It’s also a relatively sparse line, as the number of live cells is less than a hundredth of the line’s extent: https://conwaylife.com/wiki/Unidimensional_spaceship_1

https://www.youtube.com/watch?v=eMJk4y9NGvE

I'm really charmed by the linked thread and all the passion and work it belies. Congrats to those involved!

I think people will disagree about whether “Turing-complete” is powerful enough for supporting intelligence but let’s assume it does.

> So, will a random initial position (tend to) be filled with super-intelligent life forms, or will the chaos reign?

Even if it doesn’t, it might take only one intelligent life form for the space to (eventually) get filled with it (the game of life doesn’t heave energy constraints that make it hard to travel over long distances, so I don’t see a reason why it wouldn’t. On the other hand, maybe my assumption that all intelligent life would want to expand is wrong), and in an infinite plane, it’s likely (¿certain?) one will exist.

On the other hand it’s likely more than one exists, and they might be able to exterminate each other.

You might have better luck with other variants. Reversible cellular automata have a sort of 'conservation of mass' where cells act more like particles. Continuous cellular automata (like Lenia) have less chaotic behavior. Neural cellular automata can be trained with gradient descent.

https://conwaylife.com/wiki/Spaceship

https://quoteinvestigator.com/2014/01/12/history-rhymes/

Conway's game of life: https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life

Gliders: https://en.wikipedia.org/wiki/Glider_(Conway%27s_Game_of_Lif...

If you look at the placement of Journal of Cellular Automata in SciMago's Shape of Science visualization[0] you'll see that it's completely surrounded by machine learning/AI journals

[0] https://www.scimagojr.com/shapeofscience/

The Game of Life is Turing complete. And therefore a complete analysis of how to write programs in it would imply a solution to the Halting problem. Which is impossible.

>>>

Unidimensional spaceship can be interpreted as a demonstration of the progress of recent years in slow salvo technology and the various arms that use it.

The project uses 4 construction arms, with the last three sharing principles with the arms used in the RCT15 project. The first arm is newly invented just for this case. I was not part of the community at the time the principles of the first two arms were studied, but let me describe them anyway.

The one line restriction limit us to using blinkers as the basis of the first arm. Interestingly, a small perturbation at the end of some blinker configuration makes the pattern unstable, and several blinker patterns allow the perturbation "fuse" to move in a controlled manner. Various configurations have been discovered that leave no debris but move at different speeds. Some configurations have been found that produce backward-firing mwss (and leave debris), head-on collisions of mwss that transform them into gliders for both glider colors. By combining these configurations, we can trigger a fusion in the middle of a carefully chosen arrangement of blinkers that would synchronize the mwss collisions at the desired time parity at a prescribed x-coordinate and generate a glider with a prescribed phase and trajectory, so that such an arm could create any p2 recipe.

The second arm used is a binary arm, where a pair of synchronized gliders on the same trajectories are used, with one glider always present and the presence of the other gliders allowing modification of the resulting configuration. Careful study of the results of various words using letters "1" and "2" (indicating the presence of the second glider) led to the discovery of specific modifications of the target "anchor" configuration.

Some of them allow you to move the "head" of the anchor stack to move closer/farther from the base of the arm. Some sequences will generate a perpendicular glider. Not all mod 8 phases and colors are known, but with careful "head positioning" any p8 recipe could be built with such an arm. The program used for the translation only used single blinker anchor technology, which produces a glider for a cost of around 100 bits ("letters"). The agnosticisation salvas of the p8 recipe to use only the p1/p2 constraints on the glider phases (when possible) greatly reduces the number of bits required. Alternative glider paths also help, leading to the same stable configurations during a slow salvas. Currently, there is an alternative method with around 80 bits per glider using 4 different anchors deep in the "arm target stack". The code could be improved by some form of dynamic programming by compiling the salvo from the parts emitting gliders closest to the arm to the gliders further away from the arm, but there was no need to complete the project.

The third and fourth arms are extreme compression construction arms "ecca", where a programming language interpreter is created and individual incoming letters are interpreted as instructions specifying which phase (mod 2) and line of glider to emit.

We have achieved an optimal encoding that requires about 7-8 bits to emit a typical slow p2 salvo of gliders.

The instruction set includes a move direction change option, move4 (repeated), move2, move1, color option, phase option. Stopping the move4 loop results in a glider being fired "near" the current arm position after a defined number of letters. The third arm uses exactly this set of options, while the fourth arm executes move1 after a change of direction, further increasing its efficiency. The fourth arm uses "yellow lane" filtering technology, which allows its components to be recycled, resulting in a more compact and less expensive design. On the contrary ecca1 is built as p1 pattern what allows selecting less expensive options during the build by the binary arm (at few places where p8 restriction would be required in ecca2 build). The arms are capable of firing gliders with 4 combinations of phase mode 8 and color (all four combinations of phase mode 2 and color). This is perfectly fine for slow salvos with a p2 restriction, but building p8 salvos requires limiting the salvos to use only a limited set of "signature" color combinations of glider phases.

This led to a modification of the psamake program (transforming "neo" Spartan configurations for slow salvos that are built from a single block). When a bespoke subsalvo builds a p8 pattern (initial call by a single glider), a 0 degree one time turner prefix is optionally allowed for a phase/color correction. Similarly, p2 salvos are transformed to the required p8 phases corresponding to the signature.

