Game of Life News

Last Posting

2006-03-05T10:22:00.000-08:00

Notice:

This will be the last posting for this site. It's moving to a new location:

http://pentadecathlon.com/lifeNews/index.php.

All the old posts have been moved there. Update your links and bookmarks as appropriate. For now, everything here will be left as is. Eventually, the images will disappear as part of a website update on the hosting server.

Website Update Announcement

2006-02-28T14:59:00.000-08:00

Stephen Silver has made available an update (Version 25) to his Life Lexicon.

Various New Oscillators

2006-01-30T13:15:00.000-08:00

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.

New Long Period Oscillators

2006-01-11T11:10:00.000-08:00

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 simpliest version is an extended example.

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

"Rule 110" Unit Cell

2005-12-21T12:51:00.000-08:00

Jason Summers has put together a "Rule 110" unit cell. A unit cell is a Game of Life pattern which acts as if it were a cell or component in another automata, allowing the Game of Life to incorporate the abilities and results of that automata into itself. For example, several years ago David Bell created a Life unit cell which can be used to recursively simulate the Game of Life.

"Rule 110" is a 1-dimensional non-totalistic cellular automaton. A cell's next state depends on its current state and the states of its two nearest neighbors, as follows:

Gen 0	Gen 1
000	.0.
001	.1.
010	.1.
011	.1.
100	.0.
101	.1.
110	.1.
111	.0.

From Summers' description of his pattern:

The logic used in the pattern is (B AND NOT A) NOR (B XOR C), where A is the cell to the left, B is the cell itself, and C is the cell to the right. This produces the inverse of the correct rule-110 result. The result is then put through various duplication, reflection, and inversion reactions to produce four copies of an uninverted signal. One copy is sent to the cell on the left, one to the cell on the right, one is fed back into the same cell, and one is emitted upward as a visual record of the cell's states.

That the horizontal spacing (256) is a power of 2 is intentional, and might make it more efficient to run in Hashlife. The period (1200) can't reasonably be made a power of 2.

It should be easy to adjust the period by multiples of 120 generations, and the horizontal spacing by multiples of 60 cells. Other adjustments are possible, but more difficult.

As Summers notes, it would be an interesting project to build a puffer which lays down these unit cells as its output, and do so at a rate faster than they'd be needed by the "Rule 110" automata run.

Image Key:

A: Marker Tubs and initial Block
B: Glider->Spaceship reaction
C: Spaceship->Glider reaction
D: Turn Glider 90°
E: Invert & turn Glider 90°
F: Split stream
G: Duplicate stream

Red: Input streams
Green: Output streams
Blue: Internal streams

Unlabeled are a couple of signal generator Glider Guns and a couple of Fishook Eaters which are a part of the logical operators. The objects in the corners are used for alignment of multiple cells.

Using the pattern:

To use the pattern, place copies such that the "decorative still-lifes" at the corners coincide. The initial state of the cell is forced to be ON by the glider located between the tubs (A in the pattern). Remove the block infront of it to set the cell state to OFF. If the Fishook Eaters on the left and right edges don't disappear on their own in a few generations, then they can be removed manually before starting. For Game of Life programs that don't like the annotation format commands, a file without the formatting is also available

Fixed-Width and Slipping-Stripe Greyships

2005-12-18T19:46:00.000-08:00

fixed-width 2c/4 spaceship supporting a p9 wick
Hartmut Holzwart, 15 December 2005

Here are a few more greyships and related patterns constructed recently by Hartmut Holzwart:

long and short versions of a fixed-width perpendicular greyship
Hartmut Holzwart, 13 December 2005

simpler fixed-width perpendicular greyship
Hartmut Holzwart, 13 December 2005

The following two patterns are "failed spacefillers" -- they expand in the same way as a standard spacefiller for a while, until an internal instability in the boundary between the two types of stripes catches up with an expanding edge.

alternate mirror-symmetric pattern showing Gabriel Nivasch's
slipping-stripe reaction: Hartmut Holzwart, 28 November 2005

trial pattern showing a slipping-stripe reaction sent in
by Gabriel Nivasch: Hartmut Holzwart, 21 November 2005

These last two patterns, along with many of the greyships from previous postings, can also be seen here in MCell holiday colors.

Switch-engine breeder

2005-12-18T15:36:00.000-08:00

Switch-engine breeder: David Bell, 23 July 2005

Back in July, David Bell constructed a new switch-engine breeder. An orthogonal c/2 rake shoots gliders at the detritus left by a diagonal c/4 puffer, resulting in a 'natural' reaction that produces c/12 block-laying switch engines.

