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2011 August 08

Engineered Objects
Painting with pulsars

As we've been busy recently, there have been no LifeNews postings for the last couple of months. Nevertheless, there have still been miraculous discoveries in Life that need reporting; this is one such example.

Pulsar-based display device

'Triller' from Nathaniel's forum has engineered an impressive construction: a fully functional display using pulsars to represent individual pixels. The display is continually refreshed at regular intervals, updating it with the data contained within several memory loops.

As he/she has included a comprehensive description of the mechanism, it would violate Occam's razor for me to describe it in great detail. However, there are some interesting features worth mentioning:

  • Triller has opted for period-30 technology, as opposed to the more modern option of Herschel tracks. This makes the device significantly more compact than its stable counterparts.
  • The image data is contained in data loops, similar to the Golly-ticker in Golly's pattern collection.
  • The sample image is the set of hexadecimal symbols, displayed in alternately ascending and descending order.

2011 March 26

Engineered Objects
Turing machine update

Paul Rendell has now completed his Universal Turing Machine, by adjoining two stack constructors to the bounded version of the pattern. The patterns are available here, including the c/2 orthogonal and c/5 diagonal variants of the pattern.

The new Turing machine emulator is period-23040, which makes it more HashLife-amenable than the previous UTM and TM emulators (p18960 and p11040, respectively). Additionally, the diagonal stacks run faster in Golly than the oblique analogues. The c/2 version outperforms the c/5 version, apparently, despite having a larger growth coefficient.

This is the first universal computer in Life to emulate a Turing machine in linear time (Chapman's URM takes exponential time; my UCC takes quadratic time), and therefore the most efficient to date.

2011 February 16

Engineered Objects

Something amazing has happened. Two completely unrelated recent discoveries from 2010 have been elegantly unified into a single pattern.

Paul Rendell's c/12 stack constructor.

First: a summary. Last month, LifeNews published an article detailing Paul Rendell's stack constructor, a pattern capable of extending the tape of his Turing machine without limit, thereby endowing his UTM with computation universality. The original version of his stack constructor comprises two orthogonal c/2 rakes, which stretch out an expanding wave of gliders, coalescing to form the tape.

Despite working as planned, Paul was somewhat unsatisfied with his stack constructor. Its population soon explodes due to the waves of gliders, an artefact of using two orthogonal rakes to build a diagonal structure. The natural solution would be to use a diagonal puffer to extend the stack; this is precisely what he has accomplished.

The second version of his stack constructor uses c/12 rakes to provide the influx of gliders necessary for stack construction. However, there is a catch. The tape has a spatial period of 90, so the temporal period of the Cordership fleet must be twelve times that -- or 1080. Corderships, on the other hand, have a temporal period of 96n, so the smallest multiple of the desired period is 4320. This means that four rakes are required to emulate the rakes. This is accomplished in a somewhat similar way to how gliders are interleaved in pseudo-period guns, but with rakes instead.

Additionally, because his rakes use a kickback reaction, the size of the rakes are increased by another factor of two. Here is the RLE file for the completed rake. The resulting stack constructor is truly immense, similar in population count to the Caterpillar, and the corresponding RLE file is 21.8 megabytes in size!

You may be wondering where the second piece of 2010 technology comes into the equation. Recall that four rakes are interleaved for each glider in the stack constructor, which is rather sub-optimal. Clearly, then, there are two options: redesign the tape to have an offset of (say) 96 cells, instead of 90; or forget c/12 technology completely.

Adam P. Goucher suggested the latter, advocating the use of the emerging field of c/5 diagonal technology. He modified Matthias' c/5 rakes to work at p450 instead, resulting in an immense glide-reflective rake, not much smaller than the c/12 pseudo-rakes! However, after several successive optimisations, and a sudden insight from Matthias, he managed to produce a substantially smaller rake:

Adam P. Goucher's p450 rake, based on a design by Matthias Merzenich.

Paul modified the rake yet again, to form a variant capable of inserting gliders using the kickback reaction. Instead of the naïve approach of using two rakes, he used the same engine to produce both incident gliders for the kickback rake. This cuts down on the population count by a factor of two.

The stack constructor based on the c/5 rake is almost five times smaller by population count than its c/12 counterpart (RLE file). What follows is a diagram of the constructor, similar to the previous one, giving an idea of the dimensions of this beast:

Paul Rendell's c/5 stack constructor.

