Dean Hickerson has found some new oscillators with small periods in the range of five to twenty.
Jason Summers has found a Period 6 oscillator which produces an isolated single-cell spark, as well as several
oscillators with periods ranging from 15 to 30.
Scot Ellison has also found a small Period 5 oscillator.
To start the new year, here's a compendium of some oscillators found during the previous few months that never got included in a posting.
First are some Period 6 Oscillators found by Nicolay Beluchenko.
Next is a Period 30 Rotor found by Karel Suhajda that requires 4 sets of P30 Glider Guns to generate the sparks necessary to turn it into a rotor. Finding a better stabilizer would be a worthwhile small project.
David Eppstein has contributed a Period 7 Oscillator and a Period 10 Oscillator, both of which have an isolated two-bit spark appearing in the upper right corner in generation 6 and 9 respectively.
The original reflection reaction can work at higher periods; variants are shown at right with p6, p7, and p8 sparks. The reflection path is the same as a kickback reaction, but the timing is different. By comparison, a pentadecathlon-based kickback emulator (far right) is four ticks faster -- or four ticks slower, since timing can be adjusted mod 8 by changing the reflector's location.
Here is a collection of new Oscillators found over the past months.
Karel Suhajda found a new terminator for a Period 5 Wick which could already be stabilized by
a Fishhook Eater. He also found a way to combine four of them, which could also function as
a terminator for a wick or use his new terminator.
Nicolay Beluchenko took a previously known Period 5 Oscillator and showed how it could be made
into a wick several different ways. Also shown is a way to combine four into a single
oscillator, and a way to create branching, "dendritic" structures. Shown here are
three off of a central fourth.
He also found a collection of Period 3, 4 and 5 Oscillators which feature sparks
along one or more edges. One of the Period 5 sparkers can be used to support the Period 5
Wick shown above.
Suhajda also found four new ways to support a previously known Period 18 agar structure
to create oscillators. Each one is shown here in a single object. He also found another agar
of Period 44 for which Beluchenko found a stabilizer (Suhajda's orginal stabilizer used
Gliders from Glider Guns to contain the structure.)
Another of Suhajda's discoveries are a Unix [16P6.1] -like component which can be supported in
three different configurations, two requiring an acutal Unix. A wick form, however, isn't
possible. He also found a different Period 6 Oscillator with an accessible spark.
Here's another set of miscellaneous long-period oscillators found recently—
First is a huge Period 12 Oscillator found by Jason Summers. It consists of two pairs of Period 6 Fountain Oscillators
flipping back-and-forth a Period 12 Rotor.
A Period 25 Pre-Pulsar Pusher, also found by Summers. The Period 5 Oscillators provide sparks which push the Pre-Pulsar
3 cells in 11 generations, while the stable objects return it in 14 generations.
Another type is a Period 44 Oscillator. Shown here are two ways to suppress the double Pi Heptominoes thrown off
every cycle. He suggests that these Pis can be perterbed to produce other objects, including Glider Guns.
Nicolay Beluchenko found a number of ways to two or four of these Period 44 engines to interact and support each other.
Shown here are just a sample of these.
Beluchenko also found a wick version, for which Artem Dergachev found the simple Block
stabilizers.
Finally, Beluchenko was able to create a Glider Gun by changing the phase of one of the rotors
and using a Fishhook Eater to suppress part of the interacton between the two.
Jason Summers has found a new Period 24 Oscillator based on a pair of Twin Bee components stabilized
by four Period 6 Unix oscillators. From that Noam Elkies has found a couple of other ways to stabilze
this rotor.
Karel Suhajda has also found a Period 4 fountain-type oscillator. These types of oscillators feature a
spark well away from the body of the oscillator, making them useful in the costruction of Glider Guns and
other engineered patterns
Nicholay Beluchenko has found another set of small Period 3 Oscillators.
The second batch shown here are a variety which depend on smaller Period 3 Oscillators to survive, and which can be attached together in various ways. The last line shows how to use a Bipole to create trivial Period 6 Oscillators. It can
also be combined with a Period 6 Oscillator (the Unix).
Nicolay Beluchenko has found a new set of small Period 3 Oscillators,
including one with population of only 19 bits.
Beluchenko later found a way to stabilize the wick such that the end stabilizer did not protrude beyond the central spine, along with an outside corner element that allows for the creation of rectangular oscillators. (A similar, inside corner element is not known.)
Artem Dergachev has found two new classes of Period 4 wicks, along with a stabilizations for them. The first wick element
can be placed together in two different orientations, as shown in the samples. The first few orders of the homogeneous wick
(with all connections the same) is also given.
Josh Ball has found a signal source for a previously known Period 6 Lightspeed Wick and terminal
end. Shown here is a minimum case for the oscillator as well as a longer version.
Nicolay Beluchenko has found a new type of Period 4 Oscillator which can be used in both wicks and agars. The first line of the illustration shows the first four orders of the wick version, with the last entry showing some alternate ends and sides. The use of Hats [9.1] also allows variable spacing and in some cases for sparks to appear between them. The second line shows how to bound the ends to create agars.
