Game of Life News

7-Segment Hexadecimal Display

2008-07-31T11:05:57Z

Calcyman has engineered a new type of hexadecimal display. Calcyman's original version had visible "signal lines" extending through the conversion-table mechanisms to the 7-segment display area. This allowed the state of the memory bits to directly control the display, with no state information stored in the display area, but it interfered somewhat with the readability of the digits. It also used a chain of slower Herschel period doublers, which meant that the 7-segment readout was trivially extensible by moving the left or right digit outward by multiples of 3220 cells, and inserting identical copies of the center digit. The second version removed the signal lines but retained the slow Herschel track along the bottom, which meant that a rollover of more than two digits (e.g., from '999' to '000') would not be completed before the next counter increment began. The third version shown above increments all digits simultaneously, with the downside that changing the number of digits is no longer quite a trivial operation, and the height of the pattern is no longer constant as the number of digits increases.

New Small Period Oscillators

2008-06-06T23:48:16Z

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

Jason Summers has found a Period 6 oscillator which produces an isolated single-cell spark, as well as several oscillators with periods ranging from 15 to 30.

Scot Ellison has also found a small Period 5 oscillator.

New 2c/5 Greyships

2008-04-24T09:58:09Z

long thin 2c/5 greyship variants: Hartmut Holzwart, 21 Feb 2008

Hartmut Holzwart has successfully completed several families of 2c/5 greyships, based on recent searches:

2c/5 greyship examples: Hartmut Holzwart, 26 Feb 2008

more 2c/5 greyships
Hartmut Holzwart, 29 Feb 2008 (corrected 3 Mar 2008)

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2c/5 greyship with new ascending component
(at the tail of the spaceship, on the right)
Hartmut Holzwart, 3 March 2008

alternate 2c/5 greyship: Hartmut Holzwart, 3 March 2008

Service Interruption

2008-03-16T23:16:00Z

Later this week (around 21 March) the LifeNews and the pentadecathlon.com website will be offline and unavailable. It's my hope and intention to be back up and running as early as 01 April, but it may take several weeks to get back online.

Glider Collisions With 16 Bit Objects

2008-02-09T17:55:23Z

I've recently completed a run of all possible collisions between a Glider and a 16 Bit Object (both stable and oscillating). Presented in the extended entry are about 500 collsions which may be useful in the contruction of other objects, where a single Glider quickly transform the object into another unsual object, or transform in place to a common object. (In some cases, I've added a second Glider to clean up any other extraneous objects.) Not included are those cases in which there is a simple transformation which can also be exhibited by a similar collision with a smaller object.

The longevity record was established by these two collisions. They both converge on the same resulting census, but the one on the right takes 17408 generations while the one on the left takes 17641.

Among the results of this collision are, after 526 Generations, two Lightweight Spaceships heading off at right angles, and a single Glider in the opposite direction.

A number of rare or unsusal objects also appeared in the final census for some collisions. Shown here are those cases where 3 or fewer cases for a particular object are found.

Correction:

Turns out that I'd improperly included two collsiions as producing 14.487, when they actually produced a 16.487. Instead of deleting them, I've just properly relabeled them and left them in place. Thanks to Bobby Baum for noticing this.

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16.4 — 16.648

16.654 — 16.1437

16.1441 — 16.2197

16.2199 — 16.2366

16.2367 — 16.3271

16P2

I can also provide a full .zip file of all these collisions, each in a separate file, and including all objects up to 16 bits, upon request. Just use the email contact address. (I could just post this, but I'd like to actually know who finds all this of more than passing interest.)

New p5 Herschel technology

2008-02-01T12:25:38Z

Scot Ellison's smaller p5 fountain
for the p5 73-step Herschel conduit

Scot Ellison's search for a smaller p5 oscillator to support the 73-step Herschel conduit was successful, back in May of last year -- though he says that even smaller, perhaps asymmetrical, sparkers are likely to exist.

This smaller p5 fountain is included in an updated version of Hersrch, Karel Suhajda's Herschel-track search and construction program.

Adjustable p5 tandem-glider conduit

Another p5 Herschel conduit that showed up in 2007 was an adjustable diagonal track in which two gliders to travel an arbitrary distance diagonally between a transmitter and a receiver, similar to Paul Callahan's stable "tandem glider" circuits. It's constructed from known pieces: a stable converter that produces two gliders on the same lane from an input Herschel, and a p5 "doubler" that produces one output glider and/or Herschel from each pair of input gliders.

The circuit's p5 limitation is somewhat mitigated by its reversibility -- there are two mirror-image ways to receive the two gliders, whereas most tandem gliders need either a left- or right-handed receiver. (Some pairs of gliders with two-cell separation, usually produced with the assistance of a boojum reflector, can be received ambidextrously by standard receivers -- but this significantly alters the timing of the circuit.)

Depending on the position of the block, either of the two gliders can be chosen to trigger the Herschel output, while the other one resets the circuit. The circuit can also be hooked up to any glider output of a Herschel track for use as a period doubling fanout device, or a two-state track switch (two circuits on two glider outputs with alternating block positions).

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p5, p7, p22, p36, p46, and p104 pulse divider reference collection.
Original p5 pulse divider by Dietrich Leithner.
p7 and p46 versions: Stephen Silver, 31 May 2001.
p22 version: David Eppstein, 1 June 2001.
p104 version: Scot Ellison, 24 March 2003.
p36 version: Jason Summers, 26 March 2003.

Substituting oscillators of other periods (p7, p22, p36, p46) opens up other possibilities -- especially the p7 variant, since the tandem gliders are separated by 119=7*37 ticks, so the double glider stream can be reflected.

