muzik wrote:Have any more intuitive and easier to understand notations for non-isotropic non-totalistic rules been invented? I've been thinking of making some but I'm not the best at that kind of stuff.
You can't really boil down anisotropic rules to anything less than five hundred and twelve 1's and 0's, so it's kind of hard to figure out how to make that intuitive or easy to understand.
And then MAP encoding just makes things harder. The base64 encoding doesn't line up with the natural boundaries of the data; you'd really want base 256 for that -- or base 16 would be pretty good, except you'd need 128 characters instead of 86 which is already painfully long.
The most intuitive thing I can think of would be a visual notation, something like what Stephen Wolfram uses in
A New Kind of Science and
mathworld.wolfram.com. That way you could directly look up the neighborhoods that correspond to each 1 and 0 in the 512-bit binary rulestring:
- The first sixteenth of a visual notation for MAP rules
- MapRuleVisualNotation.png (14.17 KiB) Viewed 10485 times
EDIT: Fixed a binary counting mistake in the diagram above and pattern file below.
The above is just a Golly screenshot of LifeHistory reversed with Ctrl+B, by the way -- you could complete the diagram with 30 more lines:
Code: Select all
x = 63, y = 13, rule = LifeHistory
3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B$BDB.BDB.BDB.BDB.BDB.B
DB.BDB.BDB.BDC.BDC.BDC.BDC.BDC.BDC.BDC.BDC$3B.2BC.BCB.B2C.C2B.CBC.2CB
.3C.3B.2BC.BCB.B2C.C2B.CBC.2CB.3C8$3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.
3B.3B.3B.3B.3B$BEB.BEB.BEB.BEB.BEB.BEB.BEB.BEB.BEC.BEC.BEC.BEC.BEC.BE
C.BEC.BEC$3B.2BC.BCB.B2C.C2B.CBC.2CB.3C.3B.2BC.BCB.B2C.C2B.CBC.2CB.3C!
It might be worth writing a script to generate this table automatically for whatever MAP rule is currently set in Golly. But then you'd have to come up with some way of showing the outcomes -- maybe just a single ON or OFF cell under each 3x3 grouping. (I just drew in the four sample +'s and x's by hand in Paint, but you could do that with custom icons in a custom rule, I suppose.)