Sample c/5 and c/4 glider-processing convoys

2005-12-18T08:29:00.000-08:00

c/5 puffer converted into a (relatively) small p1080 rake. Add
two gliders to the loop to get p360. David Bell, 28 October 2005

Here are four patterns by David Bell, showing a variety of ways (some discovered relatively recently) for passing spaceships to affect an active pattern. The first is an engineless p1080 rake, using a design similar to the recently-posted p360 spaceship:

diagonal c/4 convoy turns a sideways glider into a forward LWSS: David Bell, 11 November 2005

The next three patterns involve diagonal c/4 convoys (spaceships that travel the same speed as a glider, but have sufficiently isolated edge sparks that they can interact non-destructively with gliders and other active patterns.) Here are some sample convoys that process input gliders to produce various types of output:

diagonal c/4 convoy which converts a single sideways glider into a toad. A toad in combination with other nearby stable/p2 patterns
(e.g., 6bo$6bobo$6boo3$11b3o$12b3o3$3o$bbo$bo!) can be converted to a backward or sideways glider by a passing convoy,
making it useful as a 'memory bit'. David Bell, 12 November 2005

Period doubling reaction for diagonal c/4 rakes, demonstrated with a p800 glider stream. Diagonal c/4 rakes are constructible
with period 28, 24, 16, or 0 (mod 32). David Bell, 2 November 2005

New perpendicular greyships

2005-12-16T09:36:00.001-08:00

perpendicular-to-the-grain greyship with new back slope
Hartmut Holzwart, 29 November 2005

Hartmut Holzwart has incorporated a variety of new reactions, slopes, and overall shapes into perpendicular ("against-the-grain") greyships. Here is a sampling:

new greyship component shown on right side
Hartmut Holzwart, 29 November 2005

mirror-symmetric against-the-grain greyship with new back slopes
Hartmut Holzwart, 2005-11-30

perpendicular greyship with 1/4 back slope
Hartmut Holzwart, 1 Dec 2005

pentagonal perpendicular greyship with 1/4 back slope
Hartmut Holzwart, 1 Dec 2005

new perpendicular greyship with central wick from an old unfinished
spacefiller: Hartmut Holzwart, 6 December 2005

perpendicular greyship with 1/2 back slope
Hartmut Holzwart, 7 December 2005

perpendicular greyship with even symmetry -- new back slope,
front end from a spacefiller: Hartmut Holzwart, 5 December 2005

greyships suggested by Gabriel Nivasch, with stripes offset by one
down the middle: Hartmut Holzwart, 7 December 2005

sample greyship-based puffer: Hartmut Holzwart, 2 Dec 2005

two even-symmetry perpendicular greyships chained together, with
small tagalongs at back end: Hartmut Holzwart, 5 December 2005

Hybrid greyships (perpendicular and parallel stripes)

2005-12-16T09:10:00.000-08:00

hybrid 2c/4 greyship: Hartmut Holzwart, 16 November 2005

Another recent new idea in the greyship line is the combination of perpendicular and parallel direction of travel ("with-the-grain" and "against-the-grain" ships) into the same greyship, with various interfaces between the striped regions. These, like previous greyships, can have arbitrarily large grey regions -- though it's somewhat trickier to change the size in some of these cases, since the phases of several edge and interface terminations must be synchronized.

alternate hybrid 2c/4 greyship: Hartmut Holzwart, 16 November 2005

hybrid greyship: Hartmut Holzwart, 18 November 2005

triangular hybrid greyship: Hartmut Holzwart, 23 Nov 2005

greyship showing new components: Hartmut Holzwart, 25 Nov 2005

hybrid greyship with a crooked internal boundary
Hartmut Holzwart, 8 December 2005

variation of the base template: sample asymmetric hybrid greyship
Hartmut Holzwart, 18 November 2005

symmetric hybrid greyship: Hartmut Holzwart, 18 November 2005

Object Miscellany

2005-12-11T13:12:00.000-08:00

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.

Extensible spaceships

2005-12-10T14:48:00.000-08:00

long and short c/3 ships with central p15/5 wick
Hartmut Holzwart, 7 December 2005

Over the past few months, Hartmut Holzwart has constructed a series of spaceships with a variety of shapes, periods, and velocities. The majority have been "greyships" of different types -- but here is a random sampling of ships that don't fit neatly into that category:

extensible thin orthogonal 2c/4 spaceship
Hartmut Holzwart, 16 November 2005

extensible p3 spaceship: a p22 wick stabilized by c/3 ships
Hartmut Holzwart, 14 November 2005

pure p12 glide symmetric tag, attached to a two-section
p2 front end: Hartmut Holzwart, 28 Oct 2005

long and short c/3 ships w/ central p14 wick, based on a ship from
Jason Summers' raw c/3 collection: Hartmut Holzwart, 14 Nov 2005

asymmetrical c/3 greyship: Hartmut Holzwart, 11 November 2005

New P7 sparker

2005-11-26T16:09:00.000-08:00

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.

Adjustable Clean c/4 Glider Rake

2005-10-27T05:46:00.000-07:00

Some recently-discovered c/4 diagonal spaceships include accessible sparks, which can be used to make alterations to other active or stable patterns in passing. Recent discoveries include alterations that reflect gliders 180 degrees, or convert a single glider into multiple gliders -- along with a c/4 wickstretcher with a wick that can be ignited by gliders, where the resulting fuse can be timed to burn out without harming the wickstretcher engine.

David Bell has used these results to complete an adjustable clean c/4 rake, with periods of the form 4508+32N. Bell's description follows:

The rake has an engine convoy at the front, two convoys forming lines behind that, and a V-shaped convoy at the back. The recipe to create the next rake in the series is:

Move the top line convoy orthogonally right by 6 cells. Move the left line convoy orthogonally down by 6 cells. Move the V-shaped convoy diagonally back by 6 cells.

This will increase the period by 32 generations.

