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2011 January 16

Open Problems
Is Life omniperiodic?

image
Nicolay's period-37 oscillator

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Matthias' period-31 oscillator

A cellular automaton is said to be omniperiodic if, for every natural number n, there exists an oscillator of period n. Some cellular automata have already been proven omniperiodic, mainly by Dean Hickerson, by finding a set of components that can be composed to produce loops of arbitrarily length, and placing multiple signals in the loop at regular intervals.

In Life, this is not so easy. We do have a set of components, namely Herschel conduits, but they only facilitate periods of 62 or greater. To prove Life omniperiodic, we also require oscillators of all periods less than 62.

Nevertheless, there has been some recent progress, utilising software such as Nicolay Beluchenko's RandomAgar search. Amongst these new oscillators is a period-37 by Nicolay Beluchenko, and a period-31 by Matthias Merzenich. Matthias noted that both of these oscillators are capable of reflecting gliders by 90 degrees.

Oscillators of periods 19, 23, 34, 38, 41, 43, and 53 are yet to be found. A continually updated status page is available on Jason Summers' website.

2011 January 03

Oscillators
A plethora of p4 hasslers

Scot Ellison has discovered a new p4 heavyweight emulator, with a different shape to the conventional one. Further, the two designs can be amalgamated to yield a hybrid emulator.

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Scot Ellison's period-4 heavyweight emulators

Actually, this was not a completely serendipitous discovery; Ellison specifically designed his hybrid p4 to reduce the bounding box of Adam P. Goucher's p36 gun, by replacing the original (much larger) p4. That gun was itself a modification of Jason Summers' original 3-engine version.

image
Reduced period-36 gun

This modification allows a similar reduction in the size of the p108 gun, which is composed of two p36 guns.

Moreover, the p4 heavyweight emulator can be contracted to progressively form a middleweight, lightweight, and underweight emulator. Noam Elkies noticed the remarkable fact that the underweight emulator can push a traffic light predecessor, enabling the construction of a p32 hassler. David Buckingham noticed an alternative mechanism, which superficially resembles Elkies' oscillator, but can be reduced to a smaller, less symmetrical form.

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Noam Elkies' and David Buckingham's p32 hasslers

Noam Elkies produced yet another p32 hassler, again based on the underweight emulator, but facilitating a completely different mechanism. A ship is used to remove two extraneous blinkers in the standard, Paleolithic way; Elkies suggests that it may be possible to coax a glider out of these blinkers in a similar fashion to the p24 gun. This monomer can be used as the basis of a p32 dimer, and Elkies postulates that a similar p36 dimer may also be possible. However, we already have a p36 gun (as mentioned earlier in this entry), so that would have limited use.

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Period-32 monomer and dimer

Continue reading "A plethora of p4 hasslers" More

2009 May 31

Oscillators
New Oscillators

44P22 26P40 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.

26P40 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.

26P40 26P40 From Beluchenko is a Period 11 Oscillator, along with several ways in which they can react.

2009 April 14

Oscillators
New Oscillators

A summary of new long period oscillators found in the last month by Nicolay Beluchenko.

New P37 First is a Period 37 Oscillator. This is the first oscillator to be discovered with this period.

New P30 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.

New P33 This Period 33 Oscillator shows how four previously known Period 33 Oscillators (92P33) can interact. These interactions can be extended to larger agars.

New P24s Here are a couple of Period 24 Oscillators based on a central Octagon like core.

New P10 Next are a pair of Period 10 Oscillators.

New P84 New P12 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.

New P9 This is a Period 9 Oscillator.

New P80 New P120 New P160 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.

2009 March 16

Oscillators
New Oscillators

A summary of new oscillators found in the last few months.

New P10 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.

New P21 New P7 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.

New P51 pair New P51 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.

New P47 This Period 47 Oscillator found by Beluchenko consists of several t-tetromino pairs that interact with each other.

