Here's a construction of a Period 177 Oscillator found by Jason Summers. It takes 8 sets of 3 Glider collisions to produce the oscillator engines. (One of the sets of three is shown in blue in the image.)
Several oscillators that got left out of the previous report of new oscillators, and a few new ones.
First are a Period 22 and a Period 40 found by Nicolay Beluchenko which should have been included previously.
Beside the obvious ways to combine two of the Period 40 oscillators by sharing a common block, he also found
several ways in which the sparks from one can support a second.
From Beluchenko is a Period 11 Oscillator, along with several ways in which they can react.
From Harmut Holzwart are some new Period 6 spaceships which move at c/6. The first is the smallest at this speed currently known. The larger is a variation on a ship previously found by Paul Tooke.
A few months ago, Calcyman came up with a substantial improvement to stable-reflector technology, using some of Paul Callahan's search results from the 1990s.
The previous smallest and fastest stable reflector, the "boojum reflector", produced an output glider 180 degrees from the input at a 9-cell offset. It contained nine still-life catalysts and took 202 ticks to recover. Calcyman's new discovery, the "rectifier", needs only five catalysts to produce the exact same reflected glider -- and it recovers in only 106 ticks.
This is an unusually short recovery time, to say the least -- because this is the first stable reflector that makes a perfect single-stage recovery.
All stable reflectors are triggered when an incoming glider strikes a "bait" still life and produces an active pattern. Until now, all known stable reflectors have fallen into one of two categories. In the first type, "destroy-then-rebuild", a glider colliding with one or more bait still lifes produces an output signal; the bait then has to be reconstructed as a separate step, by routing a branch of the output signal back to the key location.
In the second type, "rebuild-then-repair", catalysts successfully recreate the bait and an output signal from the original active pattern. But it's very difficult to find a set of catalysts that can recreate the bait in exactly the right place, allow a clean output signal to escape, _and_ suppress the remainder of the active pattern perfectly. So other unwanted still lifes generally appear along with the bait; the output signal then has to be routed around to clean up the extra junk (usually by annihilating it with a carefully-placed glider). Only then can the reflector safely accept another glider input.
The boojum reflector comes fairly close to a perfect single-stage recovery; a lucky cleanup glider is generated directly from the original active pattern, so no extra Herschel circuitry is needed. But Calcyman's new pattern is a significant step forward: it doesn't need any cleanup gliders at all!
Calcyman's article-length summary of the development of stable signal-processing technology includes examples of both "destroy-then-rebuild" and "rebuild-then-repair" reflector types. A more comprehensive collection of early stable-reflector constructions can be found in his reflector catalogue.
A summary of new long period oscillators found in the last month by Nicolay Beluchenko.
First is a Period 37 Oscillator. This is the first oscillator to be discovered with this period.
Next is a Period 30 Oscillator consisting of a four-boat engine bound by four Pentadecathlons. With suitable sparks, this engine can double any periods of 13 or greater, as in this case where the Pentadecathlon's period of 15 is doubled.
This Period 33 Oscillator shows how four previously known Period 33 Oscillators (92P33) can interact. These interactions can be extended to larger agars.
Here are a couple of Period 24 Oscillators based on a central Octagon like core.
Next are a pair of Period 10 Oscillators.
Next is a small Period 12 Oscillator, along with a Period 84 Oscillator which uses the Period 12 to suport a pair of Pi Heptominoes.
This is a Period 9 Oscillator.
Finally, here are several ways found by Jason Summers where a previously discovered Period 40 Oscillator shifts around a Blinker to create longer period oscillators.
Update:Until recently, Dean Hickerson's Life pages have been available only in Web-archive form, with no images available.
The image at right is from an intriguing family of patterns constructed in mid-2006. The family includes 'Life Computes Pi' and a number of 'Clouds' variants. There's really no substitute for watching these evolve in real time in a high-speed Life simulator, but a few surprising pictures of later stages of their evolution are shown below.