The modifications can be be made in the opposite direction to form the earlier rakes in the series. Moving the convoys by 300 cells creates the first rake in the series, having the period 4508.

New Period 7 Oscillators

2005-10-21T12:24:00.000-07:00

Scot Ellison has found some new Billiard-Table type Period 7 Oscillators.

New Oscillators

2005-10-21T11:21:00.000-07:00

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.

More new c/4 Diagonal Spaceships

2005-10-06T12:38:00.000-07:00

Harmut Holzwart has found a few new ^c/₄ Diagonal Spaceships.

Based on them, Nicolay Beluchenko then came up with another set of such spaceships by combining them with parts of other ships found earlier.

Application Announcement

2005-10-06T09:17:00.000-07:00

Tomas Rokicki has announced the release of a new version of Golly, the cross platform Game of Life program written by him and Andrew Trevorrow. From his announcement:

The important changes:

Saves patterns (RLE or macrocell formats).
Displays comments in pattern files.
Windows app can read gzipped pattern files.
Simple cell selection and editing.
Scrolling via hand cursor.
New tool bar buttons.
Numerous bug fixes and interface improvements.

The distribution now includes a pattern collection (still under development). Many of the current patterns show off Golly's hashing capabilities.

More new c/4 Diagonal Spaceships

2005-09-19T14:15:00.000-07:00

Here's another batch of new ^c/₄ Diagonal Spaceships that Nicolay Beluchenko has found.

Harmut Holzwart has extended a few of these new spaceships by adding some tagalongs for which there was previously no spaceship for attachment.

c/6 Diagonal Spaceship

2005-09-17T21:57:00.000-07:00

Nicolay Beluchenko has found the first known ^c/₆ Diagonal Spaceship.

(A list of known spaceship speeds)

Grow-By-One Pattern

2005-09-10T12:18:00.000-07:00

In his continuing quest for Diagonal Spaceships, Nicolay Beluchenko has also found what is currently the smallest known "Grow-By-One" pattern. This type of pattern is one whose population growth rate is exactly linear, without any fluctuations, adding a single bit every generation. Shown here is a slight improvement by David Bell, which starts a generation earlier than Beluchenko's orginal pattern, with a population of 44 at generation 0. (The purpose of the Lightweight Spaceship is to smooth out the fluctuations in the paired wickstretcher's population.)

The second pattern shown here is a version which is also a single object (starting with a population of 53).

New longer period oscillators

2005-09-08T13:04:00.000-07:00

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.

More new c/4 Diagonal Spaceships

2005-09-07T15:00:00.000-07:00

Nicolay Beluchenko has found another batch of new ^c/₄ Diagonal Spaceships. As before, these are all presented in no particular order.

Lineship Update

2005-09-06T10:27:00.000-07:00

On June 24th, David Bell produced an optimized version of Jason Summers' original lineship (shown in reduced scale at right -- click the thumbnail for the RLE, or here for a full picture). There have been several further developments along these lines.

Dave Greene used some of David Bell's new compact Cordership technology to produce a modified tail section for the revised lineship which repeats at p768 instead of at p96.

[The thumbnail at right shows only the modified tail section -- click here for a picture of the full pattern.]

David Bell followed this with a redesigned diagonal c/12 period 96 lineship. In this variant, the creation of the line at the front is done in pieces which are then welded together to form the line, using the repair techniques described in the "Cutting and Repairing Diagonal Lines" posting. The back end has also been reduced, since a sideways rake is not needed to ignite the line.

Again, only the smaller back end is shown in the thumbnail; a full-sized image is here.

The Cordership at the tail end of the adjustable-period lineship shown at right (full-sized image here) is responsible for igniting the stabilized end of line whenever it gets near to it. Nicolay Beluchenko points out that this Cordership could be adjusted by moving the trailing Cordership by multiples of 22 cells diagonally, rather than 88, if the front of the line were constructed in length-22 segments as well (but this would make the front of the ship much larger).

Greyship Update

2005-09-06T09:12:00.000-07:00

Hartmut Holzwart has constructed several new 2c/4 greyships (spaceships consisting primarily of alternating lines of ON and OFF cells -- see this previous post.) Here are two versions of a 2c/4 perpendicular greyship, in which the direction of travel is perpendicular to the alternating stripes, instead of parallel to them:

It's possible to shorten an arm of one of the above ships to get a triangle, as shown at right. Some further incomplete perpendicular-greyship results can be found here. Another triangle that uses some of these connections is shown at the far right.

Other greyship speeds are also possible. Here is a parallel greyship that travels at c/3 instead of c/2:

Bobsled Run Update

2005-09-06T09:01:00.000-07:00

On July 2, David Bell noticed that tub-with-tails are larger than needed to form switch-engine lanes (see the bobsled-run posting on 24 June 2005). Several smaller still lifes with tub-shaped protrusions can provide the same catalysis; boats, barges, long boats, long barges, etc. can all be used. At right is a revised switch-engine 'bobsled run' using boats as catalysts.