2011 January 11

Engineered Objects
Swimming with Switch Engines

David Bell has assembled a Cordership-based puffer and period-256 swimmer factory to create a growing swimmer lane. A swimmer, by the way, is a switch engine stabilised by two tracks of boats. Period 256 is the lowest possible period for swimmers to follow each other; it is completely serendipitous that there is a reasonably small gun of this size.

David Bell's extensible swimmer channel

Almost instantaneously afterwards, he designed a new type of breeder based on a fuse. After a while, Dave Greene provided an appropriate fuse, enabling the construction of this gargantuan breeder. Again, this design utilises switch engines, and superficially resembles an earlier breeder by Dean Hickerson.

Specifically, the frontal puffer lays down a fuse, which is reburned at a slower rate to produce a wave of parallel switch engines, positioned such that they partially clean up the debris of adjacent switch engines. The overall principle is similar to the 'frozen MWSS rake' that appeared years ago on LifeNews, but adapted to form a breeder, as opposed to a rake. It is thus not a great leap of imagination to refer to this as a 'frozen breeder'.

Continue reading "Swimming with Switch Engines" More

2011 January 10

Engineered Objects
Turing machines

This is the fourth article in a projected series of twenty or so, covering the last couple of years of Life discoveries. After this profusion of old news, LifeNews will return to its former state of publishing recent discoveries. Or so we hope...

Approximately one decade after implementing his original Turing machine in GoL, Paul Rendell has built a universal version. Universal Turing machines are those capable of emulating any other Turing machine, depending only on the initial input on the tape.


A particularly small universal Turing machine (henceforth abbreviated to UTM) is the 7-state 4-symbol machine by Minsky. There even exists a UTM with only two states and three symbols, discovered by Stephen Wolfram. However, the initial 'program' must be infinite, so this is of relatively little practical importance. Indeed, Rendell decided that the program should be as compact and intuitive as possible, and fit within the limitation of his architecture.

Paul Rendell's UTM has 13 states and 8 symbols, fitting comfortably within the (16,8) limitation of his Life architecture. There are actually 16 logical states, but they can be compressed into 13 actual states, by allowing a particular state to serve two distinct, non-interfering purposes.

A more detailed description of Rendell's UTM can be found in Chapter 26 of Game of Life Cellular Automata.

Despite the machine being universal, the Life pattern, strictly speaking, is not. For a Turing machine to be universal, it must have access to an unlimited storage tape; otherwise, it is a weaker machine known as a linear-bounded automaton. There are two approaches to creating an unlimited storage tape in GoL. One is to write into empty space, as used in Adam P. Goucher's irrational number calculators (see previous post). Paul Rendell decided on a more impressive and ambitious approach: to build a puffer that extends the stacks, faster than they can be used by the Turing machine!

The stack constructor consists of a number of orthogonal rakes, travelling in two perpendicular directions, which incrementally extend the tapes via glider syntheses. The rakes insert the gliders into convoys using the standard kickback reaction.

One of 333 identical rakes in the stack constructor

Continue reading "Turing machines" More

2011 January 09

Engineered Objects
Phi and pi calculators

Overview of phi calculator
Blueprint for Adam P. Goucher's calculators -- the diagram for the
phi calculator is shown here, but the pi calculator is very similar.
Decimal output is displayed in the upper right corner.

In mid-February 2010, Adam P. Goucher announced the completion of a large Life pattern that could calculate the decimal digits of phi (the golden ratio): 1.61803398874989484820... This was followed a week later by a similar pattern that output the digits of pi. The pi calculator was the embodiment of a 40-year-old speculation by John Conway about the feasibility of a pi-printing pattern.

Macrocell file for phi calculator (copy and paste into Golly, or open the file from Golly's File menu)

Macrocell file for pi calculator

sample output from Adam P. Goucher's phi calculator
The first 16 digits displayed
by the pi calculator
sample output from Adam P. Goucher's phi calculator
The first 7 digits displayed
by Adam P. Goucher's phi calculator
A common feature of the two calculators is the printer attachment, which accepts input on eleven glider lanes (for digits 0 through 9 plus a decimal point) and produces readable output on a SW-NE diagonal, when the pattern is zoomed out sufficiently far (individual pixel-blocks in the digits are actually separated by 64 cells diagonally, so the output is easily readable at scales around 2^5:1, as shown.

