Hi!
Has anyone come across the problem of encoding an arbitrary q-state 2D 1-range cellular automaton in Conway's Game of Life? I'm very interested in this problem, because it's important in my research. I haven't found anything about it in the literature and I suppose that such a construction would require big macrocells, created out of many spaceships and similar structures and I'm completely unfamiliar with this craft.
If anyone has any idea about how to tackle this problem or where to seek advice, I will be very grateful for your information!
Thanks!
Marian Marek Kędzierski
Macrocells
Re: Macrocells
As far as I know there are only unit cells able for simulating arbitrary 2-state range 1 cellular automata. These are Megacells created by calcyman. Example pattern is here http://calcyman.awardspace.co.uk/life-m ... umarole.mc These Megacells are using stable circuitry and aren't using many spaceships (expect for differentiation of on/off states). But encoding arbitrary 2D cellular automata in Life is absolutely possible, even with larger neighborhoods, as Life is proven universal CA.
PS. I am also from Poland
If you have questions, you can PM me
PS. I am also from Poland
If you have questions, you can PM meFirst question ever. Often referred to as The Question. When this question is asked in right place in right time, no one can lie. No one can abstain. But when The Question is asked, silence will fall. Silence must fall. The Question is: Doctor Who?
Re: Macrocells
Actually, it's easy to see that there's no macrocell capable of handling a CA with arbitrarily many states — one macrocell and its associated neighborhood can only hold so much information at any given moment, so even if there's no reason one that can handle a variable number of states couldn't be built (indeed one that can simulate two "layers" of CGoL at once has been built), it must have a maximum number of supported states.
Presumably for a CA with any number of states, there *would* still exist a macrocell capable of handling it, but these should get successively bigger… at some point I suspect the overhang of macrocell equipment would even take over the initial advantage in size over an UC approach (though not in speed).
Presumably for a CA with any number of states, there *would* still exist a macrocell capable of handling it, but these should get successively bigger… at some point I suspect the overhang of macrocell equipment would even take over the initial advantage in size over an UC approach (though not in speed).
Re: Macrocells
I know about this problem, but it is possible to build large enough unit cell which can store up to, say, 10 bits of cell state. This will give 1024 possible states, which is more than Golly 256 state limit. Also, if cell will be sufficiently slow and will have enough number of inputs and outputs it will be able to simulate larger neighborhood (or make approach possible to implement in Golly - use 1 cell to encode more sub-states)
First question ever. Often referred to as The Question. When this question is asked in right place in right time, no one can lie. No one can abstain. But when The Question is asked, silence will fall. Silence must fall. The Question is: Doctor Who?
Re: Macrocells
Hi guys! Thank you a lot for your help! It was very valuable!