FractalFusion wrote:I'm not sure what constitutes an acceptable level of math in this context. Does there have to be new results? Or rather, is it a survey of interesting things that have already been done, or is being studied?
There are umpteen research projects on my current backlog that have at least some mathematical component. It would be great if someone wanted to work on one of them:
-- Build the smallest-known glider guns for all periods from 14 to 999.
The glider gun GitHub project has everything pretty well organized, but the 'confirmed' folder doesn't actually contain an entry for each gun period. Quite a few still have to be constructed based on some simple adjustments to a template gun in the 'variable' folder.
-- Come up with a "one-time turner" toolkit equivalent to
Chris Cain's stable duplicator script. Stable duplicators are re-usable, but also fairly large and awkward; sometimes you just want to build a constellation of small still lifes that can be hit with a single glider to construct... well, any glider-constructible object, like a c/10 copperhead spaceship for example. Michael Simkin has a good collection of one-time turners and splitters, but the sorting and labeling hasn't been done to make it really easy to pick out a constellation with exactly the right timing for a specific purpose.
Like the previous item, this mostly just takes a lot of modulo-8 math, with the addition of some slightly brain-bending parity issues. To be specific: if you reflect a glider 180 degrees using a 90-degree color-preserving one-time turner combined with a 90-degree color-changing one-time turner, you can get two different output timings depending on which turner comes first (because the glider travels a half-diagonal farther in one case than the other).
-- The quadratically growing replicator made an appearance on codeholic's list. Of course that's a fairly large project (though it's a lot smaller than it used to be before
simeks' single-channel construction toolkit showed up.) It's fairly easy to break the project up into manageable pieces now, and just tackle one or two pieces.
For example, it's probably a good idea to start by finding four stable reflector circuits arranged in an adjustable-size diamond, so that 1) the total time around the loop is a power of two, or a small multiple of a power of two, and 2) loops in the same orientation will be separated by an exact power-of-two distance (or again, maybe a small multiple of a power of two, if it turns out to be too difficult to get an exact power of two both spatially and temporally).
The power-of-two obsession is just because Golly can simulate pure power-of-two repeating patterns a lot faster using the HashLife algorithm. Maybe that's kind of an arbitrary mathematical limitation to place on a replicator design -- but it sure will be impressive to watch it run, if it works out the way I hope it will!
If anyone is interested in picking up any of these projects, just let me know and I can provide more details. Or a longer list of ideas would be easy to generate, if that's any use...!