The pattern to the right is the starting configuration for 'Life Computes Pi', which consists of four breeders creating lines of guns that recursively stifle each other's output. The gliders appear to be spiraling outward, but in fact each set of four guns affects only itself, and any finite area around the center of the pattern will eventually repeat an earlier state.
As the number of ticks (t) increases, the population of the entire pattern approximates (pi-2)/720 t^2. At four million ticks, when the images below were captured, this works out to a value of pi correct to two places after the decimal point... so this is not quite the most efficient way to calculate pi.
The image to the right shows the large-scale shape generated by this family of objects after several million generations. The variant shown here is known as 'Clouds', because a complex feedback effect between the quadrants creates ever-larger rough-edged clouds of gliders as the pattern grows in size.
Dean Hickerson's original block-deleting 2c/3 termination almost certainly wasn't designed with this in mind, but it happens to absorb a double-length signal in exactly the same way as a standard signal -- the final stable state is the same in either case. This means that communication speeds approaching 2c/3 can be implemented over long distances in any direction, not just diagonally.
In the accompanying diagram, the input Herschel signal is circled in red. The output signal can be any of a number of optional glider outputs in the Herschel circuit at the bottom.
Two elbows in a row will not work (there's no known way to turn a double-length 2c/3 signal). But in the absence of layout constraints, a single elbow is sufficient to send a 2c/3 signal anywhere in the universe.
A summary of new oscillators found in the last few months.
First is a Period 10 Oscillator found by Nicolay Beluchenko. Like the Period 6 Unix, this oscillator can be chained together in a variety of ways.
Here is also are several of Period 7 Oscillators that he found. Noam Elkies showed how two of the smaller ones could be combined with a Bi-Block to produce a Period 21 oscillator.
This Period 51 Oscillator found by Beluchenko is also the first oscillator of that period found which is not a combination of smaller period oscillators. These oscillators can also share their common blocks when properly phased.
This Period 47 Oscillator found by Beluchenko consists of several t-tetromino pairs that interact with each other.
This Period 30 Oscillator found by Jason Summers consists a pair of t-tetrominos which repeatedly bounce back after being pushed together.
A Period 3 Oscillator with an isolated spark found by Beluchenko.
A good highway robber can absorb a glider and produce an output signal, without disturbing gliders on nearby lanes, even one cell farther away from the highway-robber device.
Calcyman's new construction rebuilds the loaf bait and is ready for another glider input in 1244 ticks.
With a month-long search using a customized version of the 'gfind' search program in October of last year, Paul Tooke completed a new c/6 spaceship based on a flexible self-supporting pushalong component supplied by Hartmut Holzwart.
The pushalong component can follow behind another copy of itself and supply the necessary sparks to keep it going -- surprisingly, three different phases work equally well, as shown in the right-hand spaceship in the diagram.
A very unusual feature of this spaceship is that it has a strong central forward spark, and it travels slowly enough to allow this spark to interact with other objects without destroying the spaceship. Many types of spaceships have side sparks that can be used to modify or clean up other objects in passing. But this new c/6 can simply run right over the top of some still lifes, small oscillators, and constellations, and continue unharmed -- as the left-hand spaceship demonstrates.
Calcyman has designed a multi-stage stable glider reflector with a recovery time of 466 ticks -- an improvement over the long-standing record of 497 ticks, at the cost of a somewhat larger bounding box.
Lucas Brown has constructed a new type of breeder, in which a rectangular array of high-period glider rakes moves eastward while producing gliders that crash to form p30 glider guns. Gliders from the p30 guns crash together in turn to produce streams of northbound spaceships.
Here is the same breeder after 5000 generations -- the seventh LWSS factory has just begun to produce spaceships, and the component p30 glider guns in the eighth factory have started up but their gliders have not yet collided. Click this image for a closer view of the initial breeder pattern.
