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- H.Koenig
- Adam Goucher
- Dave Greene

« April 2006 | Main | June 2006 »

Back in February, Jason Summers constructed a complex assembly of c/2 orthogonal rakes that builds a zigzag wick. The pattern uses glider constructions similar to those found in David Bell's c/12 diagonal wickstretchers from last year.

p103079214841 (prime: 4^13*1536-263) oscillator/gun --

p1536 base loop, 13 quadruplers, and a 263-step glider advancer.

Dave Greene, 31 Mar 2006 (with correction by Tomas Rokicki)

p1536 base loop, 13 quadruplers, and a 263-step glider advancer.

Dave Greene, 31 Mar 2006 (with correction by Tomas Rokicki)

Like the 2003 examples, this pattern consists of a Herschel/glider loop (period 1536 this time, instead of period 1450) attached to a series of thirteen 'quadrupler' conduits of two different types, L-shaped and straight. Each quadrupler allows only one Herschel signal in four to get through to the next conduit.

In the starting configuration, the first three quadruplers are set to absorb three signals each: an extra block has been added to the first two L112 quadruplers and the first Fx70 quadrupler, which has a standard F166 dependent conduit appended to suppress the following Herschel's first glider. So the circuit initially counts down from 63. When all circuits are empty, a signal gets through to activate the 263-step glider advancer -- after which the circuit counts down again, this time from 4^13-1.

As usual with this kind of Herschel-track construction, Karel Suhajda's 'Hersrch' search program was used to design the base loop, and to locate an efficient connecting circuit between the end of the quadrupler chain and the glider advancer. The continuing challenge, of course, is to fit an oscillator with a higher prime period into a bounding box with a smaller number of cells.

Here's another batch of puffer orbits found by Jason Summers.

In the following tables, the percentages are approximate, intended to illustrate how common or rare a particular puffer might be. The bit patterns are not the actual puffer, but a simpler pattern which will eventually evolve into the puffer.

The first puffer presented here is a based on a large Period 3 which moves at a speed of
^{c}/_{3}. It also has a slightly smaller Period 12 variation.

P222+102 | ≈97% |

P114+3 | ≈3% |

306P3H1V0 | 0.04% |

P273+130 | 0% |

P180+161 | 0.005% |

450+239 | trace |

304P12H4V0 | trace |

The next set of puffers are based on a Period 28 Spaceship.

213P28H7V0 | 99.94% |

140+90 | 0.04% |

P168+109 | 0.02% |

P56+14 | trace |

Another pair of puffers are based on a Period 2 Spaceship previously used to create a Period 8 Glider rake, both of which are shown also.

P224+124 | 99.98% |

P32+7 | 0.02% |

The final set includes a previously known B Heptomino based Tub puffer.

P24+4 | 99.87% |

P12+7 | 0.13% |

P2724+4153 | 0.02% |

Thanks to John Green for pointing out that a number of the RLE files in the Puffer Orbits would not download properly. In fixing the problem and reviewing other possible problems, I found several other bad links. Please let us know when those things happen. If you can't see the images, or get and run the RLE files, then a mistake was made and it needs to be fixed. Or you may be using a combination of browsers and operating systems with which we are unfamiliar and may not realize we are breaking.

'Gotts Dots': sprouts its nth switchengine at t ~ 2^(24n-6) --

41 ON cells, growth rate O(t ln t)

Bill Gosper, 11 March 2006

41 ON cells, growth rate O(t ln t)

Bill Gosper, 11 March 2006

Nicolay Beluchenko created some sample diagonal greyships in various shapes, with a "grey" level of 1/3 ON cells (instead of the usual 1/2 for orthogonal greyships with 'stripes' or 'chicken-wire' agars.) Since these new "ships" are really an independent series of tubstretchers and tubeaters packed together as closely as possible, it's obviously possible to move the pieces farther apart from each other to produce lower fractions of ON to OFF cells.

It may also be possible to construct extensible multi-tubstretcher and multi-tubeater spaceships that support this agar -- where each stretcher or eater is connected directly to the next one, and can't be separated -- but this has not been accomplished as yet. Multistretchers and multieaters with wider spacings have been previously posted, however. Tubstretcher-based patterns composed of more than 1/3 ON cells are not possible. Thus, to produce a diagonal greyship that maintains a 1/2-ON agar, it would be necessary to devise diagonally moving extensible patterns that stabilize the edges of some other type of agar -- either an oscillating agar, or an extensible series of waves (moving wicks), or perhaps an orthogonally symmetric stable pattern -- most likely the 'stripes' agar.

It may also be possible to construct extensible multi-tubstretcher and multi-tubeater spaceships that support this agar -- where each stretcher or eater is connected directly to the next one, and can't be separated -- but this has not been accomplished as yet. Multistretchers and multieaters with wider spacings have been previously posted, however. Tubstretcher-based patterns composed of more than 1/3 ON cells are not possible. Thus, to produce a diagonal greyship that maintains a 1/2-ON agar, it would be necessary to devise diagonally moving extensible patterns that stabilize the edges of some other type of agar -- either an oscillating agar, or an extensible series of waves (moving wicks), or perhaps an orthogonally symmetric stable pattern -- most likely the 'stripes' agar.

However, since the stripes are not diagonally symmetrical, each of the edges would need a different type of support. Whether such a construction is possible is currently an open question. The main problem is that diagonal spaceships could not repeat at period 4, because each stripe is two cells away from the previous one -- so p8 spaceships would be needed.

Unfortunately p8 is not really within reach of currently available Life search programs (mainly David Bell's 'lifesrc' and Jason Summers' ' WinLifeSearch' port). Some fairly large leaps in efficiency and/or CPU speed would be needed to make this a likely goal. [Readers are, of course, invited to prove this statement wrong -- or to supply the necessary advances in search technology.]

new c/4 diagonal spaceships: Nicolay Beluchenko, 7 April 2006

front and back joints for a moving (c/4 diagonal) wick posted by

Hartmut Holzwart, producing a stabilized modular c/4 spaceship.

Nicolay Beluchenko, 21 March 2006

Hartmut Holzwart, producing a stabilized modular c/4 spaceship.

Nicolay Beluchenko, 21 March 2006

Here are separate commented files for Beluchenko's previous wave-based spaceships in this series, from 7 April 2006, posted last month in a combined pattern:

spaceship made with wave endsterminations for Hartmut Holzwart's second wave from March 2006

shorter front termination of Hartmut Holzwart's March wave

new wave composed of pieces of previously known waves

extensible signal that moves at

speed 2c/3 through 'stripes' agar,

at right angles to the stripes

Hartmut Holzwart, 24 April 2006

speed 2c/3 through 'stripes' agar,

at right angles to the stripes

Hartmut Holzwart, 24 April 2006

It was shown in 1993 that signals travelling parallel to the striped medium must move at the speed of light -- but it turns out that non-destructive signals perpendicular to the stripes are also possible, and these follow different rules. In particular, they can move at a speed of 2c/3 orthogonally, slower than lightspeed but faster than a spaceship can travel through vacuum.