There are several other prerequisites for building a ship. We should implement a storage where the bits to be fed into the binary arm and later into the ecca1 and ecca2 arms are encoded. Fortunately, a slow salvo of 8 gliders fired symmetrically into the central "spine" of the track from both sides (the ship cannot lose symmetry) will create 4 blocks near the spine if there was nothing there, or move the blinker from its given position by 2 pixels (east) emitting glider back.

There are a few more requirements to build the ship. We should implement a storege of bits that will be fed into the binary arm and later into the ECCA1 and ECCA2 arms. Fortunately, a slow salvo of 8 gliders fired symmetrically into the central “spine” track from both sides (the ship cannot lose symmetry) will create 4 blocks near the spine if there is nothing there, or move the blinker from its current position by 2 pixels (east) emitting glider backward.

The fuse arm fires 8 90 degree glider producing switch engines “GPSE90” that fire the slow salvo and convert the blinkers on the spine into a traveling signal.

The signal is then fed into the binary arm by a pair of gliders firing the gliders back. One of the gliders is reflected so that they annihilate on impact. The glider signal from the tape annihilates the glider from one stream (negative signal), so the reflected glider from the other stream is not annihilated at the start of the arm. The ever-present glider of the binary arm is created by a gun of the corresponding period (repeated in the third and fourth arms).

The fuse arm creates a reflector (p8bouncer) and a seed for a pair of corderships so that the first bit read triggers the corderships in synchronized phase to allow annihilation (and reflection).

To trigger the fuse arm, we need a target for the arm gliders to be modified. This is what the pre-fuse does. It releases a glider, travels some distance, and releases a perpendicular lwss on collision course with the glider. The collision leaves behind debris (the target of the fuse arm) and launches two gliders into the spine. One of them hits its mirror image and creates a biblock, while the other triggers the fuse arm in the middle.

We already know what the fuse arm does, the binary arm creates ecca1 and triggers a meteor shower creating a reflector on the input signal path. When the arm's anchor stack is removed, ecca1 starts interpreting the input bits. The goal of the ecca1 arm is to clean up the west. It destroys the remnants of the dirty mwss creations and reconstructs the initial bliner configurations shifted 2 pixels to the east (we can't build anything on the spine due to symmetry, but we can modify the already presented content of the spine). It also creates ecca2, the hive needed to transition to the one-dimensional state and the ship needed at the end of the tape cleaning.

Ecca1 finishes its work by destroying its reflector on the input signal path.

Ecca2 is responsible for cleaning up the east. It is built with a destruction seed (computation supported by the gSoD program), which means that one incoming glider on the correct path will cause the pattern to disappear. The destruction seed generates two gliders. One of the goals of ecca2 is to create seeds of destruction of the reflectors on the input path - one destruction seed for the reflectors of ecca1 and one for the reflector, thus triggering the binary arm. The ship created by ecca1 near the spine converts a pair of cleaning mwss into a single glider, which triggers the destruction seed of ecca2. The exit gliders of ecca2 seed of destruction, are navigated by one time reflectors to the destruction seeds of the reflectors of ecca1 and the binary arm.

Ecca2 converts ecca1 into a ship (a disposable turner), which would play its role at the very end of the ship's period (a slow destructive salvo combined with the trivial task of pslmake). (the rest of the blinker of the binary arm stack is also destroyed by ecca2).

ECCA2 should also clean up the remains of the gun used by the binary arm (in the current version we stopped it with ecca1, but it would probably be equally or more efficient to stop it with ecca2) (slow 2 salvo is used there and half honey farm to honey farm slow salvo move collection helps a lot in such design).

The most important task of ecca2 is to stop the tape reading mechanism and clean it up. The salvo of synchronized gliders stops the GPSE90 and the corderabsorbers are assembled in time to stop the cordership pair (as a tool a program was used that automatically combines a pre-calculated splitters and reflectors (consisting of at most two small objects) to create a given pair of synchronized parallel gliders). The glider streams fired from the corderships do not stop at the same time, so the 3 escaping gliders are also stopped by the seed created by ecca2. In order for ecca2 to create a seed to stop the GPSE90, it must clean up the irregularities of the GPSE90's trajectory debris. (destructive salvo calculated into a periodic pattern...). Similarly, the far-end cleanup converts the debris of the stalled GPSE90 into a periodic pattern. Ecca2 must send corderfleets cleaning a periodic pattern (of arbitrary length). Therefore, it must create corderabsorbers on the other side (we chose corderabsorbers close, ships travelling from far). (used a program to search for corderfleets cleaning compatible periodic patterns) ... the corderships were created using modern 11 cluster seeds (except for the one closest to the arm, where 12 cluster seeds were used to fit close to the arm)).

The corderfleet was also used to destroy the remnants of a pair of corderships. The last task of ecca2 was to fire a salvo to create two mwss that would clean the blocks created during the tape reading (this would trigger a seed of ecca2 destroyal at the end).

The corderabsorber for the last cordership is modified and instead of annihilating with the cordership it emits a perpendicular glider that hits the boat from the ECCA1 conversion to bounce to the behive and converts it into a one-dimensional pattern, starting a new generation.

The ECCA2 compiler used agnosticised lane phase recipes and chose the optimal route from the options (shortening the tape as much as possible). This optimization was not done in ECCA1, binary or fuse arm.