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2011 January 10

Extensible Spaceships
First c/5 greyship, and a new c/3

Extensible edge for a c/5 greyship: Hartmut Holzwart, 28 Feb 2010
The previously known base c/5 ship is shown at the left
In February and March of 2010, Hartmut Holzwart found the necessary repeatable components to allow the construction of a striped greyship with a new speed -- one-fifth of the speed of light, with the direction of travel parallel to the stripes in the adjustable-sized center region.

Complete c/5 greyship: Hartmut Holzwart, 20 Mar 2010
By combining the ascending and descending components,
arbitrarily large c/5 spaceships can be created.
Finding an element for the descending back slope of the c/5 ship was difficult, as can be seen by the length of the supporting structure; a spider finally provided a compatible supporting spark.

c/3 greyship: Hartmut Holzwart, 12 Apr 2010
The new component along the northeast edge allows for a steeper
c/3 termination of the striped area than was previously possible.
The next month, Holzwart also found a new termination for c/3 greyships, allowing a different angle of descent at the back of the ship.

2006 May 12

Extensible Spaceships
Diagonal Greyships

extensible diagonal c/4 1/3-ON parallelogram/trapezoid greyships
Nicolay Beluchenko, 13 April 2006
Nicolay Beluchenko created some sample diagonal greyships in various shapes, with a "grey" level of 1/3 ON cells (instead of the usual 1/2 for orthogonal greyships with 'stripes' or 'chicken-wire' agars.) Since these new "ships" are really an independent series of tubstretchers and tubeaters packed together as closely as possible, it's obviously possible to move the pieces farther apart from each other to produce lower fractions of ON to OFF cells.

It may also be possible to construct extensible multi-tubstretcher and multi-tubeater spaceships that support this agar -- where each stretcher or eater is connected directly to the next one, and can't be separated -- but this has not been accomplished as yet. Multistretchers and multieaters with wider spacings have been previously posted, however.

extensible diagonal c/4 1/3-ON rhombic greyship
Nicolay Beluchenko, 13 April 2006
Tubstretcher-based patterns composed of more than 1/3 ON cells are not possible. Thus, to produce a diagonal greyship that maintains a 1/2-ON agar, it would be necessary to devise diagonally moving extensible patterns that stabilize the edges of some other type of agar -- either an oscillating agar, or an extensible series of waves (moving wicks), or perhaps an orthogonally symmetric stable pattern -- most likely the 'stripes' agar.

However, since the stripes are not diagonally symmetrical, each of the edges would need a different type of support. Whether such a construction is possible is currently an open question. The main problem is that diagonal spaceships could not repeat at period 4, because each stripe is two cells away from the previous one -- so p8 spaceships would be needed.

Unfortunately p8 is not really within reach of currently available Life search programs (mainly David Bell's 'lifesrc' and Jason Summers' ' WinLifeSearch' port). Some fairly large leaps in efficiency and/or CPU speed would be needed to make this a likely goal. [Readers are, of course, invited to prove this statement wrong -- or to supply the necessary advances in search technology.]

2006 March 03

Extensible Spaceships
Greyships -- New Shapes and Speeds

Holiday-season tree-shaped greyship
Hartmut Holzwart, 5 January 2006

alternate Christmas-tree-shaped greyship
Hartmut Holzwart, 9 January 2006
Hartmut Holzwart has been continuing his work on greyships with a variety of shapes and speeds.

fixed-width greyship using a termination by Jason Summers
Hartmut Holzwart, 13 January 2006

prototype of 2c/5 greyship, with 'room for improvement'
Hartmut Holzwart, 27 January 2006

c/3 greyship with front slope of 0 [rectangular front]
Hartmut Holzwart, 1 February 2006

c/4 greyship, resizable in both dimensions
Hartmut Holzwart, 2 March 2006

Hartmut Holzwart's greyship blinker puffer without the greyship
Jason Summers, 23 December 2005

greyship puffers: p8 blinker puffer and p144 dirty puffer
Hartmut Holzwart, 22 December 2005

c/4 greyship -- somewhat limited flexibility in resizing
Hartmut Holzwart, 17 February 2006

c/4 greyship with fixed-width section connecting to back slope
Hartmut Holzwart, 2 March 2006

2005 December 10

Extensible spaceships


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

Continue reading "Extensible spaceships" More

2005 August 03

New c/4 Diagonal Spaceships

New Diagonal c/4 spaceships 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.

New Diagonal c/4 wave

P28 Diagonal Puffer Finally, he also discovered a 150 Bit Period 28 diagonal puffer which creates a Tub and a Beehive every cycle.

Update: 2005-Aug-06

Diagonal C4 Spaceships A few more diagonal spaceships found by Nicolay Beluchenko.

2005 June 24

Engineered Objects
Switch-engine 'bobsled run'

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.

Switch-engine 'bobsled run'  David Bell  20 June 2005

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.

2005 June 04

Extensible Wickstretcher-like Spaceship

description 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.)

2005 May 09

Wicks & Fuses
Extensible Wickstretchers and HALFMAX

Wickstretcher 1  Hartmut Holzwart  22 April 2005 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.

Wickstretcher 2  Hartmut Holzwart  22 April 2005 Wickstretcher 3  Hartmut Holzwart and Karel Suhajda  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.

smaller c/2 p80 puffer  Jason Summers  24 April 2005 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.)

Wickstretcher 4  Hartmut Holzwart  3 May 2005 Wickstretcher 5  Hartmut Holzwart  25 April 2005 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.

Wickstretcher 6  Hartmut Holzwart  3 May 2005 Wickstretcher 7  Hartmut Holzwart  4 May 2005 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.

Half-plane-filler (HALFMAX)  Jason Summers  4 May 2005
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

HALFMAX2  6 May 2005 minimal wickstretcher  6 May 2005 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

3-line wickstretcher  Jason Summers  21 May 2005 smaller 4-line wickstretcher  Jason Summers  21 May 2005 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)."

HALFMAX3  Jason Summers  15 May 2005 5-line wickstretcher  Jason Summers  21 May 2005 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.

2005 March 19

Pi Waves and Pi Tracks


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.