Long barges can be used as a common boundary between two adjacent lanes without any possible interference. Barges are sufficient if traffic in adjacent lanes is in opposite directions, or if the timing of traffic in two parallel lanes can be controlled to avoid mirror-image switch-engine phases. At right is a p3450 'swimmer' -- a switch engine doing laps in a lane made of boats:

More new c/4 Diagonal Spaceships

2005-08-21T16:29:00.000-07:00

Nicolay Beluchenko has found a host of new ^c/₄ Diagonal Spaceships. The smallest has only a population of 40 bits. Many of these are related by being made up of simpler subparts, having extensible sections, or by adding tagalongs to previously known spaceships. Except for the sample shown at right, these are all presented in no particular order.

New long period oscillators

2005-08-19T15:56:00.000-07:00

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.

Update: 2005-08-20

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.

Anteater Spaceships

2005-08-17T12:46:00.000-07:00

Around the end of July, Nicolay Beluchenko and Hartmut Holzwart produced a series of "anteater" spaceship patterns which could provide a moving c/4 diagonal termination point for an oblique wave of "ants". "Ants" wicks are unusually versatile, in that each eight-bit "ant" can follow directly behind the previous ant, or it can be offset by either one or two cells.

In the patterns that follow, each ant must be offset one cell from the previous one. With this configuration, each individual ant is a P1 pattern that travels due south at the speed of light, but the wave of ants as a whole can also be interpreted as a P4 pattern traveling northwest at c/4, thus matching the speed and direction of the c/4 terminal pattern.

The waves of ants should be assumed to extend to infinity (so don't run these spaceships for too many ticks -- they tend to crash when they run out of ants.) The construction of a matching antstretcher for these anteaters is currently an open problem.

Left: c/4 diagonal anteater: Nicolay Beluchenko, 29 July 2005
Right: c/4 double anteater

Left: c/4 anteater-related spaceships
Right: anteater-related double puffer based on Hartmut Holzwart's 29-bit spaceship (B29)

Left: c/4 anteater connected to puffer: Nicolay Beluchenko, 29 July 2005
Right: central glide-symmetric anteater element used as a tagalong: Nicolay Beluchenko, 30 July 2005

Left: alternate anteaters connected to sparking ships using glide-reflecting tagalong elements: Nicolay Beluchenko, 30 July 2005
Right: small anteater based on c/4 domino-spark ship: Hartmut Holzwart, 4 August 2005

New Sawtooth Patterns

2005-08-10T00:40:00.000-07:00

David Bell has constructed two new smaller sawtooth patterns. The first one undercut the size of the previous smallest known sawtooth by 6 cells.

To improve on this new record, Bell constructed a 4-engine Cordership with a minimum population of 134, compared with the 3-engine Cordership's minimum population of 149:

There is at least one other variant with a larger population, but which still beats the 3-engine Cordership. This has a minimum population of 136:

The problem with the 3-engine Cordership is that the 2-engine "wing" component swings wildly in population from small to large, and in the 3-engine Cordership the two (overlapping) wing components are locked together in a non-optimal relative phase, so that whenever one half has a small population, the other half has a large population.

By adding another switch engine in the middle to create two independent wing components, the relative phases can be adjusted in an optimal manner to reduce the population, even taking the extra switch engine into account.

Note: these new Corderships have a smaller minimum population, but the 3-engine Cordership still has a smaller average population. The average population of the 3-engine Cordership is 193.125, whereas the average population of the 134-cell-minimum Cordership is 217.854.

David Bell constructed a sawtooth with a minimum repeating population of 262 based on the 136-cell-minimum Cordership:

Bell has also created a revised moving-sawtooth pattern using the small c/3 period 27 rakes discovered since they were constructed. Further optimization is probably still possible.

The pattern works in the same way as Bell's previous moving sawtooths, by using the output of c/3 rakes to ignite the blinkers from a c/2 blinker puffer, with the number of blinkers to be consumed growing on each cycle.

Another possible sawtooth design using 'lineship' technology, which Bell has not been able to complete as yet, is presented here.

New c/4 Diagonal Tubstretcher

2005-08-05T16:35:00.000-07:00

Nicolay Beluchenko has noticed that a previously known spaceship can be converted into a small Tubstretcher. As shown at left, the four blue bits convert the ship into the smallest known puffer of any variety.

This puffer can be combined with a Tub burning fuse, found by Harmut Holzwart, to create spaceships of any length. The smallest, at 74 bits, is shown here. (The Tub fuse is hilighted in blue.)

New c/4 Diagonal Spaceships

2005-08-03T19:21:00.000-07:00

Nicolay Beluchenko has found some new ^c/₄ diagonal spaceships. He also noticed that some previously known spaceships can be reworked and combined to yield a series of extensible ships.

Finally, he also discovered a 150 Bit Period 28 diagonal puffer which creates a Tub and a Beehive every cycle.

Update: 2005-Aug-06

A few more diagonal spaceships found by Nicolay Beluchenko.

Website Announcement

2005-07-28T22:27:00.000-07:00

Nick Gotts has put together a new weblog based site, Natural History of Conway's Game of Life, in which he will be presenting some of the results of his investigations into simple starting pattern. The first posting deals with "Patterns with Eventful Histories", patterns which can interact in non-periodic ways and which have been followed for up to 2^36 (over 137 billion) generations.

Cutting and Repairing Diagonal Lines

2005-07-19T17:57:00.000-07:00

David Bell recently asked if it was possible to detect a long diagonal line without destroying it, and if it was possible to send a signal through a diagonal line. The answers to both questions hinge on the ability to cleanly break and then repair the line. The glider constructions for such actions, while not optimum, have been found.