Like the 2003 examples, this pattern consists of a Herschel/glider loop (period 1536 this time, instead of period 1450) attached to a series of thirteen 'quadrupler' conduits of two different types, L-shaped and straight. Each quadrupler allows only one Herschel signal in four to get through to the next conduit.
In the starting configuration, the first three quadruplers are set to absorb three signals each: an extra block has been added to the first two L112 quadruplers and the first Fx70 quadrupler, which has a standard F166 dependent conduit appended to suppress the following Herschel's first glider. So the circuit initially counts down from 63. When all circuits are empty, a signal gets through to activate the 263-step glider advancer -- after which the circuit counts down again, this time from 4^13-1.
As usual with this kind of Herschel-track construction, Karel Suhajda's 'Hersrch' search program was used to design the base loop, and to locate an efficient connecting circuit between the end of the quadrupler chain and the glider advancer. The continuing challenge, of course, is to fit an oscillator with a higher prime period into a bounding box with a smaller number of cells.
Nicolay Beluchenko has found a new Period 15 Oscillator which is based on a pair on interacting T-Tetrominos stabilized by sparks from 4 Period 3 Oscillators. A number of phases of the T-Tetromino pair resemble phases of the Pentadecathlon whose halves have been separated by a column.
Nicolay Beluchenko has found a way to stablize the edges and corners of the Period 4 Snowflake
Agar, allowing the creation of Period 4 Oscillators.
Other components exist, which can be used to create these simplest forms of the agar oscillator.
Nicolay Beluchenko found a way to terminate some c/4 Waves
found earlier by Hartmut Holzwart, allowing for the creation of a variety of spaceships.
A variant casing for a previously known Period 2 Oscillator Rotor (top line) has been found by Ian Osgood (middle line). dgreene then noticed that one or both of the outside diagonal rotor bit-pairs can be suppressed, giving two more new Period 2 Rotors. The 6 bit Rotor (31P2) is a new Rotor, while the smaller object is just a previously unknown casing.
Scot Ellison has found a new Period 7 Sparker.
Nicolay Beluchenko found a much smaller Period 4 super-fountain style oscillator, and then managed
to shrink it further.
A fountain-type oscillator is one which has a phase in which a spark is separated from the body of the oscillator by several cells distance. The maximum possible distance is the oscillator's period less one. These isolated sparks make the oscillators useful in guns and other engineered objects.
Beluchenko also has found a Period 4 Oscillator component (which comes in two varieties) which can
be supported by Period 2 components.
By using Period 2 components to connect them, any number of these Period 4 components can be combined
to create wicks and rings.
He also found another set of Period 4 Oscillators whose halves can be recombined in various forms.
And finally one last small Period 4 Oscillator.
Jason Summers has found a few new long period oscillators. First is a Period 22 Oscillator
whose basic rotor can be repeated. Shown beside the simplest version is an extended
example.
He has also found a Period 14 Oscillator and a Period 27 Oscillator with similar rotors.
Here a number of new Game of Life objects discovered in the past few months, in no particular order:
A Period 360 c/5 spaceship found by David Bell. Removing one or two of the circulating gliders gives a Period 1080 spaceship instead
Nicolay Beluchenko has found a 20 bit variant on a known Period 3 oscillator.
Scot Ellison has found a set of Period 7 Oscillators, one as small as having a population of 38 Bits, which have some isolated sparks in one of their phases.
A pair of Diagonal c/4 Double Wickstretchers found by Nicolay Beluchenko.
A tagalong for the recently discovered Diagonal c/6 Spaceship, found by Nicolay Beluchenko.
P7 oscillator with a weak spark (glider deletion due to David Eppstein)
Though no uses have been found for this particular pattern as yet, oscillators that can delete gliders can sometimes be useful for specialized signal processing. One example is in low-period Herschel conduits. The FNG (first natural glider) released by a moving Herschel is often the key factor determining the allowable "compression" of a circuit: a second Herschel can't pass through most conduits until after the glider from the previous Herschel has gotten out of the way. In some cases, an oscillator can "reach in" slightly and delete a glider more quickly, or in a tighter space, than a still-life eater can manage.
Scot Ellison has found some new Billiard-Table type Period 7 Oscillators.
Karol Suhajda has found a previously unknown Period 4 wick element, along with a stabilization of it.
He also found a new Period 6 Heavyweight Spacehip Emulator.
Jason Summers has found a couple of new longer period oscillators. One is fairly small, with a period of 22, the other has a period of 28 and requires some fairly large Period 7 oscillators to help stabilize it.
Jason Summers has found configuration of stable objects (shown right) which can restore themselves when hit by a pair of sparks. The reaction takes 20 generations to stabilize, and the sparks are easily accessible, so this can be used in a number of period doubling reactions.
The top row of oscillators to the right show how the reaction can be used to triple oscillators with periods of 7, 8 and 9 to create oscillators with periods of 21, 24 and 27. The second row shows doubling reactions with periods 15, 16 and 18 going to 30, 32 and 36 respectively. It should be possible to double any period between 10 to 19.
Finally, the reactions can be chained together to create a Period 22 wick.