New P47 This Period 30 Oscillator found by Jason Summers consists a pair of t-tetrominos which repeatedly bounce back after being pushed together.

New P47 A Period 3 Oscillator with an isolated spark found by Beluchenko.

2009 January 08

Oscillators
New Oscillators

New P7 Oscillator Nicolay Beluchenko has found some new oscillators. First is a new Period 7 oscillator (on right) which is based on a variation of a symmetrical Period 7 Oscillator found earlier by Dean Hickerson.

New P29 Oscillator New P12 Oscillator Next are a new Period 12 Oscillator and a new variation in the family of known Period 29 oscillators.

New P13 Oscillator Variations New P13 Oscillator Finally there is a Period 13 Oscillator which can be combined with itself and with other oscillators. First are examples of the three ways in which two of these can share a common block. Jason Summers also pointed out that four of these oscillators can be combined to create an oscillator where none of the cells are stable, making it the first such oscillator known with a prime period greater than two.

Multi-P13 Oscillator This Period 13 Oscillator can also be combined with objects of other periods to create objects with much longer periods that are multiples of 13. Examples here show oscillators with periods of 39, 52, 65, 78 and 104 generations. (The Period 39 by Jason Summers; the rest were found by Beluchenko.)

2008 November 23

Oscillators
New Small Period Oscillators

37P4 Nicolay Beluchenko has found a new, small Period 4 oscillator.

44P30 Quad Queen Bee He has also found a new variation of the old Queen Bee Shuttle in which four of them form a closed loop. This is a variation of a known wick structure.

Update:

Turns out the Period 30 oscillator (or one very much like it) was first encountered 38 years ago by William Gosper. It was the first Period 30 oscillator built from the discovery that Queen Bee shuttles could interact with each other and survive. For some reason, in all the years since this object never made it into my list of known oscillators.


New Period 3 Oscillators Dean Hickerson's search programs have uncovered a host of new small oscillators with periods ranging from 3 to 12.

New Period 4 Oscillators

New Period 5 Oscillators

New Period 6 Oscillators

New Period 7 Oscillators

New Period 8 Oscillators

New Period 9 Oscillators

New Period 10 Oscillators

New Period 11 Oscillators

New Period 12 Oscillators

2008 June 06

Oscillators
New Small Period Oscillators

New small period oscillators Dean Hickerson has found some new oscillators with small periods in the range of five to twenty.

28P5 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.

28P5 Scot Ellison has also found a small Period 5 oscillator.

2008 January 06

Oscillators
Some New Oscillators

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.

P6 Oscillators First are some Period 6 Oscillators found by Nicolay Beluchenko. P6 Oscillators

P30 Oscillator 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.

P7 Oscillator P10 Oscillator 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.

2007 December 17

Discovery
New 180-degree glider reflector, period 4 and up

2007-12-16-reflector-pN.rle
p6, p7, p8, and p22 versions of Noam Elkies'
spark-assisted glider reflection reaction,
with a previously-known p15 'kickback simulator'
included at the far right for timing comparisons.
From patterns by Jason Summers, 5-6 October 2007.
Noam Elkies responded to the challenge of finding a period-4 glider reflector by designing a new type of 180-degree reflector based on a spark-assisted block reconstruction. Jason Summers built a faster version at p22 (upper right), which produces a glider on the same path two ticks earlier.

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.

2007-12-16-Lx134-p8-and-p4.rle
Lx134 conduit, p8 and p4 versions -- recovery times 172 and 292
Reflector by Noam Elkies, 15 Nov 2007, improved by David Eppstein
David Eppstein contributed a p4 oscillator that could accomplish the same catalysis as the p22 oscillator above; improved versions are shown in the period 4 and period 8 reflectors at right, cleaning up the extra debris in an Lx134 conduit.

Continue reading "New 180-degree glider reflector, period 4 and up" More

2007 July 28

Oscillators
New Oscillators

Here is a collection of new Oscillators found over the past months.