Bell showed that it was possible to repair a two cell break with a Loaf predecessor, and then Karel Suhajda and H.Koenig were able to find a 3 Glider construction of a Loaf that worked perfectly. Mark Niemiec also posted some similar contructions by David Buckingham which can also be used to close up a line.

A way to break a line was then posted by H.Koenig. Two gliders cause the diagonal line to become a pair of clean burning fuses, and then a pair of reactions consisting of two Gliders and a Lightweight Spacehip (LWSS) (previously discovered by Jason Summers) create the domino sparks which halts the burning fuses. This results in a twenty bit gap where the diagonal line used to be. This construction is not complete, however, because two of the gliders would interfere with each other if they came from infinity. Also, the gap created is much larger than it could be.

David Greene then showed how to use a pair of reactions using a Pond, a LWSS and three Gliders to lengthen a diagonal line by 4 bits can be used to close a gap by 8 bits. So a gap of 8n+2, with 10 bits as the minimum, becomes the more useful reactions.

Bell then showed how a Glider collision with a stable object could be used to cleanly cut a line. The added cost in Gliders used to construct and place the stable object (in this example, a Block and a Loaf) is outweighed by the flexibility in timing and and in the placement of the reaction which ends the burning of the fuse. Greene also showed a a way to place and ignite a Tub to make a 10 cell gap. But the 9 cell gap can be expanded to 10 by simply delaying one of the fuse stablizers by one generation and shifting it slightly. (Any reaction can be made arbitrarily wide in the same fashion.)

All of these reactions require a glider to be placed as close as possible to the diagonal line. Bell showed an example of a reaction of 2 LWSSs and a Glider which can place the Gliders needed in the previous reactions, as well as one that can place a Loaf near the line for the 9 bit gap.

There are some issues remaining. It would be useful if all the Gliders and LWSSs in the gap cloing reactions camefrom the same side of the diagonal line, as that would make timing issues a lot easier. Also a demonstration of a reaction that can detect the presence of the line needs to be made. Finally, for use in other patterns, the reactions which cut or repair a diagonal line that are triggered by a single Glider (or a set of Herschel Track components) needs to be actually built.

New Record Methuselah

2005-07-14T22:54:00.000-07:00

Andrzej Okrasinski has found a new methuselah record holder, a 15 bit intial pattern with a final population of 1623 after 29053 generations. David Bell quickly found a 13 cell predecessor, bringing the record to 29055.

Some of the more unusual objects which make an appearance but which aren't in the final census include a Lightweight Spaceship [9P4H2V0.1], a Fishook Eater [7.3], a Long Barge [8.9], a Big S [14.492], a Bi-Pond [16.2630] and an unnamed 13 bit object [13.182].

Size	Discoverer	Gens	Final Pop.	Final Pattern, Census
13	[David Bell]	29055	1623	102(4.1), 2(4.2), 15(5.1), 6(6.2), 57(6.4), 1(7.2), 18(7.4), 5(8.7), 2(12.41), 135(3P2.1), 1(6P2.1), 1(6P2.2), 28(5P4H1V1.1)
15	[Andrzej Okrasinski]	29053

Note: Not all of the paths of escaped gliders are shown.

c/2 and 2c/4 "greyships"

2005-07-09T09:39:00.000-07:00

Hartmut Holzwart and Jason Summers have been investigating possible shapes for 2c/4 "greyships" that include an extensible striped region of half-ON, half-OFF cells. Triangles, diamonds, and other shapes are possible.

This technology can be extended to produce more complex shapes with a variety of slopes. Some components also exist for a ship traveling perpendicular to the "grain" of the stripes, instead of parallel, but currently not enough to produce a complete ship. See this blog for details.

Switch-engine 'bobsled run'

2005-06-24T13:56:00.000-07:00

David Bell has discovered an unusual catalytic reaction involving a tub-with-tail and a switch engine. Tub-with-tails can be arranged in a double line to produce an extensible diagonal switch-engine conduit.

The reaction is unusual for several reasons:
1) Tub-with-tails don't usually catalyze alone -- a tub-with-tail is more commonly paired with a block or other still life, which makes it capable of 'eating' a glider or similar active pattern.
2) The catalysis used in the bobsled run is a reaction that has not been used in previously known Herschel/B-heptomino/R-pentomino/pi conduits.
3) While Herschels do make an appearance in this conduit, they don't play an important role -- in fact, they must be suppressed in order for the reaction to be repeatable.

One possible open problem would be to construct converters to attach to each end of the 'bobsled run', one taking a Herschel (or glider, spaceship, etc.) as input, and one producing one of these standard signals as an output.

New Period 24 Oscillator

2005-06-19T12:09:00.000-07:00

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.

New Compact Corderships

2005-06-18T19:19:00.000-07:00

David Bell has constructed a new, compact 5-engine Cordership that contains a releasable sideways glider, and has compiled a series of related results. The pattern at the far right shows a number of ways for the Cordership's northeast edge blocks to be suppressed, allowing the sideways glider to escape.

These new results build on other new Cordership constructions recently -- in particular, a small 3-engine Cordership discovered by Paul Tooke (with the help of Paul Callahan's handy 'gencols' utility) on January 12 of last year. David Bell discovered that it can turn an LWSS 90 degrees, as shown here.

