Lightspeed signals

(Updated December 2008)

A spaceship in Life cannot travel through empty space faster than at c/2. However, it is possible to make a stable "wire" where "signals" travel through it at the speed of light, leaving the wire intact.

In LifeLine there appeared the following lightspeed signals:

Lightspeed signals have always caught people's imagination; some speculated about using signals for communications, logical operations, and things of this nature.

More realistically, some hoped to turn a signal around a corner. If one could enclose a signal in a loop, one could build oscillators of any desired period, by making a loop of the appropriate size and inserting regularly-spaced signals in it.

This technique has been realized in Herschels with so-called "stable Herschel conduits", and in gliders with stable glider reflectors. However, since signals could presumably be packed more closely, they would allow smaller periods, and thus fill some of the remaining gaps in the list of known oscillator periods.

Dean Hickerson wrote his "drifter searcher" program in order to try to turn a 2c/3 diagonal signal around a corner. He didn't succeed; he just found a few signal turners that are not sufficient to close a loop. However, he did find many interesting things with his program, including lots of new oscillators. He also succeeded in making signal loops in a few other CA rules, proving them omniperiodic. However, this is part of a different story.

More signals

In his glossary, Alan Hensel included some further examples of lightspeed signals:

(Note that some of these signals can be trivially altered by adding or removing an isolated cell towards the front.)

Hensel found some higher-period signals by computer search:

Noam Elkies also pointed out the following signal:

Sources and sinks

Some signals can be absorbed, thus preventing the pattern from blowing up when the signal reaches the end of the wire:

It is also possible to build oscillators that emit signals at some specific period. The pattern then needs another oscillator of the same period at the other end, to absorb the signals.

Lightspeed bubbles

Unaware of Hensel's previous searches, I did my own searches for signals (using David Bell's lifesrc). I found many examples with larger and larger sizes:

In some of these signals, the front part supports several variations, including a few "tagalongs":

Some signals can be extended arbitrarily horizontally or vertically:

This raised a question: Can we make a signal with an arbitrarily long and wide empty "bubble"?

Answer:

This signal has a tail whose length must be proportional to the bubble's width. It's still an open problem to make a bubble with a fixed-length tail.

The following pattern illustrates some tagalongs of different periods for the front part of the bubble.

Finding tagalongs like these is simple: Just draw some garbage at the bubble's front edge and see what happens. Since the bubble travels at the speed of light, the front end cannot get destroyed. However, the tagalong must be "clean", i.e. it must not puff any garbage which would otherwise hit the rear part of the bubble.

I then used lifesrc to search for short-period tagalongs. Here are some samples:

(Of course, since a bubble's engine is p2, a bubble will always have an even period.)

Added Aug. 2007: Hartmut Holzwart recently found these signals with periods 3 and 5:

He also found a p1 bubble:

Adding some of the odd-period tagalongs shown above to the front of this bubble will result in odd-period signals.

Period doublings

The next question was: Is it possible to build bubbles with arbitrarily large periods, similarly to what was done with spaceships and puffers?

One way to make arbitrarily-large-period spaceships is by having some sort of a signal that loops back and forth. By increasing the size of the loop, one increases the spaceship's period. A classical example is the following p1136 ship:

Here the signal travels forwards in the form of a blinker fuse that burns faster than c/2. It then travels backwards (relative to the spaceship) in the form of a pair of gliders, which are then reflected by the 4 rear HWSSs. We can increase the period just by pulling the rear HWSSs farther away.

However, this scheme cannot be used in lightspeed signals for the very fact that they move at the speed of light! This makes it impossible for a signal to move forward relative to it.

The only possibility would be a signal that loops up and down within the lightspeed signal.

Another alternative is to make some sort of a period-doubling mechanism. One way is by making a "memory bit", in which a small-period oscillator changes its phase each time it is hit by a glider. The glider stream should have a period divisible by the oscillator's period. If one finds the necessary reactions, the oscillator will change phase when hit by the first glider, then change back to its original phase when hit by the second glider, and so on. The two types of reactions will hopefully puff different kinds of smoke, which can be used to build another glider stream with the doubled period.

David Bell found the following example, which uses a p24 tub puffer:

Inspired by this pattern, I found the following period-doubling mechanism for a lightspeed signal:

Here's a complete example, which uses two period-doublings in series to produce a p128 lightspeed bubble:

Lightspeed bubbles and superstrings

On October 2001 I became aware of Peter Rott's work on "superstrings"—orthogonal rows of cells that run at the speed of light. Rott has got superstrings that emit different things, like gliders:

To incorporate superstrings into a bubble, we need a front-end tagalong that puffs tubs at p4. Since sometimes the tub tracks are separated by an odd distance, we must be able to puff tubs at the two possible types of positions: where the tubs' centers lie on a row that to the right is dead, and where the centers lie on a row that to the right is alive.