It would be nice to have p6, p8, or p9 versions, but unfortunately no pipsquirter or other sparker below p10 seems to work with the current mechanism -- p7 is a special case.

Pulse dividers can be used as period doublers, but the "reset" glider is actually period-independent. The p104 case shows how the necessary one-bit spark can come from any periodic glider source.

New 2c/5 Spaceship

2008-01-27T19:40:20Z

Harmut Holzwart has found an new Period 5 ^2c/₅ Spaceship.

Nicolay Beluchenko then found that a spark from this object could be used to convert Lightweight Spaceships into Gliders. He used this reaction to create the Period 150 Pseudo-Rake shown here. The Spacehip Gun at the bottom generates a stream where each spaceship becomes a forward-moving Glider.

Oscillator Construction

2008-01-07T00:28:26Z

Jason Summers has found an unoptimized construction of the "Smiley" [17P8,1] Period 8 Oscillator.

New Spaceship Flotilla and Constructions

2008-01-06T23:57:29Z

Victor Pecanins noticed that a previously known Spaceship escorted flotilla (42P20H10V0) could have its central element extended by several bits.

Mark Niemiec then came up with constructions for both these flotillas. And as he points out, there are certainly more variations with different length ships out there.

Some New Oscillators

2008-01-06T19:24:05Z

To start the new year, here's a compendium of some oscillators found during the previous few months that never got included in a posting.

First are some Period 6 Oscillators found by Nicolay Beluchenko.

Next is a Period 30 Rotor found by Karel Suhajda that requires 4 sets of P30 Glider Guns to generate the sparks necessary to turn it into a rotor. Finding a better stabilizer would be a worthwhile small project.

David Eppstein has contributed a Period 7 Oscillator and a Period 10 Oscillator, both of which have an isolated two-bit spark appearing in the upper right corner in generation 6 and 9 respectively.

New 180-degree glider reflector, period 4 and up

2007-12-17T10:02:35Z

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.

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Noam Elkies' previous block-restoration reaction (4 October 2007)
used with a kickback reaction to suppress a p63 glider stream.
Any p63+56N should be possible. P7 mechanism by Jason Summers.

The reflection's one-half-diagonal offset is the same as that of a kickback reaction, but the timing is different. Combining this reflector with a kickback reaction or a previously-known kickback simulator makes it possible to construct a variety of glider-relay oscillators, and thin certain odd-period glider streams.

Two conduits containing successful H-to-R-to-H stages, with
p8 glider-to-pi converters helping out with the catalysis.
Based on a p15 Herschel fanout device that produces mirror-image
R-pentominoes at generation 262 -- remove the eater near the
input glider path to see the mirror-image Rs.

The reaction can also be modified to produce pi heptominoes instead of output gliders, as shown in this example where glider-assisted p8 oscillators use a pi heptomino to solve a difficult Herschel-conduit problem in close quarters: a beehive catalyst needs to be shoved back one cell after a signal passes through the conduit. (At p15 this task can be accomplished by a pentadecathlon, which allows both output R pentominoes to be used.)

Early MWSS gun in Golly 1.3

2007-12-17T09:35:44Z

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.

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p1100 pure-period MWSS gun (centinals and Herschels)
Dave Greene, 28 September 2007

For comparison purposes, here's a p1100 MWSS gun incorporating Herschel technology, which first became available more than a decade after Gosper's MWSS gun was constructed. This new gun would fit comfortably between most of the adjacent glider trails in the original MWSS gun:

Frozen LWSS fuse / rake

2007-12-17T07:40:42Z

Sideways LWSS rake based on a glider+constellation->LWSS reaction.
This puffer produces a row of still-life constellations, each
of which can output an LWSS and two gliders when hit by a glider.
The result is a repeating sideways LWSS generating reaction
at the back, progressively thawing the "frozen LWSS" string.
David Bell, 4 November 2007.

David Bell has constructed a two-stage sideways LWSS rake, where the first stage builds "frozen LWSSs" -- a chain of repeated still-life constellations -- and the second "thawing" stage consists of a glider that follows the chain (at a much slower speed) and liberates the stored LWSSs.

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glider-to-LWSS still life in X-shaped pattern, using 2LWSS->2G
David Bell, 30 October 2007

Three fuses built from variants of an MWSS-to-MWSS still life
conversion reaction from Jason Summers, 29 October 2007,
David Bell, 9 November 2007

modified version of a glider-to-MWSS still life from Jason Summers
(29 October 2007) allows an MWSS input trigger instead of a glider.
David Bell, 30 October 2007

Four fuses using different variants of a glider-constructible
still life that produces an MWSS when annihilated by a glider.
Still lifes in the fuses on the right also output an extra glider.
David Bell, 11 November 2007

Prime Number Calculators

2007-12-15T17:35:06Z

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.]]>

Detail of four-primers pattern after 100,000 ticks.

All four quadrants use the same basic structure of reflected gliders to perform the prime-sieving operation. After running 100,000 generations in Golly (which seems fairly quick, in spite of the lack of regularity in the northbound output) the center of the above pattern looks like this:

Update: smaller Garden of Eden previously known

2007-12-10T02:13:40Z

Achim Flammenkamp's 12x11 Garden of Eden --
black cells ON, blue-gray cells must be OFF
Achim Flammenkamp, 23 June 2004

Paul Kwiatkowski has pointed out that Nicolay Beluchenko's 12x12 pattern, based on a 12x13 Garden of Eden pattern from June 14, 2004, is not the smallest known "orphan". Achim Flammenkamp discovered a 12x11 GoE a week later, on June 23, 2004:

It is still an open question whether 11x11 or smaller Garden of Eden patterns exist.