Jason Summers has also found some new Period 72 Oscillators based on a pair of B-Heptominos pseudo-shuttle. The examples show how a single pair and two pairs can be supported by smaller period oscillators.
Jason Summers has found a new Period 24 Oscillator. The Heavyweight Emulators at the top and bottom can be replaced by other P4 or P6 oscillators at the expense of symmetry, producing slightly smaller objects.
Earlier, Nicolay Beluchenko pointed out that only 3 of the 6 possible state combinations for the top cell on the line of bilateral symmetry of a "P5 squirter" type oscillator were known, as shown to the right. The sequences are—
Dean Hickerson has found the three missing sequences. The three new Period 5 Oscillators are shown to the right.
Karel Suhajda has found a new Period 6 double "Heavyweight Spacehip Emulator" (HW Emulator) oscillator. Two bit domino sparks, like those on the Heavyweight Spaceship, alternately appear on the top and bottom every three generations.
Jason Summers has found a way to construct a 40 Bit Period 5 Oscillator from a Tub and 24 Gliders.
Nicolay Beluchenko has found a new, large period 5 "T-nose" oscillator. The T-nose may be useful in supporting p5N reactions that need an ON cell at a key point to suppress or modify part of the reaction.
The most exposed part of the T-nose (the foot of the "T") consists of two cells that die simultaneously in the next generation, one from underpopulation and one from overpopulation. This leaves some extra space for any nearby active patterns to evolve away from the spark area, and for any leftover remnants of the suppression reaction to die off— as compared to a standard p5 thumb, volcano, or other sparker.
Previously known T-nose oscillators are all period 4.
dgreene: Added background information.
The Pi Heptomino, shown to the left in an alternate form which occurs in waves and tracks, is a commonly occurring pattern which in 173 generations results in a small constellation of objects. One of the earlier discoveries in the Game of Life was that a Pi Heptomino reappears 30 generations later while having moved 9 cells. This is equivalent to the Pi moving at the speed of 3c/10. Unfortunately, the exhaust immediately overwhelms the new Pi.
In Lifeline #3 (Sept.1971), p.18, it was reported that Denis Wilson had discovered that when an infinite string of Pis were properly spaced, the entire string moves as a wave at the speed of 3c/10. It generates a somewhat complicated exhaust which eventually disappears. No way of stabilizing the ends has been found.
In Lifeline #4 (Dec.1971), p.3, it was shown by Mike Beeler how a pair of Blocks allowed the Pi to reproduce several more times before being consumed by its exhaust. With two properly spaced rows of Blocks parallel to the direction of travel, the Pi can move by consuming the rows of Blocks until self-destructing when the rows end.
The rows of Blocks can be laid down by a puffer. Since no known spaceships move at the same speed as a Pi, this results in a spaceship which slowly lengthens. Here the Period 18 puffer moves at c/2, in effect every 180 generations adding 4 Block pairs to the track that will be consumed by the Pi.
A single Pi can also move along a single trail of Blinkers. This Pi in the "Pi Crawler" takes 45 generations to reappear, having moved 17 cells in the process, resulting in a speed of 17c/45. As above, a puffer of another velocity can be used to lay down a track for the Pi to travel along. More importantly, a Blinker is left behind, allowing multiple Pi Crawlers to use the same trail of Blinkers. This reappearance, along with spaceships which lay down the Blinker trails, is the basis for Gabriel Nivasch's Caterpillar. See his article for more details.
In a discussion of waves in general, Jason Summers mentioned a Pi Wave which, while not well known, was discovered a while ago, and which lays down trails of Twin Blocks. As with the clean Pi Wave, there's no known way to stabilize the ends.
He also presented some new Pi Waves in which adjacent Pis are not in exact phase with each other as with the earlier Pi Waves.
Also, Nicolay Beluchenko presented some new Pi Tracks in which a first Pi climbs the track as with the earlier Blinker trail, above. But in the process, the Pi alters the track, leaving behind a different track. A second Pi can follow on this track, cleanly burning it.
Beluchenko also discovered a track in which a pair of streams of Heavyweight Spaceships (HWSSs) can be used to support a Pi's movements.
Jason Summers has found a way to bound a period 7 agar using the halves of a previously known period 7 billiard table oscillator (46P7).
Scot Ellison has found a terminal element for a previously known extensible or wick oscillator. The objects in the top line were previously known, while the remaining oscillators use this new variation. The basic rotor element is also shown.
Nicolay Beluchenko has reported two new variations for known Period 6 oscillators, and three other new Period 6 oscillators.
Nicolay Beluchenko has discovered a large set of related Period 4 oscillators. They are based on components which can connect to the rotor component he calls the "Olive", shown at right. This component can be connected to other Period 4 oscillators and rotors when one of the right cells outlined in red is active during generation 4n+1, and then when one of the left cells is active in generation 4n+3. Three examples supported by various P4 with suitable sparks are shown.
Also shown are a selection of the new objects reported. Not all of these include the Olive component, but contain components which can be combined with it to produce other oscillators.
Noam Elkies has found a pair of related period 6 oscillators, while Nicolay Beluchenko has found a new period 4 oscillator.