New P5 Wick Terminator 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.

New P5 Wicks 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. New P5

New P3s New P4s New P5s 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.

New P18 and P44 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.)

New P6s 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.

2007 May 17

Oscillators
New Long Period Oscillators

Here's another set of miscellaneous long-period oscillators found recently—

694P12 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.

140P24 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.

P44 oscillators 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.

moreP44 oscillators 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.

more P44 oscillators Beluchenko also found a wick version, for which Artem Dergachev found the simple Block stabilizers.

P44 glider gun 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.

2007 May 11

Oscillators
Some new oscillators

80P24 144P24 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.

225P4 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

2007 February 25

Oscillators
More New Period 3 Oscillators

Period 3 Oscillators Nicholay Beluchenko has found another set of small Period 3 Oscillators.

Period 3 Oscillators 2 Period 6 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).

2007 February 17

Oscillators
New Small Period 3 Oscillators

New P3 Oscillators Nicolay Beluchenko has found a new set of small Period 3 Oscillators, including one with population of only 19 bits.

2006 December 13

Oscillators
More Period 4 Wicks

New P4 Wick Element New P4 Oscillators by N.Elkies and N.Beluchenko New P4 Wicks by N.Elkies and N.Beluchenko Noam Elkies has found a new Period 4 wick element, along with a way to stabilize it into an oscillator. Nicolay Beluchenko came up with some other stabilizations, which allowed for elements to alternate along their central spine.

New P4 Oscillators by Nicolay Beluchenko New P4 Wicks by Nicolay Beluchenko 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.)

2006 December 10

Oscillators
New Period 4 Wick Oscillators

New P4 Wick Element New P4 Oscillators by A.Dergachev New P4 Wicks by A.Dergachev 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.

New P4 Wick Element New P4 Wicks by A.Dergachev

2006 August 12

Oscillators
Period 6 Wick Oscillator

P6 Wick Oscillator 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.

2006 July 08

Oscillators
New Period 4 Oscillator Type

New P4 Oscillators 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.

2006 May 13

Oscillators
Prime-Period Oscillator: p103079214841

2006-03-31-p103079214841.rle
p103079214841 (prime: 4^13*1536-263) oscillator/gun --
p1536 base loop, 13 quadruplers, and a 263-step glider advancer.
Dave Greene, 31 Mar 2006 (with correction by Tomas Rokicki)
Here is a sample Herschel-based oscillator with a 12-digit-prime period, along very similar lines as the 11-digit-prime oscillators constructed in 2003, but with alternative 'glider advancer' technology and more compact connecting circuitry.

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.

2006 May 12

Oscillators
New Period 15 Oscillator

180P15 oscillator 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.

2006 April 09

Oscillators
Misc. New Oscillators and Spaceships

32P20H10V0 Jason Summers has found a simple new way to stabilize one of the first known puffer trains, the Period 20 B-Heptomino Puffer Train, turning it into a small 2c/4 Period 20 Spaceship.


Period 4 Snowflake Agar 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.

Period 4 Snowflake Agar Other components exist, which can be used to create these simplest forms of the agar oscillator.


c/4 wave spaceship 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.

2006 March 01

Oscillators
New P2 Oscillators

New P2 Oscillators 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.

2006 January 30

Oscillators
Various New Oscillators

P7 Sparker Scot Ellison has found a new Period 7 Sparker.


P4 &quotSuper-Fountains" 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.


P4 Beluchenko also has found a Period 4 Oscillator component (which comes in two varieties) which can be supported by Period 2 components.

P4 wicks & rings By using Period 2 components to connect them, any number of these Period 4 components can be combined to create wicks and rings.


P4s He also found another set of Period 4 Oscillators whose halves can be recombined in various forms.


P4 And finally one last small Period 4 Oscillator.

2006 January 11

Oscillators
New Long Period Oscillators

description 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.

description He has also found a Period 14 Oscillator and a Period 27 Oscillator with similar rotors.