Continue reading "Phi and pi calculators" More

2010 February 04

Engineered Objects
Prime numbers

The 'Primer' is a well-known Life pattern used to calculate prime numbers. The pattern expands in two directions, resembles a breeder, and emits a stream of spaceships representing prime numbers. The presence or absence of a spaceship at a particular generation indicates whether the number is prime or composite. It works by testing whether each integer is divisible by any smaller integer, apart from itself and 1. This is similar in principle to the Sieve of Eratosthenes.

Firstly, we present a new Primer by Jason Summers, which uses continual streams of spaceships to reflect the internal glider streams. Previous designs used static reflectors of periods 15 or 30. Jason's new Primer is substantially smaller than the previous prime number generators.

Jason Summers' new Prime number generator

In 2010, Jason engineered a Fermat Prime Calculator based on this new Primer and a Caber tosser he discovered. It is rigged up to explode if any Fermat Primes above 65537 are discovered. In other words, this machine exhibits infinite growth if and only if no Fermat Primes exist above 65537. It has been proven that all Fermat Primes up to and including 2^2^33+1 are composite, so this pattern will grow for at least 10^10^9 generations before halting.

The Fermat Prime Calculator

Because this is linked to an unsolved problem in mathematics, it is unknown whether this is an infinite-growth pattern, or whether it has a bounded (but astronomically high) final population. This serves to demonstrate that Life patterns are capable of unpredictable behaviour.

Continue reading "Prime numbers" More

2009 August 01

Engineered Objects
Completed Universal Computer/Constructor

In early June, Calcyman completed a glider-constructible universal computer/constructor -- a Life pattern that can be programmed to perform arbitrary calculations and optionally to construct Life patterns according to the results of those calculations.

It is conjectured that the UCC can be programmed to build any glider-constructible Life pattern, up to and including a complete working copy of itself, since the UCC's circuitry is made entirely from stable Spartan components (eight or fewer cells per still life).

Further details can be found in the LifeWiki entry on the UCC, and in the draft programming instructions in this archive file. The 228K pattern file linked to by the image at right is a compressed Golly macrocell format.

A 73K two-state macrocell version and a 400K compressed RLE version are also available. These files do not include the annotations available in the image link, which uses a multistate "LifeHistory" rule to help make the UCC's circuitry easier to trace and understand. Golly 2.1 and later versions have the necessary table and color files to display the annotations.

The UCC is is a possible next step towards a working Life replicator, the previous step being Paul Chapman's 2004 prototype programmable constructor (which is partially incorporated in Calcyman's pattern). However, the current UCC is huge -- nearly half a million ON cells in a six-billion-cell rectangular region -- which may put it safely beyond even a hashlife algorithm's ability to simulate a complete replication cycle.

Continue reading "Completed Universal Computer/Constructor" More

2009 March 17

Engineered Objects
Working 2c/3 Signal Elbow

2c/3 signal elbow:  Calcyman, 2 June 2008
Working stable 2c/3 signal elbow
Last June, Calcyman noticed the surprising fact that the standard wire termination for normal 2c/3 signals works just as well for the double-length signals put out by a previously known 90-degree 2c/3 signal elbow.

Dean Hickerson's original block-deleting 2c/3 termination almost certainly wasn't designed with this in mind, but it happens to absorb a double-length signal in exactly the same way as a standard signal -- the final stable state is the same in either case. This means that communication speeds approaching 2c/3 can be implemented over long distances in any direction, not just diagonally.

In the accompanying diagram, the input Herschel signal is circled in red. The output signal can be any of a number of optional glider outputs in the Herschel circuit at the bottom.

Two elbows in a row will not work (there's no known way to turn a double-length 2c/3 signal). But in the absence of layout constraints, a single elbow is sufficient to send a 2c/3 signal anywhere in the universe.

2009 March 14

Engineered Objects
Smaller "Highway Robber"

Calcyman's compact highway robber, 27 Feb 2009
Highway-robber glider reflector, recovery time 1244 ticks
Calcyman has constructed a much smaller Herschel-based "highway robber" glider reflector. These patterns are named for their ability to "steal" a glider from the edge of a glider highway -- a diagonal region of the Life universe along which many gliders may be travelling on closely parallel lanes.

