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2006 March 24

Greyships & Spacefillers
c/4 greyships

small extensible c/4 greyship
Hartmut Holzwart, 24 March 2006
Hartmut Holzwart has been continuing his work on c/4 greyships, and has produced a number of new variants on the original.

greyship enclosing chicken-wire agar
Hartmut Holzwart, 20 Mar 2006

two related c/4 greyships
Hartmut Holzwart, 24 March 2006

new c/4 greyship variant
Hartmut Holzwart, 23 March 2006

c/4 greyship: Hartmut Holzwart, 6 March 2006

new slopes for c/4 greyships
Hartmut Holzwart, 16 March 2006

c/4 greyship variant 1
Hartmut Holzwart, 16 March 2006

c/4 greyship variant 2
Hartmut Holzwart, 16 March 2006

c/4 greyship: Hartmut Holzwart, 24 March 2006

2006 March 20

Glider Constructions
P2 Slow Salvo Eater Recipes

Paul Chapman's Glue project is producing some interesting results. Glue (or rather Glue 2) is a search program that finds "natural" constructions of singlets (indivisible p1 and p2 patterns) by starting with a target object -- usually a block -- and bombarding it with a p2 slow salvo of gliders.

Here, 'salvo' means that all the gliders come from the same direction; 'slow' means that glider #n+1 must not arrive until the reaction from glider #n's collision has settled down into stability or a p2 oscillation, and 'p2' means that the only timing constraint on the gliders is that an even or odd phase may be specified. (Many intermediate collision results contain blinkers, beacons, toads, or other p2 patterns, and a glider on a given input lane can interact with a p2 target in two possible ways.)

Click on the image to download the pattern in Koenig's annotation format. Annotated RLE allows for multiple layers in different colors, with the extra information specified by h, v, and color parameters in the header; it is backwards compatible with standard RLE (at least for most Life editors.)

Here is a text file containing the individual recipes in RLE format, with comments giving the lane list for each recipe. Note: some of the recipes build an eater that is a mirror image in the main diagonal of the one shown above.

Here's a screenshot of the current version of the Glue 2 search program used to generate these recipes:

Some additional images and details are also available, including an MCell-format version.


2006 March 07

Life Variants
Colored Life

forward-shooting switchengine interacts with a dirty Schickoidal
backrake to produce complex long-term behavior
Bill Gosper, 26 February 2006
Bill Gosper has been doing some fascinating original research on patterns with 'simple' initial states but complex long-term behavior, using the new cross-platform hashlife-capable Game of Life simulator, Golly.

slight variation on previous pattern
emits an unprecedented glider burst at 5e10.
Bill Gosper, 26 February 2006

At 2.3e12 (Golly screenshot here) this pattern seems
to have regularized: the last twelve bursts from the left formed
a geometric progression of trapezoids. But the top two corners
of the next "trapezoid" are missing, as were several previous.
To see that the trapezoid progression is exactly doubling,
click with the up/down scaling cursor on the limit point.
Bill Gosper, 27 Feb 2006
The following are Gosper's detailed notes on the "Gotts-puzzle" pattern shown at right:

...[O]bserve that the bursts forming the bottom-left corners are acute Vees (inset) flying backwards! In fact, the inset shows two backwards mirror image Vees flying apart. This is seriously weird by the following argument.

Experiments on this scale nearly always take on a characteristic expanding star shape, with typically eight or fewer "limit" points, each receding with the velocity vector of a hypothetical glider or spaceship launched from the Origin by a Big Bang. (Any finite initial configuration (Origin) is infinitesimal compared with with these billions-wide star diagrams.) The diagrams are often crisscrossed by numerous linear features at many different angles, e.g., the patterns on Nick Gotts' weblog or the pattern shown below.

Unlimited novelty:  nick-gotts-g at 2,000,000 ticks
Golly screen shot of 'nick-gotts-g' around generation 2,000,000

'nick-gotts-g': 2006-02-27-hashlife-puzzle2.rle
nick-gotts-n type rake interaction with apparently unlimited novelty
The interaction of the downward puffer's trail with the first
bounce of its backrake produces two very sparse LWSS waves.
Bill Gosper, 27 Feb 2006
The above screenshot shows the complex long-term behavior of the 'nick-gotts-g' pattern shown at right, which consists of two interacting rakes. Here is a larger screenshot of the same pattern at 4.9e8 ticks.

The components of each line have equal velocity vectors, easily determined by which of the star-points radiates the extended line. The Origin is a ninth point which radiates all lines of immobile objects. (The production of particles with a nonstandard velocity would create an additional star-point.) Lines joining two star-points are guns or puffers. Thus the little tick designated by the red arrow in gottspuzz.png can only be a wave of a million or so spaceships (MWSS in fact) pointing toward the N spaceship limit, which unfortunately is graphically inapparent because no spaceships are actually escaping. (They can't be heading S because there was a single pixel NW-SE jog in that tick that my screenshot was too slow to catch.)

