Miscellaneous topics in Conway's Game of Life -- unfinished projects of all kinds and conditions

29 May 2005

2c/3 transceiver, Mark Minus One

What follows is the first draft of a Game-of-Life circuit with a new, faster type of signal -- two-thirds of the speed of light diagonally! This is a big improvement in signal speed. Even Jason Summers' light-speed 'telegraph' can theoretically approach only half the speed of light diagonally, and it is considerably more unwieldy even than this pattern, and harder to re-use. Besides the telegraph, the fastest repeatable diagonal signal was a simple glider, at c/4.

Input is a Herschel, output is a glider. For comparison purposes, an extra reference glider has been added near the input Herschel. Despite the horrific and unnecessary inefficiency of the Herchel-to-2c/3 converter, and the fact that the output glider is produced from a 'backward' part of the 2c/3-to-glider converter, the output signal still manages to catch up to the reference glider!

Nothing about this pattern is properly optimized. For example, there's no good reason for the input Herschel ever to travel north; the conduit delivering the sacrificial beehive to the key point of the 2c/3 transmitter is ridiculously long; and the four boojum reflectors had to be moved embarrassingly far to the northwest to get the timings to work out.

The stair-step diagonal Herschel conduit at the left edge of the pattern is an artifact of an old toolkit I put together a year or two ago, which allows a shotgun for a synchronized glider salvo (like the three closely-spaced gliders traveling northeast from this area) to be constructed relatively quickly, though at considerable cost in efficiency. This part of the pattern took me less than an hour to put together, but it should be possible to fit a shotgun that fires twice as quickly into less than half the space.

Mark Minus One 2c/3 transceiver  Dave Greene  29 May 2005

After some optimization on the transmitter, it will be possible to use this technology to build the world's first period-independent pseudo-Heisenburp device, which can absorb a glider and produce as many output signals as needed -- including a new glider with exactly the same path and timing as the original!

[Previous Heisenburp devices all require the input glider to be aligned to some particular period, or they fail catastrophically. On the other hand, these periodic patterns can be "true" rather than "pseudo" Heisenburp devices: they produce output signals without destroying, or even temporarily affecting, the input glider.]

The 2c/3 signal track was discovered by Dean Hickerson in March 1997; Noam Elkies came up with several ingenious recipes for getting a repeatable signal started in a 2c/3 track, early this year, after I came up with a convoluted way of getting a signal out of a 2c/3 track. Further optimization is no doubt possible at both ends...

Update: May 1, 2007 -- Finally got around to doing the optimization work; the results can be seen in the latest version of the Golly project, Golly 1.2. Run heisenburp.py in the Scripts folder (you need to have Python installed, but it will take you all of maybe five minutes, and it's worth it.)

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