A good highway robber can absorb a glider and produce an output signal, without disturbing gliders on nearby lanes, even one cell farther away from the highway-robber device.

Calcyman's new construction rebuilds the loaf bait and is ready for another glider input in 1244 ticks.

Continue reading "Smaller "Highway Robber"" More

2009 February 28

Stable Reflector with Record Recovery Time

Calcyman has designed a multi-stage stable glider reflector with a recovery time of 466 ticks -- an improvement over the long-standing record of 497 ticks, at the cost of a somewhat larger bounding box. Calcyman's 466-tick-recovery stable reflector

The reflector can be used as a glider-to-Herschel converter with the same recovery time, by replacing the final glider-producing conduit with a standard Fx176 component. This makes it possible to build glider-to-spaceship converters with 466-tick recovery times, also, by replacing the initial glider-to-Herschel stage in Stephen Silver's LWSS, MWSS, and HWSS converters.

New pattern: LWSS breeder

Lucas Brown has constructed a new type of breeder, in which a rectangular array of high-period glider rakes moves eastward while producing gliders that crash to form p30 glider guns. Gliders from the p30 guns crash together in turn to produce streams of northbound spaceships. Lucas Brown's LWSS breeder

Here is the same breeder after 5000 generations -- the seventh LWSS factory has just begun to produce spaceships, and the component p30 glider guns in the eighth factory have started up but their gliders have not yet collided. Click this image for a closer view of the initial breeder pattern. LWSS breeder after 5000 ticks

2009 January 11

Engineered Objects
Pentadecathlon Crane

Pentadecathlon shift A pair of Gliders can be used to shift a Pentadecathlon over one cell while changing its phase by four generations. This interaction takes a total of 34 generations to complete.

Pentadecathlon Crane From this, David Bell has built a structure, that he calls a "Pentadecathlon Crane", which uses this interaction to continously "lift" the Pentadecathlon. It uses a set of four Period 184 Slide Guns (Glider Guns in which every Glider produced follows a different track, each farther from the main gun mechanism) to strike the Pentadecathlon every 94 generations. (Shown here are Generations 0 and 376, with the Pentadecathlon having been shifted four cells to the North.)

Pentadecathlon Hassler Nicolay Beluchenko also pointed out that this mechanism can be used to create Pentadecathlon Hassler-type oscillators. Hasslers are oscillators in which a simpler object is repeatedly shifted back and forth. Here's a Period 188 version.

2008 July 31

Engineered Objects
7-Segment Hexadecimal Display

Calcyman has engineered a new type of hexadecimal display.

Continue reading "7-Segment Hexadecimal Display" More

2007 December 17

New 180-degree glider reflector, period 4 and up

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.

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

Engineered Objects
Early MWSS gun in Golly 1.3

Bill Gosper's original p1100 MWSS gun, circa 1984
Bill Gosper's original four-barrelled p1100 MWSS gun, circa 1984
-- perhaps only the 3rd gun pattern constructed in Conway's Life.
The bounding box is over 12,000 cells on a side.
Golly 1.3 was released last month, with a number of useful improvements to editing functionality: unlimited undo/redo support, configurable keyboard shortcuts for scripts and edit operations, and scripting support in Perl as well as Python.

An early LWSS gun by Bill Gosper, constructed around 1984, serves as the Rosetta Stone for the two scripting languages. This is a very large, sparse pattern of centinal reflectors, with a central column of signal splitters that produce the gliders needed to maintain eight p1100 LWSS streams.

The pattern takes up about 60K as RLE, or about 750K as a flat file; it can be reduced to about 5K of Python or Perl script (see Golly 1.3's Scripts collection). The Perl version is somewhat larger, but appears to be able to recreate the pattern slightly faster.

Continue reading "Early MWSS gun in Golly 1.3" More

2007 December 15

Engineered Objects
Prime Number Calculators

Four prime-number calculators:
-- 1st quadrant (upper right):
Original sieve by Dean Hickerson, 1 November 1991
-- 2nd quadrant (upper left): new sieve #1
Uses every glider relay, p60 instead of p40 LWSS rake.
-- 3rd quadrant (lower left): new sieve #2
Vertical guns replaced with an equivalent reflector.
-- 4th quadrant (lower right): new sieve #3
Contains no glider guns, only pentadecathlon reflectors.

