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| Golly |
| Golly is a free program that allows you to easily explore much larger patterns at higher speeds than any web-based applet ever could. |
Marijn Heule, Christiaan Hartman, Kees Kwekkeboom and Alain Noels systematically searched the entire space of 10-by-10 patterns with fourfold rotational symmetry, finding a Garden of Eden with 92 specified cells (56 live, 36 dead). Moreover, they proved the non-existence of Gardens of Eden within a 6-by-6 box.
Read the whole story at pentadecathlon.com
If you asked a fellow Life enthusiast for the most important GoL discoveries in the 1990s, the Herschel track must surely feature. With a few elementary conduits, it is possible to design tracks capable of moving a signal to anywhere in spacetime (as long as there is enough 'manouevring room' and sufficient time), and placing it in any orientation. Herschel tracks underpin all but two of the known stable reflectors, and support the construction of glider guns for every period greater than or equal to 62.
Firstly, what is so special about the Herschel? Is it really so much more useful than any other transient objects? It appears that the answer is both yes and no: other objects can be used, but they must eventually decay into Herschels. This is illustrated rather eloquently by a simple matrix. The row represents the input; the column represents the output. A red blob indicates if a primary (one-stage) conduit exists to transform the input into the output. Clicking on the matrix will enable you to download a complete collection of primary conduits. (A collection of all conduits, primary and composite, is provided later in this article.)
Some of these conduits are new discoveries. The Pi-to-R converter was discovered by Guam on the conwaylife.com forums, published in the form of a quaternary Herschel conduit: H-Pi-R-B-H. The completed conduit takes 309 generations to turn a Herschel anticlockwise, so is designated L309. In terms of the number of intermediary objects, L309 is the most complex Herschel conduit to date. Indeed, its 309-tick delay is rather rapid for a quaternary conduit.
Read the whole story at pentadecathlon.com
Matthias Merzenich has discovered a c/7 diagonal spaceship -- the first of its speed. This raises the total to thirteen reasonably-low-period spaceship velocities, specifically eight orthogonal (c/2, c/3, c/4, c/5, 2c/5, c/6, 2c/7, 17c/45) and five diagonal (c/4, c/5, c/6, c/7, c/12). Of course, an infinite number of spaceship velocities are known, as the Gemini can be adapted accordingly.
Moreover, Matthias has actually discovered an infinite family of such spaceships, as one of the frontal components can support itself to yield an extensible spaceship.
Read the whole story at pentadecathlon.com
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.
'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:
Read the whole story at pentadecathlon.com
Nathaniel Johnston's website, conwaylife.com, is now back online, so the forums are accessible once again. Moreover, the homepage is updated with relevant blog entries from his blog, b3s23life, and even LifeNews itself!
Read the whole story at pentadecathlon.com
Since time immemorial, there has been a desire to find a c/5 orthogonal anteater. The motivation arises from the existence of a c/4 diagonal antstretcher, which produces a compatible oblique line of ants. By fusing the two components seamlessly, a growing spaceship could be created.
Matthias Merzenich has finally found this long-awaited anteater, enabling completion of the antstretcher.
Eight copies of this can be combined to create another example of a 'space-nonfiller' (a term coined by Jason Summers), the earliest such example being discovered by him in 1999, which expanded at the vacuum speed limit.
Read the whole story at pentadecathlon.com
Stephen Silver, 20 April 2011.
Uses a breeder by Nick Gotts.
At right is a diagram shows what the full pattern looks like, with a sample section of the generating line of cells expanded to explain the mechanism used to construct the breeder. Line sections are arranged to produce exactly-timed two-glider salvos, which collide to produce LWSSes, which in turn collide to build the breeder. A multi-step reaction at the X axis produces the second glider in each pair with an exactly-timed delay relative to the first one.
The breeder is based on Nick Gotts' 26-cell quadratic-growth pattern. It is incrementally constructed by colliding LWSS streams travelling parallel to the baseline.Read the whole story at pentadecathlon.com
The Q-toothpick cellular automaton (defined earlier this month by Omar E. Pol) is described by the following simple rules:
- On an infinite square grid, draw a quarter circle from one corner of a square to the opposite corner of that square:
- Call an endpoint of a quarter circle (or a “Q-toothpick”) exposed if it does not touch the endpoint of any other quarter circle.
- From each exposed endpoint, draw two more quarter circles, each of the same size as the first quarter circle you drew. Furthermore, the two quarter circles that you draw are the ones that can be drawn “smoothly” (without creating a 90° or 180° corner). Thus the next two generations of the automaton are (already-placed quarter circles are green, newly-added quarter circles are red):
The name “Q-toothpick” comes from its analogy to the more well-studied toothpick automaton (see Sloane’s A139250 and this paper), in which toothpicks (rather than quarter circles) are repeatedly placed on a grid where exposed ends of other toothpicks lie. In this post, we will examine how this automaton evolves over time, and in particular we will investigate the types of shapes that it produces.
Counting Q-Toothpicks
While the Q-toothpick automaton appears quite random and unpredictable for the first few generations, evolving past generation 6 or so reveals several patterns. The following image depicts the evolution of the automaton for its first 19 generations.
Read the whole story at njohnston.ca
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.
Read the whole story at pentadecathlon.com
To celebrate Paul Tooke's 50th birthday, this article is dedicated to one of his recent discoveries. Happy birthday, Paul!
Paul has recently been assembling patterns to defy common intuition about breeders, and thus help to determine a valid definition for what constitutes a breeder.
He has used the principles behind Gemini -- glider loops and universal construction -- to build unusual breeders with obscure properties. For example, he has engineered a SSS breeder, which amounts to a slide puffer (slide gun with stationary output) constructing more slide puffers. Moreover, he has designed it to have O(t^1.5) growth, rather than the O(n^2) typical of most breeders.
Read the whole story at pentadecathlon.com