, long boat, and blinker.
To use the octohash database, clone the octohash Git repository, or try the "Download ZIP" option under the "Code" dropdown. In Golly, select the active pattern you want to create with a 1G collision. For example, if you want to create a pentadecathlon by hitting a seed constellation with a trigger glider, place any of the 15 phases of a pentadecathlon in the Golly universe, select it, and run find-octohash-Python3.py.
There turns out to be exactly one constellation of two common objects inside 12x12 that produces a clean pentadecathlon when hit by exactly the right glider:
The original find-octohash.py works with Python 2.x and Golly 3.x. Presumably most users going forward will be using Golly 4.0 or above, so will need to run find-octohash.Python3.py instead.
Unlike synthesise-patt.py vs. synthesise-constellation.py, the octohash search script works equally well for stabilized ash or for active patterns, because the database records a seven-byte hash value for every generation of every collision.
Aidan F. Pierce's collisrc.py (short for "collision search") script randomly collides gliders with a given still life and records any interesting still lifes it finds, and is primarily designed to find new or reduced components. The latest version can be found here, and a list of search parameters can be found here. You can also try out Alex Greason's version of the script which relies on Shinjuku and runs on large numbers of still lifes, trying a set number of collisions for each one.
(rest of tutorial coming soon)
Sometimes the reaction involved in a synthesis produces not only the target product but also some leftovers. For instance, a 20-bit still life appears in the following reaction:
To make a synthesis from it, you need to get rid of the surrounding objects with extra gliders. But where should they go? Well, there are a couple of handy programs that can help you out.
For this part of the tutorial, you will need to use Python scripts with Golly.
An easy way to locate the cleanup gliders is to apply gameoflifeboy's glider-destruction.py (see here). Given a pattern, the script attempts to find a clean 1-glider destruction for it; if there isn't one, it tells you the results with minimum bounding box and population. As usual, save the script in Scripts\Python folder.
Since the pattern is rotationally symmetric, considering one half is enough. Select the upper right constellation and copy it to a new pattern:
Run the script and — presto! It gives a solution:
Pasting it back, we find that it is compatible with the target still life. So the cleanup is done successfully:
However, it should be noted that we are lucky in this case. The results from the script is not guaranteed to be actually usable, as either the glider or the cleaning reaction may crash into the target. Besides, the suggested method is not always the most efficient if there isn't a clean 1-glider destruction.
Seeds of Destruction Game
- Also see: Tutorials/Seeds of Destruction Game
For this part of the tutorial, you will need to install Java.
Seeds of Destruction Game is an interactive application that allows one to modify a pattern by hovering the mouse around and see the effects immediately. Basically the idea is simple — put a glider somewhere manually, observe and repeat — but what is italicized makes the trial-and-error process easier.
A brief summary of the procedure, for those who don't bother to read another tutorial:
- Copy the pattern to be cleaned to clipboard.
- In Seeds of Destruction Game, click the third button from below when its label reads "Puzzle". (If instead it reads "Seed", use mouse wheel to change.) This loads the pattern to the application and creates a new "Puzzle (something)" entry on the right.
- Ensure that the first button from above is labelled as "Glider" (if not, use mouse wheel again to change). Adjust the orientation and parity of the glider shown in the second button by rolling mouse wheel.
- Click somewhere to lay down the glider and observe how the pattern evolves by rolling mouse wheel on the "Start" and "Gens" buttons. If the result is not satisfying, click the "Puzzle (something)" entry on the right to reset and start a new attempt.
- Upon obtaining a good result, click the fifth button from above. This loads the current pattern to clipboard in LifeHistory RLE format (if the label shows "Golly") or in plain two-state RLE format ("Life").
With Seeds of Destruction Game, it is even possible to suppress debris by throwing a glider into the active soup. In the following synthesis for a variant of gray counter, the uppermost glider was found in this way, which tamed quite a lot of mess:
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.
- Note that this restriction is in place to prevent the queue of user-submitted synthesis components from exceeding the object size limit of one megabyte. If you wish to submit more than about a megabyte of syntheses at a time, you're probably better off submitting a merge request to Shinjuku containing a .sjk file of your syntheses so that it doesn't exceed the size limit.
- xWSSes are allowed to substitute for gliders, and Shinjuku will automatically attempt to convert them into their respective three-glider collisions. However, because the conversions all happen at the same time, the resulting synthesis may not be valid due to gliders crossing paths, and the conversion must instead be done manually.
- Each individual step, including the gliders/xWSSes, must be separated by at least 20 empty rows/columns.
- It is recommended that every glider/xWSS should begin interacting before generation 1000 if possible, and each step should overall stabilize by generation 4000. If Catagolue does not parse your synthesis properly, there's unfortunately not much that can be done about it other than posting it somewhere else (e.g. the forums or Discord).
- 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.
Also, if you're submitting a new or newly-improved component to Catagolue, don't worry about manually applying it to every single possible object in the database, because Shinjuku's transfer.py does this automatically. The script has to be invoked manually, but as long as there's at least one synthesis featuring your component, the script will consider it when automatically creating new syntheses. Do note, however, that it will only attempt to synthesise objects that either already have a synthesis or are strict still lifes with 20 bits or less; in other cases you may want to consider submitting the synthesis yourself.[note 1]
- Ian07 (March 9, 2020). Re: Shinjuku: a database of glider syntheses (discussion thread) at the ConwayLife.com forums
- Adam P. Goucher (October 13, 2019). "level-2 and level-3 transfer searches". GitLab.
- Alex Greason (June 9, 2020). "Transfer run targeting all still lives with at least one soup in an official symmetry but no synthesis". GitLab.
- Still Life Synthesis Thread (discussion thread) at the ConwayLife.com forums
- Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
- Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
- Soup-based syntheses (discussion thread) at the ConwayLife.com forums
- Randomly enumerating glider syntheses (discussion thread) at the ConwayLife.com forums
- 4 glider syntheses (discussion thread) at the ConwayLife.com forums
- Synthesis components (discussion thread) at the ConwayLife.com forums