New sieves by Jason Summers, 15 October 2005.
A few years ago Jason Summers constructed three new versions of Dean Hickerson's 1991 Life prime-number calculator. These all produce the same strings of spaceships: an LWSS appears at time 60N if and only if N is prime. This is twice as fast as the original 1991 pattern, which is included for comparison (upper right quadrant).

In the pattern at right, the LWSS streams from the two bottom quadrants are set up to annihilate each other. The top two streams -- one at 60N and one at 120N -- are reflected upward along the central axis for comparison purposes. The spaceships representing 2, the first number in each series, are exactly in alignment.

Continue reading "Prime Number Calculators" More

2007 May 14

Engineered Objects
Golly 1.2's hexadecimal counter

Version 1.2 of the cross-platform CA editor Golly was rolled out in mid-April. The main new feature is multiple layers that can be either stacked or tiled, showing either separate universes or multiple views of the same universe. Sample scripts and show possible ways to use this.

hexadecimal counter in action
/Hashing-Examples/ hexadecimal counter using modified metapixels
Among other additions to the pattern collection, updated versions of some of Stephen Silver's archive from 2004 have been added to the /Spaceships folder. And Hashing-Examples now includes a two-digit hexadecimal counter using metapixel technology -- a 30K pattern file that encodes a 32768x20480 pattern with over two million ON cells:

Some more detail on the hex counter, with a series of screenshots at different scales, can be found in this weblog entry.

2007 March 03

Logic Elements
New Herschel Conduit Discoveries

Herschel-controlled glider demultiplexer
Brice Due, 23 August 2006
Last August, Brice Due ran some interesting searches with Paul Callahan's catalyst search program, ptbsearch. His first discovery was a compact 'demultiplexer' -- a Herschel-to-boat converter where the boat can be used to reflect a glider. Unlike previously known Herschel-to-boat converters, the glider has a clear path through the circuit if the boat is not present:

F171 Herschel conduit discovered by Brice Due on 31 Aug 2006
The next discovery was a previously unknown F171 Herschel conduit -- the first new addition to the elemental Herschel conduit list in almost eight years:

glider #22: Brice Due, 2 September 2006
Another unrelated ptbsearch discovery was a Herschel-to-glider converter, #22, with a new output lane:

Continue reading "New Herschel Conduit Discoveries" More

2006 March 01

Engineered Objects
New p2 'Blinker-Keeper' and H-to-G Converters

p1134 gun based on David Bell's doubling of a blinker-keeper
p1110+24N, N=1: Dave Greene, 13 November 2005
In November, David Bell found a way to recycle a glider from a 'blinker-keeper' mechanism discovered a couple of months previously, to produce a series of compact guns whose periods were multiples of 5, 6, 7, or 8. This improved a number of the glider guns in Jason Summers' extended gun collection.

p496 "blinker keeper" oscillator maintains an accessible blinker
toward its left edge, deleting and recreating if necessary
Here is the original 'blinker-keeper' pattern on which the new guns were based: a blinker is reconstructed every 496 generations if it is found to be missing.

p488+8N pi-factory gun with alternate p2 H->G
(p488 in gun collection is smaller; this just shows the new H->G)
Dave Greene, 20 Sep 2005
p496 bootstrapped pi-factory gun: Dave Greene, 20 Sep 2005
(can produce Herschel output via standard Fx176 conduit)
The blinker-keeper in turn was based on a pair of new Herschel conduits, which could also be used in building a series of compact guns, this time improving the size of glider guns in the main gun collection.

2005 December 21

Engineered Objects
"Rule 110" Unit Cell

Rule 110 Unit Cell

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 0Gen 1

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

2005 September 10

Engineered Objects
Grow-By-One Pattern

Grow By One Pattern 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.)

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

2005 September 06

Engineered Objects
Bobsled Run Update

revised switch-engine 'bobsled run' using boats as catalysts:  David Bell, 2 July 2005 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.

P3450 switch-engine swimmer based on a p9660 swimmer by David Bell, 2 July 2005 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:

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 February 07

Engineered Objects
Stable 2c/3 signal receiver

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.

Stable 2c/3 signal receiver; recovery time = 2175 ticks 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 dgreene 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.

2004 December 31

New 17c/45 Spaceship: The Caterpillar

Pi Crawler 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.