Bell has also produced a series of related Cordership-rake patterns: A Cordership-based glider-to-backward-LWSS reaction
A 'beehive-puller' Cordership
A p96 forward glider rake
A new smaller p384 'Freeze-Tag' spaceship
A reaction converting two forward gliders to an HWSS
p192 backward HWSS rake
A p96 backward HWSS rake
A p768 backward HWSS rake
A p96 forward LWSS rake
A p96 forward MWSS rake
An alternate p96 forward MWSS rake
A p768 forward LWSS rake
A high-period Cordership-based feedback loop
A wide thin p96 backward rake
A p288 'litterbug' spaceship
A p96 backward LWSS rake
An alternate p96 backward LWSS rake
A p96 backward MWSS rake based on a loaf puffer
A backward LWSS puffer based on an eater/tub-with-tail puffer

Related to this last pattern, he notes that a line of tub-with-tails "can support one side of a switch engine without being modified. Two diagonal lines of them can support one or more switch engines at the ends, and one line can support a 3-engine wing component."

Update: 24 June 2005 2:20p

A diagonal c/12 p96 glide-symmetric double backward rake
A p96 three-stage tail producing a double-backward-rake spaceship
A p96 block-staircase puffer tail for the double backward rake
A p96 diagonal c/12 period 96 sideways glider-inserter rake
... And an updated version of Jason Summers' c/12 p96 diagonal lineship: see the new posting on this subject.

Extensible Wickstretcher-like Spaceship

2005-06-04T22:34:00.000-07:00

Hartmut Holzwart has found a Lightweight Spaceship convoy which consists of a Period 4 wickstretcher head, a Period 19 wick and a Period 4 fuse. Shown is the simplest version with only one copy of the wick and one with two copies of it. (Note that there are no known Period 19 oscillators, so finding stable ends for this wick may take a while, but it could be the foundation for such an oscillator.)

New 3c/6 fuses

2005-05-26T07:15:00.000-07:00

Hartmut Holzwart has discovered two new 3c/6 fuses. He comments that there appear to be many more of these awaiting discovery.

Extensible Wickstretchers and HALFMAX

2005-05-09T07:22:00.000-07:00

Hartmut Holzwart and Jason Summers have successfully tamed a extended family of wickstretchers, beginning with the one at right -- a p4 wickstretcher with two central lines and a p8 tail, constructed by Holzwart on 22 April 2005.

This was followed by several related results. To the right is an alternate form of the wickstretcher, created by Holzwart, with the right side replaced by a pure p4 tail section. On the far right is another phase of the above wickstretcher, with the tail replaced by a p6 fencepost constructed by Karel Suhajda on the same day.

Starting from a related p80 puffer ship, Jason Summers produced a new smaller p80 puffer -- 8 cells wider than the known p4 ships in Paul Tooke's collection, but about 20 cells shorter. As with the old ships, there's also an alternate, much less prolific p80 orbit -- as well as a p20 "bread-and-honey" orbit (loaves are created, then converted to beehives a few generations later.)

Holzwart also produced a four-central-line wickstretcher, and later a smaller version of the original minimal wickstretcher as well (with no central lines in the wick) -- both completed by a p4 c/2 tail rather than a fencepost.

Based on a "double fencepost" pattern of Holzwart's (not shown) Summers found a way to provide an independent fencepost for each of the two active edges of a wick -- allowing any number of stable lines to be added in the middle (the example at right shows a wick with a 14-line "sandwich".) Other possible modifications include changing the phase of the two edges relative to each other, as in the asymmetrical wickstretcher and fencepost at the far right -- or simply shifting one section of the wick by two cells relative to an adjacent section, as shown by the "spacers" (four-line-thick oblongs) toward the center of the pattern below.

Finally, Summers succeeded in using the new wick and fencepost technology to produce this semi-spacefilling pattern, which expands in three directions at half the speed of light -- producing a triangular region that grows to fill half the plane. [Previous spacefillers have all been diamond-shaped, expanding at c/2 in all four cardinal directions to fill the entire plane.]

Update: 9 May 2005 07:22

On May 6, Hartmut Holzwart produced smaller versions of both the original basic wickstretcher and of Jason Summers' HALFMAX pattern (far right).

Update: 26 May 2005 06:45

On May 21, Jason Summers produced sample patterns that allow the construction of wickstretchers with any number of central lines, by adding the appropriate number of four-line "spacers" to one of the four extensible base patterns. He observed: "For each number of lines, there are eight possible wicks, made by changing the relative position and phase of the two sides of the wick (except for zero lines, where there are only two)."

Wickstretchers with 3, 4, and 5 central lines are shown here. On the far right is Summers' latest HALFMAX optimization, backed up by one generation to reduce the population to 903 cells.

New Transcendental Patterns

2005-05-05T19:49:00.000-07:00

Dean Hickerson has presented a pair of new transcendental patterns he's created. These consist of puffers and guns, which grow in what appear to be unpredictable ways.

