Nick Gotts has put together a new weblog based site, Natural History of Conway's Game of Life, in which he will be presenting some of the results of his investigations into simple starting pattern. The first posting deals with "Patterns with Eventful Histories", patterns which can interact in non-periodic ways and which have been followed for up to 2^36 (over 137 billion) generations.
Cutting and Repairing Diagonal Lines
David Bell recently asked if it was possible to detect a long diagonal line without destroying it, and if it was possible to send a signal through a diagonal line. The answers to both questions hinge on the ability to cleanly break and then repair the line. The glider constructions for such actions, while not optimum, have been found.
Bell showed that it was possible to repair a two cell break with a Loaf predecessor, and then Karel Suhajda and H.Koenig were able to find a 3 Glider construction of a Loaf that worked perfectly. Mark Niemiec also posted some similar contructions by David Buckingham which can also be used to close up a line.
A way to break a line was then posted by H.Koenig. Two gliders cause the diagonal line to become a pair of clean burning fuses, and then a pair of reactions consisting of two Gliders and a Lightweight Spacehip (LWSS) (previously discovered by Jason Summers) create the domino sparks which halts the burning fuses. This results in a twenty bit gap where the diagonal line used to be. This construction is not complete, however, because two of the gliders would interfere with each other if they came from infinity. Also, the gap created is much larger than it could be.
David Greene then showed how to use a pair of reactions using a Pond, a LWSS and three Gliders to lengthen a diagonal line by 4 bits can be used to close a gap by 8 bits. So a gap of 8n+2, with 10 bits as the minimum, becomes the more useful reactions.
Bell then showed how a Glider collision with a stable object could be used to cleanly cut a line. The added cost in Gliders used to construct and place the stable object (in this example, a Block and a Loaf) is outweighed by the flexibility in timing and and in the placement of the reaction which ends the burning of the fuse. Greene also showed a a way to place and ignite a Tub to make a 10 cell gap. But the 9 cell gap can be expanded to 10 by simply delaying one of the fuse stablizers by one generation and shifting it slightly. (Any reaction can be made arbitrarily wide in the same fashion.)
All of these reactions require a glider to be placed as close as possible to the diagonal line. Bell showed an example of a reaction of 2 LWSSs and a Glider which can place the Gliders needed in the previous reactions, as well as one that can place a Loaf near the line for the 9 bit gap.
There are some issues remaining. It would be useful if all the Gliders and LWSSs in the gap cloing reactions camefrom the same side of the diagonal line, as that would make timing issues a lot easier. Also a demonstration of a reaction that can detect the presence of the line needs to be made. Finally, for use in other patterns, the reactions which cut or repair a diagonal line that are triggered by a single Glider (or a set of Herschel Track components) needs to be actually built.
New Record Methuselah
Andrzej Okrasinski has found a new methuselah record holder, a 15 bit intial pattern with a final population of 1623 after 29053 generations. David Bell quickly found a 13 cell predecessor, bringing the record to 29055.
Some of the more unusual objects which make an appearance but which aren't in the final census include a Lightweight Spaceship [9P4H2V0.1], a Fishook Eater [7.3], a Long Barge [8.9], a Big S [14.492], a Bi-Pond [16.2630] and an unnamed 13 bit object [13.182].
|Size||Discoverer||Gens||Final Pop.||Final Pattern, Census|
102(4.1), 2(4.2), 15(5.1), 6(6.2), 57(6.4), 1(7.2), 18(7.4), 5(8.7), 2(12.41), 135(3P2.1), 1(6P2.1), 1(6P2.2), 28(5P4H1V1.1)
Note: Not all of the paths of escaped gliders are shown.
c/2 and 2c/4 "greyships"
Hartmut Holzwart and Jason Summers have been investigating possible shapes for 2c/4 "greyships" that include an extensible striped region of half-ON, half-OFF cells. Triangles, diamonds, and other shapes are possible.
This technology can be extended to produce more complex shapes with a variety of slopes. Some components also exist for a ship traveling perpendicular to the "grain" of the stripes, instead of parallel, but currently not enough to produce a complete ship. See this blog for details.
(Disclaimer— I have no association with anyone or any organization, and speak only for myself. Links and quotes are provided for information only.)