2005 December 11

Oscillators
Object Miscellany

Here a number of new Game of Life objects discovered in the past few months, in no particular order:


2005-12-11-P360-spaceship.rle A Period 360 c/5 spaceship found by David Bell. Removing one or two of the circulating gliders gives a Period 1080 spaceship instead


2005-12-11-20P3.rle Nicolay Beluchenko has found a 20 bit variant on a known Period 3 oscillator.


2005-12-11-P7-osc.rle 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.


2005-12-11-P7-osc.rle A pair of Diagonal c/4 Double Wickstretchers found by Nicolay Beluchenko.


2005-12-11-P6tagalong.rle A tagalong for the recently discovered Diagonal c/6 Spaceship, found by Nicolay Beluchenko.

2005 November 26

Logic Elements
New P7 sparker

weak P7 sparker

P7 oscillator with a weak spark (glider deletion due to David Eppstein)

Toward the end of October, Scot Ellison published a new oscillator with a weak P7 spark:

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.

2005 October 21

Oscillators
New Period 7 Oscillators

New P7 Oscillators by Ellison Scot Ellison has found some new Billiard-Table type Period 7 Oscillators. 560P7

Oscillators
New Oscillators

New P4 Wick Element New P4 Wicks by K.Suhajda Karol Suhajda has found a previously unknown Period 4 wick element, along with a stabilization of it.

New P6 He also found a new Period 6 Heavyweight Spacehip Emulator.

2005 September 08

Oscillators
New longer period oscillators

description 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.

2005 August 19

Oscillators
New long period oscillators

New Reaction 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.

New Oscillators 1 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.

New Oscillators 2 Finally, the reactions can be chained together to create a Period 22 wick.

Update: 2005-08-20

New P72sJason 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.

2005 June 19

Oscillators
New Period 24 Oscillator

156P24 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.

2005 May 05

Oscillators
New Period 5 Oscillators

3 P5s (10000)(10100)(11010) 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—

(10000)
(10100)
(11000)
(11010)
(11100)
(11110)

3 P5s (11000)(11100)(11100) Dean Hickerson has found the three missing sequences. The three new Period 5 Oscillators are shown to the right.

Oscillators
New Period 6 Oscillator

description 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.

2005 April 09

Oscillators
Period 5 Oscillator Construction

40P5.5 40P5.5 construction Jason Summers has found a way to construct a 40 Bit Period 5 Oscillator from a Tub and 24 Gliders.

2005 April 02

Oscillators
New Period 5 Oscillator

description 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.

Update: 2005-Apr-09 18:55

dgreene: Added background information.

2005 March 19

Oscillators
Pi Waves and Pi Tracks

Background

Pi Heptomino Basic Pi 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.

Basic Pi-Wave 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.

Pi-Block 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.

449P180H90V0A32.1 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.

Pi Crawler 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.

Recent News

Pi Wave 2In 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.

New Pi WavesHe also presented some new Pi Waves in which adjacent Pis are not in exact phase with each other as with the earlier Pi Waves.

New Pi TracksAlso, 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.

Pi HWSS trackBeluchenko also discovered a track in which a pair of streams of Heavyweight Spaceships (HWSSs) can be used to support a Pi's movements.

2005 March 11

Oscillators
New Period 7 Oscillators

P7 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).

2005 March 09

Oscillators
New Period 4 Oscillator Variants

New P4 Rotor New P4s

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.

2005 January 30

Oscillators
New Period 6 Oscillators

description Nicolay Beluchenko has reported two new variations for known Period 6 oscillators, and three other new Period 6 oscillators.

2005 January 23

Oscillators
New Period 4 Oscillators

Olive Olive P4s P4s

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.

2004 December 30

Oscillators
New Oscillators

P6 oscillator P4 oscillator Noam Elkies has found a pair of related period 6 oscillators, while Nicolay Beluchenko has found a new period 4 oscillator.