Dear fellows,
We are studying possible extensions of Game of Life (GoL) to larger neighbourhoods.
Up to now we have just tried with Moore neighborhood with r=2 (is to say, counting 8+16 = 24 nearest neighbours) and we have found a set of rules that produce similar behaviour, i.e. 1) no unbounded growth + 2) blinkers, gliders and stable clusters emerge (and also an interesting cluster that orbits around a point. We called it “dog” or “orbiter”).
(A video showing it can be seen in a project that we created recently: “Mysteries of Game of Life”).
It seems likely that many equivalent GoLs can be found for different neighbourhoods (in square grids). Do you know about some results regarding this question?
Probably similar research has been conducted by others. Are you aware of some published material in this direction?
Thanks
There is an acceleration technique using
hash tables for game of life.
https://en.wikipedia.org/wiki/Hashlife
It reminds me of the speedup theorems in Turing machines.
https://en.wikipedia.org/wiki/Linear_speedup_theorem
Regards,
Joachim
There is a book dedicated to the study of Game of Life: Game of Life Cellular Automata edited by Adamatzky (2010).
http://www.springer.com/us/book/9781849962162
Dear Joachim, Vladimir and Antony
Thank your your interesting comments.
As Vladimir pointed out a possible extension is to "extrapolate" GoL to hexagonal grids...
another option would be to do it in 3D square grids as in: C. Bays “Candidates for the Game of Life in Three Dimensions,” Complex Systems, 1 (1987) 373–400.
We were searching for extensions in 2D square grids but counting different number of neighbours.
You were right Antony. In the book (Adamatzky) some related papers are cited:
S. Adachi, J. Lee, F. Pepera and H. Umeo. Kaleidoscope of life: A 24-neighbourhood outer-totalistic cellular automaton. Physica D 237 (2008) 800–817
However in that CA there is a difference:
"...a cell becomes or stays alive if the number of living cells in its neighborhood is 4; otherwise the cell dies or remains dead ... Unlike in the Game of Life, a cell’s state itself is irrelevant to its next state (The rule is inner-independent)"
they cited also this one:
Evans, K.M.: Larger than Life: threshold-range scaling of Life’s coherent structures. Physica D 183, 45–67 (2003)
there is a lot of info there and in there references therein.
Thanks
An example of how the area "visited" by Kaleidoscope of Life grows...
I have also worked on a similar project, create behavioral metrics, which I have used to find other Automata cellular (CA) similar to the GoL, in 2D with the same neighborhood of GoL and I have approximately 1000 CA, where I have found gliders and a self-replicating CA group.
You can read my work in this papers https://www.researchgate.net/publication/269417091_Search_of_Complex_Binary_Cellular_Automata_Using_Behavioral_Metrics, if you are still interested, we can find a way to collaborate, I am passionate about this project.
Extending my work and looking for Cellular Automatas with r = 2 similar to GoL theoretically is not complicated, the challenge is in the implementation to improve the algorithms and implement them in CUDA.
Dear Juan Carlos,
Thank you for your answer.
And yes, sure, we could collaborate
Just curiosity
Did you find easy extensions of Game of Life in 3D?
Best
The very best GoL software is obtained here:
http://golly.sourceforge.net/
Golly supports GoL, WireWorld, Von Neumann, and a good number of other cellular spaces. Further, Golly is easily extended to support other systems of cellular automata, and the developers are very active, and wonderfully supportive of users of their tools.
I recommend that you do your work on top of Golly.
Following Daniel Dennett's insistence (in his amazing 1991 paper "Real Patterns") that "every philosophy student should be held responsible for an intimate acquaintance with the Game of Life", I have used the lovable little cellular automata of Conway's Game of Life in at least two published philosophical arguments:
Article Choosing between the Long and Short Informational Routes to ...
Article Can Pragmatists Believe in Qualia? The Founder of Pragmatism...
My concerns as a philosopher no doubt differ from yours. Still, I hope you will enjoy...
Cheers!
Marc
It's been a while since you asked the question, but since it was recently revisited, you can check:
- Stephan Rafler's "SmoothLife"
- Bert Chan's "Lenia"
interesting attempts to extend GoL to larger neighborhoods and a continuous state space.
Thanks Marc and Nikolaos for your comments
Marc, I will check your papers, thanks
Our original interest in Game of Life was somewhere "philosophical". the question was: - Can Game of Life model brain dynamics?
https://www.mdpi.com/2297-8747/23/4/75
Nikolaos, very very interesting this Smooth Life and Lenia extensions
(links to the papers for those interested)
Article Generalization of Conway's "Game of Life" to a continuous do...
Preprint Lenia - Biology of Artificial Life
thanks a lot
best
A
To Marc Champagne:
The argument for knowing GoL must be based upon the notion that a similar knowledge of von Neumann's 29-state CA is implausible, since vNCA are "just too hard to understand."
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