Thus when several rays emanate from the vertex of an internal wave crossing, it is easy to see the chain of causality, i.e. which lines are inputs and which are collision products, because components along a ray are older toward its star-point.

In other words, Vees fly frontwards.

And one of the two arms (apparently the sparser) of these backwards Vees heads at an "inexplicable" angle, i.e., not through a star-point!

New P2 Oscillators

c/6 orthogonal spaceship Paul Tooke's spaceship searches have come up with a new c/6 Orthogonal Spaceship.

2006 March 04

Smaller Garden of Eden pattern

smaller (12x12) Garden of Eden pattern with 80 ON cells, based on
Achim Flammenkamp's 81-cell 13x12 orphan from 14 June 2004.
Single cell in rightmost column removed, and two other cells moved.
Nicolay Beluchenko, 11 February 2006
Nicolay Beluchenko has modified a previous 'orphan' (Game of Life pattern which has no possible predecessors, and thus can only appear at generation 0) to slightly reduce both the bounding box and the number of ON cells. Changed cells are shown at right: cells only in the original version are in blue, cells only in the new version are in red.

UPDATE: A week after producing the pattern on which Nicolay Beluchenko based his optimized version, Achim Flammenkamp built a smaller Garden of Eden pattern consisting of 72 ON cells inside a 12x11 bounding box. This 23 June 2004 discovery is the smallest Garden of Eden currently known.

Wicks & Fuses
Wick and Wave Stabilization

fencepost for a known p6 wick: Jason Summers, 23 January 2006

fencepost for a known p6 wick: Jason Summers, 23 January 2006

easy-to-tame barber pole: Jason Summers, 23 January 2006
Jason Summers has done some work on creating 'fencepost' stabilizations for the ends of previously known but untamed fenceposts and barber poles.

c/4 diagonal eater spaceship for untamed oblique barber pole
Nicolay Beluchenko, 5 February 2006
Hartmut Holzwart and Nicolay Beluchenko have been working on the moving equivalent of a fencepost, for an oblique p4 wave pattern that can be stabilized at the trailing end by a c/4 'eater' spaceship, along the lines of recent 'anteater' patterns. A matching 'stretcher' end for the same wave is currently an open problem.

smaller eater for untamed diagonal c/4 barber pole
Hartmut Holzwart, 10 February 2006

eater #3 for untamed diagonal c/4 wave
Hartmut Holzwart, 13 February 2006

eater #4 for untamed diagonal c/4 wave
Hartmut Holzwart, 13 February 2006
Here are some further results from Hartmut Holzwart related to this wave pattern.

eater #5 for untamed diagonal c/4 wave
Hartmut Holzwart, 13 February 2006

untamed diagonal c/4 wave connected to another wave
Hartmut Holzwart, 13 February 2006

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

2006 March 01

Antstretchers and tubeaters

c/4 diagonal antstretcher, with an anteater of the same speed
Nicolay Beluchenko, 5 January 2006
After a long search, Nicolay Beluchenko has successfully found an 'antstretcher' pattern to match his previously discovered 'anteater'. Individual ants in the 'ants' wick supported between these two structures have an apparent speed of travel equal to the speed of light. Ants can either follow one another exactly, or can be offset by either one or two cells; in this case, the speed of the antstretcher and anteater dictate a one-cell offset between ants.

smaller version of antstretcher
Hartmut Holzwart, 11 Jan 2006
slightly different version of original antstretcher, using a
known small ship (shown on the left) to complete the pattern
Hartmut Holzwart, 11 Jan 2006

Glide-symmetric double antstretcher and a 90-bit spaceship
Nicolay Beluchenko, 5 January 2006

c/4 diagonal combined antstretcher and tubstretcher
Nicolay Beluchenko, 7 January 2006
Another new combination that has turned up is a connection between a tubstretcher and a tubeater, producing the interesting object at right. Further exploration of tubstretchers and tubeaters yielded the collection of new adjustable-length spaceships (and a puffer) shown below.

component allowing the construction of a tubstretcher/eater series
Nicolay Beluchenko, 15 January 2006
standard blinker puffer version of Nicolay Beluchenko's tubeaters
Hartmut Holzwart, 13 Jan 2006

pairs of known c/4 diagonal spaceship components can eat tub wicks:
Nicolay Beluchenko, 13 January 2006
three more variants of single and double tubeaters
Nicolay Beluchenko, 13 January 2006

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.

New P2 Oscillators

New P2 Oscillators A variant casing for a previously known Period 2 Oscillator Rotor (top line) has been found by Ian Osgood (middle line). dgreene then noticed that one or both of the outside diagonal rotor bit-pairs can be suppressed, giving two more new Period 2 Rotors. The 6 bit Rotor (31P2) is a new Rotor, while the smaller object is just a previously unknown casing.