The first is a "Ruler" generator:

This produces groups of LWSSs headed west, with gaps of fixed size between them. The lengths of the groups form the 'ruler' sequence, 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 ... (Sloane's A001511). The first group of length n is emitted about generation 96*2^n. The pattern uses a Corderman eater puffer found by Paul Tooke (Jan 2004), a p48 glider gun by Noam Elkies (Jun 1997), a p8 glider reflector by Noam Elkies (Sep 1998), and a p24 LWSS puffer (source unknown).

Shown are the starting pattern at Gen 0 and later at Gen 850, after 1-2-1-3-1 as been emitted. (Note: They've been rotated 90° to better fit the page.)

The second object is "Jagged Lines":

Jagged lines of gliders, formed by a drifting collision of two Lightweight Spaceships (LWSS) streams, crash to form an approximately vertical jagged line of pairs of blocks. I don't know if the line stays within a bounded distance of the center line, or extends infinitely far to the left, or to the right, or both.

Shown are the starting pattern at Gen 0 and later at Gen 850, shortly after the second block pair has been created. (Note: They've been rotated 90° to better fit the page.) Hickerson also simulated the placement of the block pairs and presented a plot showing the first 11,426,769 Twin Blocks produced by Gen 4,113,636,213. (The horizontal:vertical scale is 488:1 to emphasize the shifting locations.) The dimensions of the jagged line of Twin Blocks are cells 140,480 wide with a tail 685,605,960 cells long.

Hickerson says that he doesn't think it's a random walk:

There are some large portions of it that are almost symmetric across horizontal lines. Also, the transitions between successive minimal and maximal x-coordinates are rather brief. I.e. it spends a long time far to the left of the center line, then moves quickly to a point far to the right, spends a long time there, etc. I think there's an approximate scale-invariance; if you expand the picture by appropriate factors horizontally and vertically it'll look almost the same. But I don't understand it well enough to say what those factors are.

Gabriel Nivasch points out that if the Pre-Block (shown in red), which is responsible for the asymmetry of the pattern, is removed, then the pattern generated is one generated by a growing sequence which starts out with zero and adds four new items at the end while sequentially reading the digits already laid out. The additions are

0 -> 1 0 1 0
1 -> 1 0 1 1

which gives the initial sequence of "0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1".

New Period 5 Oscillators

2005-05-05T17:55:00.000-07:00

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)

Dean Hickerson has found the three missing sequences. The three new Period 5 Oscillators are shown to the right.

New Period 6 Oscillator

2005-05-05T12:42:00.000-07:00

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.

New Wick and Fuse

2005-04-26T03:05:00.000-07:00

Hartmut Holzwart has discovered a new p4 wick that is also a p48 fuse:

Block Array Constructions

2005-04-20T13:01:00.000-07:00

Jason Summers has found a way to take a previously known method of constructing 4 sets of Twin Blocks from Pi Heptominos, and attach another pair of Twin Blocks at each end, for a construction of a 2 x 8 array of Blocks.

He's also found a way to extend any 2 x n array of Blocks.

In both cases, the preliminary construction for some of the target objects needed are not shown.

Period 5 Oscillator Construction

2005-04-09T18:47:00.000-07:00

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

New Period 5 Oscillator

2005-04-02T08:43:00.000-08:00

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

Dave Greene: Added background information.

Pi Waves and Pi Tracks

2005-03-19T13:25:00.000-08:00

Background

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.

Recent News

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.

New Period 7 Oscillators

2005-03-11T17:28:00.000-08:00

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).

New Period 4 Oscillator Variants

2005-03-09T14:17:00.000-08:00

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.

New Methuselah Records

2005-02-21T11:26:00.000-08:00

Tomas Rokicki has announced some of the results of a survey for methuselahs. The table below shows the record holding patterns for given bit sizes. More information can be found at his webpage. Other information about methuselahs, can be found at Dean Hickerson's website. Andrzej Okrasinski also announced his finding of the current record holding pattern.

Size	Name	Gens	Final Pop.	Final Pattern, Census & Discoverer
	r Pentomino	1103	128	8(4.1), 1(5.1), 1(6.2), 4(6.4), 1(7.4), 4(3P2.1), 6(5P4H1V1.1)
5		1105
6		1108
7	Acorn [Charles Corderman]	5206	633	34(4.1), 8(5.1), 3(6.2), 30(6.4), 2(6.5), 5(7.4), 2(8.7), 1(8.8), 41(3P2.1), 13(5P4H1V1.1)
8	[Tomas Rokicki]	7467	952	51(4.1), 2(4.2), 11(5.1), 4(6.2), 35(6.4), 16(7.4), 2(8.7), 1(14.475), 61(3P2.1), 1(6P2.1), 24(5P4H1V1.1)
	Rabbits [Andrew Trevorrow]	17331	1749	109(4.1), 4(4.2), 18(5.1), 7(6.2), 65(6.4), 18(7.4), 3(8.7), 136(3P2.1), 2(6P2.1), 40(5P4H1V1.1)
9	[Paul Callahan]	17410
10	[Tomas Rokicki]	17423
11	[Tomas Rokicki]	17465
12-18	[Tomas Rokicki]	23334	2898	207(4.1), 7(4.2), 23(5.1), 12(6.2), 115(6.4), 2(7.2), 32(7.4), 4(8.7), 171(3P2.1), 1(6P2.1), 2(6P2.2), 70(5P4H1V1.1), 1(9P4H2V0.1)
19	[Andrzej Okrasinski]	28786	3091	196(4.1), 6(4.2), 31(5.1), 9(6.2), 143(6.4), 3(6.5), 34(7.4), 6(8.7), 2(12.41), 1(14.475), 213(3P2.1), 47(5P4H1V1.1)

Note: Not all of the paths of escaped gliders are shown.