Fortunately, lifesrc was able to find such objects:

Now we're ready to incorporate Rott's superstring technology into lightspeed bubbles. For example:

Lightspeed signals on beehive trails (Updated Dec. 2008)

All the lightspeed signals we have seen so far travel through the same medium, which consists of alternating horizontal stripes of live and dead cells. We will now see a completely different type of lightspeed signal, one that does allow the feasible construction of stable transmitters and receivers.

On October, 2002, Jason Summers found the following fuse that burns through a beehive trail at the speed of light:

The fuse leaves behind an identical beehive trail, but in a different position. A train of ten of these "pulses" restores the beehive trail to its original position, so it is an authentic lightspeed signal!

In 2003 Jason designed a "telegraph" based on the beehive wire. At one end of his device is a transmitter, which sends a lightspeed signal through the wire (a "short" one) once every 1440 generations. An input LWSS, however, causes the transmitter to send a "long" signal instead of a short one. At the other end is a receiver, which outputs an LWSS if it receives a long signal, and nothing if it receives a short signal. Jason's device is available here.

Although Jason's telegraph allows lightspeed communication (in orthogonal directions at least), it does not solve the problem of building a stable transmitter and receiver for a lightspeed signal.

Recently in June 2008, Calcyman finally solved this problem by modifying Jason's telegraph, and constructing a stable transmitter and receiver of lightspeed signals for the beehive wire.

Calcyman's construction heavily relies on stable Herschel technology for manipulating gliders. The transmitter (at the right) requires the arrival of five synchronized gliders. In the above pattern there are five p91080 guns (circled) feeding these glider inputs. It would be a routine (just tedious) exercise to wire up, via further stable Herschel machinery, these five inputs to a single glider input.

The receiver (at the left) converts a lightspeed signal into an output glider. Note that the receiver contains two diagonal 2c/3 wires with their own transmitters and receivers! (See below for more about these 2c/3 wires.) These 2c/3 wires speed up internal communication within the receiver, thus reducing its recovery time.

Note that the above device only achieves lightspeed communication in orthogonal directions. If we were to use it to transmit information diagonally (through an L-shape), the speed would degrade to c/2. On the other hand, a diagonal lightspeed signal could be used for lightspeed communication in orthogonal directions also.

Open problems on lightspeed signals

Here is a list of currently open problems regarding lightspeed signals:

• • To find a diagonal lightspeed signal. Currently, the only diagonal signals known have speeds of 2c/3, 5c/9, and c/2:

Added Aug. 2007: Dave Greene recently built a stable transmitter and receiver for the 2c/3 wire. It's huge and slow, but it works!

(See also Jason's "lightspeed.lif" pattern in his "jslife" collection for a different way to achieve diagonal lightspeed communication.)

• • To construct a stable transmitter and/or receiver for some lightspeed signal that runs through the "standard" striped medium.

  • To close an arbitrarily wide empty bubble (like the ones depicted above) with a tail that has constant length, instead of a tail whose length is proportional to the bubble's width.

  • To find lightspeed signals of all possible periods that run through the striped medium, similar to what people have been trying to do with oscillators and spaceships. With the technology shown in this article, we can achieve all periods that are powers of 2, plus periods 3 and 5 (plus the least common multiples of these periods).

More sub-lightspeed signals

In April 2006 Hartmut Holzwart discovered that signals can move through the striped medium perpendicular to the orientation of the stripes! His signals have speed 2c/3:

Hartmut also proved that 2c/3 is the maximum speed a signal can travel "against the grain" of the striped medium.

• • Can we find other sub-lightspeed signals that travel through stable media? (We are primarily interested in signals that move faster than a spaceship can travel through empty space.)

More on diagonal lightspeed communication (Aug. 2007)

We are still missing a diagonal lightspeed signal. Here is a slightly inferior means of transmitting information diagonally at the speed of light.

Here we have two components, a "Short" one and a "Long" one, which can be put together in series, forming an infinite p4 "rope" that moves diagonally up at the speed of light.

(In the above pattern we added an interface to a regular wick at the leading end, and a clean termination at the trailing end.)

However, since the S and L components have different sizes, if we put many S's in odd positions and many L's in even positions or vice versa, then the rope will gradually shift sideways. Also, if we put many consecutive L's, the bits will be spaced further apart than if we put many consecutive S's.

We can solve both of these problems by encoding each 0 by "SSLL" and each 1 by "LLSS".

Building a fixed transmitter and receiver for this thing seems out of the question, however.

Change history

December 2008

• • Added Calcyman's stable transmitter and receiver.

August 2007

• • Added Hartmut's p3 and p5 signals.

  • Added Hartmut's p1 lightspeed bubble.

  • Added diagonal lightspeed rope.

  • Added link to Dave Greene's 2c/3-signal transceiver.

August 2006

• • Added p6 signal source by Josh Ball.

  • Added against-the-grain 2c/3 signals.

January 2005

• • Added beehive-trail lightspeed singals.

  • Added list of open problems.