Research progress & Grandfather problem

[voris]

Hello, I am writing an essay about Game of Life and I could use some help regarding the following two questions:

1) Is there a summary of important Life discoveries? Some milestones of research progress till today?
2) Has The Grandfather Problem described by Conway in Lifeline issue 6 ever been solved?

Thanks in advance.

[Extrementhusiast]

Let's start with the second question first. The grandfather problem has not been solved yet, even after about 40 years, as far as I know. As for the first question, here are a few landmarks, with their significances:

• Bill Gosper's p30 glider gun; first infinite growth pattern
• Breeder 1; first infinite growth pattern with superlinear growth
• "Garden of Eden 1"; first pattern with no "father"
• 25P3H1V0.2; first spaceship found, other than the standard four (glider, LWSS, MWSS, HWSS)
• Sawtooth 1212; first such pattern to be constructed
• 13-engine Cordership; first such ship to be found (now there are at least six)
• Herschel conduits; essentially the basis of most circuitry systems
• Bistable switch; useful in circuitry
• Paul Callahan's original stable reflector; first such pattern
• Boojum reflector; first stable reflector to reflect a glider 180 degrees
• Caterpillar; first pattern with a very large population
• Lidka; longest-lasting methuselah not found by the current and ongoing Soup Search (?)
• And, of course, the Gemini; the first knightship and the slowest spaceship found to date

I may have included some relatively unimportant patterns and left out some relatively important patterns, but I hope this answers your question.

[Sokwe]

Some corrections to that list:

• 25P3H1V0.2 was not the first spaceship found after the glider and standard spaceships. Some spaceships based on the standard spaceships were found in the 1970's (such as the Schick engine). The first spaceships found that were not based on the standard spaceships were period-2 and included 64P2H1V0. 25P3H1V0.2 was the first spaceship found that traveled at a speed other than c/2 orthogonal or c/4 diagonal. The period-2 and period-3 spaceships were found by Dean Hickerson.
• There are an infinite number of known corderships due to the various combinations of switch engines. The first one, the 13-engine cordership, was found by Dean Hickerson.
• The Boojum reflector was not the first 180-degree stable reflector (Paul Callahan's original reflector was capable of this); however, it was the smallest and fastest stable reflector until the discovery of the rectifier by Adam P. Goucher. The Boojum reflector was found by Dave Greene.
• The caterpillar is more than just a large pattern. It is the a unique spaceship that was built based on a few simple reactions. It was primarily built by Gabriel Nivasch and Jason Summers with David Bell.
• Andrzej Okrasinski found a 20x20 pattern that lasts for 35201 generations (see here). Lidka is much smaller, however. The current record holder for 20x20 patterns, Fred, was found by 'Schneelocke' using Nathaniel Johnston's soup search (it lasts for 35426 generations).
• Gemini is not a knightship in the strictest sense; however, Dave Greene used the gemini template to create the first true knightship. The original gemini was built by Andrew J. Wade.

Some specific important patterns (discoverer and date in parentheses):

• Gospe glider gun - first known infinite growth patter (Bill Gosper, 1970)
• breeder 1 - the first pattern with superlinear growth pattern (Bill Gosper, early 1970's)
• Garden of Eden 1 - the first Garden of Eden (Roger Banks, 1971) Current smallest Gardens of Eden were found by Nicolay Beluchenko (2009-2010)
• caterpillar - an enormous 17c/45 orthogonal spaceship (Gabriel Nivasch and Jason Summers with David Bell, December 31, 2004)
• gemini - the first method of creating arbitrarily-slow spaceships as well as the obliquely-traveling spaceship (Andrew J. Wade, May 2010).

Some types of patterns that are considered important:

• New spaceship speeds (c/4 diagonal discovered by Richard Guy; c/2 orthogonal discovered by John Conway; c/3, c/4, and 2c/5 orthogonal and c/12 diagonal by Dean Hickerson; c/5 orthogonal by Tim Coe; c/5 diagonal by Jason Summers; 2c/7 orthogonal by David Eppstein; c/6 orthogonal by Paul Tooke; 17c/45 by Gabriel Nivasch and Jason Summers with David Bell; c/6 diagonal by Nicolay Beluchenko; Arbitrarily slow spaceships by Andrew J. Wade)
• stable technology (originally developed by David Buckingham with his herschel loops which facilitated all oscillator periods above 60 and all gun periods above 61 - see here and here)

Some significant open problems:

• Prove or disprove the omniperiodicity of Life (periods of 19, 23, 34, 38, 41, 43, and 53 are still unknown)
• The grandfather problem
• Find a Life replicator (that creates multiple copies of itself i.e. not gemini)
• Prove or disprove the existence of a still life whose only predecessor is itself

There are many more important patterns and topics that I didn't get into. It takes a while to get familiar with all that has been done. Try starting with the links here. Also, the wiki is the most comprehensive guide to Life topics (it is still missing a lot, however). If you're looking for some pattern collections, try the ones here. For running Life patterns you should use Golly.