Stable 2c/3 signal receiver

2005-02-07T19:54:00.000-08:00

On 23 January 2005, Noam Elkies found a collision of 8 gliders with an LWSS that could repeatably create an input signal travelling at two thirds of the speed of light (2c/3) in the "transmitter" end of Dean Hickerson's stable diagonal 2c/3 "signal track" from 18 March 1997.

The new signal-inserting collision is shown on the left edge of the pattern below; the rest of the pattern is a stable 2c/3 signal receiver constructed by Dave Greene on February 6.

One remaining open problem is the construction of a similar stable pattern to produce the "transmitter" collision from a single input signal.

New Period 6 Oscillators

2005-01-30T11:02:00.000-08:00

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

71 Glider Collisions

2005-01-29T21:32:00.000-08:00

Jason Summers has made available two labeled reference tables of the results of the 71 possible glider collisions:

Glider collisions sorted by input path and direction:

Glider collisions sorted by output:

New Period 4 Oscillators

2005-01-23T21:24:00.000-08:00

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.

Lightspeed Signals Update

2005-01-10T11:31:00.000-08:00

Gabriel Nivasch has updated his webpage on lightspeed signals. These are structures and objects in which a signal propagates faster than the empty space limit of ^c/₂.

New Diagonal c/5 Spaceship

2005-01-09T15:33:00.000-08:00

Jason Summers has found a new diagonal ^c/₅ spaceship. With a population 86 bits in its smallest phase, it becomes the smallest known example for this speed and direction. It is less than one third the size of the next largest example, which has a population 295 bits.

New Blinker Puffer

2005-01-07T13:50:00.000-08:00

Harmut Holzwart has found a smaller version (on the left) of a ^c/₂ Period 8 Blinker pair puffer first reported by Chris Lu in August of 2002 (on the right).

New c/5 Spaceships

2005-01-04T17:25:00.000-08:00

Paul Tooke has found some new ^c/₅ spaceships.

New 17c/45 Spaceship: The Caterpillar

2004-12-31T17:27:00.000-08:00

Gabriel Nivasch has announced the construction of a spaceship which travels at the speed of ^17c/₄₅. It is based on a "Pi Crawler" reaction, where a Pi Heptomino moves up a string of Blinkers leaving the string undisturbed. This means that multiple Pi Crawlers can use the same string of blinkers, and if multiple tracks are properly positioned, they can interact with each other to act as glider puffers or rakes. These gliders can then be used to create ^c/₂ Orthogonal Spaceships which in turn can run ahead of the Pi Crawlers and lay down the necessary Blinker tracks. For more information on how all this works, see Nivasch's earlier report on the Caterpillar components.

The spaceship itself has a period of 270, and is huge. The dimensions are 4195 cells wide by 330,721 cells deep. Starting with a population of 11,967,399, ranging from 11880063 (gen 113) to 12019156 (gen 210). Nivasch reports that he wrote a program which fitted together 51 different .rle subpatterns that make up the Caterpillar into the final, working pattern. This is the first known spaceship which travels at this speed (0.378c), and the largest object ever actually constructed to date.

Jason Summers has made available a zipped 7.1Meg copy of the .rle file, It has been reported that this .rle file will successfully load and execute with the Life32 program by Johan Bontes, or with Hashlife by Tomas Rokicki. With Life32, just wait a bit for it to load, and be sure to zoom down to a reasonable subsection of the entire pattern, otherwise each generation will take an inordinate amount of time to display. Properly zoomed down, it only takes about a second per generation.

Update: 2005-Jan-03

Gabriel Nivasch has updated his web page to provide a 1:40 scale illustration of the entire object.

New Oscillators

2004-12-30T21:53:00.000-08:00

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

New 2c/5 Spaceship

2004-12-22T11:54:00.000-08:00

Harmut Holzwart has found a new ^2c/₅ spaceship. The red shaded area can be repeated. The lower pattern shows the Order 3 version.

Update: 2004-Dec-30

Turns out that this is not a true spaceship, as there is an unsuppressed spark on the trailing edge, that interferes with the spaceship's operation.

Lightbulb Construction

2004-12-18T09:50:00.000-08:00

Mark Niemiec has built some new lightbulb constructions. They're based upon a naturally occurring Lightbulb found by Andrzej Okrasinski, from a simple predecessor found by Karel Suhajda with some refinements by H.Koenig and Dave Greene. The first shows 11 gliders which form a symmetric version using a House as the inductor. The second shows how a 10-bit inductor can be built instead, and the final line shows how that inductor can be converted to a 7-bit Bookend, using a total of 16 Gliders.

As Niemiec points out, there are no known ways to convert any of these inductors to a snake, allowing not only the construction of the minimal form of the Lightbulb, shown above left, but also many other oscillators and objects

New 2c/4 and Diagonal c/4 Spaceships

2004-12-17T20:40:00.000-08:00

In the past few months, Harmut Holzwart has found a number of new 2c/4 and diagonal c/4 spaceships.