[math-fun] Conway's "Life" & Covid rule
According to wikipedia, "3. Any live cell with more than three live neighbors dies, as if by overpopulation." In retrospect, this appears to be a "social distancing" rule. In various generalizations of "Life" -- e.g., with different sets of rules, on different grid patterns -- e.g., hex, etc. -- are there other interesting versions of "Life" with (and without) "social distancing" rules?
Well, you need *some* rule that kills off cells. Otherwise once a cell becomes live it remains live forever, so there would be no motion (e.g. gliders), only spreading. Tom Henry Baker writes:
According to wikipedia,
"3. Any live cell with more than three live neighbors dies, as if by overpopulation."
In retrospect, this appears to be a "social distancing" rule.
In various generalizations of "Life" -- e.g., with different sets of rules, on different grid patterns -- e.g., hex, etc. -- are there other interesting versions of "Life" with (and without) "social distancing" rules?
in fact, Life Without Death (i.e. Life but where nothing ever turns off) is a pretty fun CA rule, which can do a fair amount of computation: http://tuvalu.santafe.edu/~moore/pubs/griff.html - cris
On May 10, 2020, at 12:30 PM, Tom Karzes <karzes@sonic.net> wrote:
Well, you need *some* rule that kills off cells. Otherwise once a cell becomes live it remains live forever, so there would be no motion (e.g. gliders), only spreading.
Tom
Henry Baker writes:
According to wikipedia,
"3. Any live cell with more than three live neighbors dies, as if by overpopulation."
In retrospect, this appears to be a "social distancing" rule.
In various generalizations of "Life" -- e.g., with different sets of rules, on different grid patterns -- e.g., hex, etc. -- are there other interesting versions of "Life" with (and without) "social distancing" rules?
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What about any live cell with more than *two* live neighbors dies (as an example of slightly more "social distancing" ? I seem to recall that Wolfram did a catalogue of a number of different variations; I don't recall if varying this rule was in his catalog. I could imagine different definitions of "neighborhood", different #'s of dimensions, non-orthogonal axes (e.g., hex), etc. In some of these variations, there may be zero 'nearest' neighbors, but the "interaction field" might extend a further distance. At 11:34 AM 5/10/2020, Cris Moore via math-fun wrote:
in fact, Life Without Death (i.e. Life but where nothing ever turns off) is a pretty fun CA rule, which can do a fair amount of computation: http://tuvalu.santafe.edu/~moore/pubs/griff.html
- cris
On May 10, 2020, at 12:30 PM, Tom Karzes <karzes@sonic.net> wrote: Well, you need *some* rule that kills off cells. Otherwise once a cell becomes live it remains live forever, so there would be no motion (e.g. gliders), only spreading.
Tom
Henry Baker writes:
According to wikipedia,
"3. Any live cell with more than three live neighbors dies, as if by overpopulation."
In retrospect, this appears to be a "social distancing" rule.
In various generalizations of "Life" -- e.g., with different sets of rules, on different grid patterns -- e.g., hex, etc. -- are there other interesting versions of "Life" with (and without) "social distancing" rules?
I just tried this rule (B3/S2, as opposed to the classic B3/S23) in Golly. Impressionistically, it is much less rich than classic Life. I ran several large random agars. They all "settled" inside 20 generations; the steady state consists of a sparse field of less than a dozen varieties of still-lifes and period-two oscillators; nothing manages to crawl more than five or six cells outward from the original rectangular boundary of the agar. All of the surviving objects are familiar from Life; they just happen not to depend on S3. I can't see anything novel. This does not preclude the possibility of engineering more interesting exotic objects under the modified rule. But I am guessing that spaceships will turn out to be impossible. (This is a challenge for anybody who is familiar with search programs to prove me wrong!) B3/S3 is similarly boring. B3/S34 takes much longer to settle, and the steady state features a novel period-16 oscillator, all of whose phases are pentominoes. On Sun, May 10, 2020 at 3:25 PM Henry Baker <hbaker1@pipeline.com> wrote:
What about any live cell with more than *two* live neighbors dies (as an example of slightly more "social distancing" ?
I seem to recall that Wolfram did a catalogue of a number of different variations; I don't recall if varying this rule was in his catalog.
I could imagine different definitions of "neighborhood", different #'s of dimensions, non-orthogonal axes (e.g., hex), etc. In some of these variations, there may be zero 'nearest' neighbors, but the "interaction field" might extend a further distance.
At 11:34 AM 5/10/2020, Cris Moore via math-fun wrote:
in fact, Life Without Death (i.e. Life but where nothing ever turns off) is a pretty fun CA rule, which can do a fair amount of computation: http://tuvalu.santafe.edu/~moore/pubs/griff.html
- cris
On May 10, 2020, at 12:30 PM, Tom Karzes <karzes@sonic.net> wrote: Well, you need *some* rule that kills off cells. Otherwise once a cell becomes live it remains live forever, so there would be no motion (e.g. gliders), only spreading.
Tom
Henry Baker writes:
According to wikipedia,
"3. Any live cell with more than three live neighbors dies, as if by overpopulation."
In retrospect, this appears to be a "social distancing" rule.
In various generalizations of "Life" -- e.g., with different sets of rules, on different grid patterns -- e.g., hex, etc. -- are there other interesting versions of "Life" with (and without) "social distancing" rules?
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participants (4)
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Allan Wechsler -
Cris Moore -
Henry Baker -
Tom Karzes