## Definition of "Cellular Automata"## Cellular AutomataCellular automata have their origin in systems described by [John von Neumann] and [Stanislaw Marcin Ulam] in the 1940s.Cellular automata are - by definition - dynamical systems which are discrete in space and time, operate on a uniform, regular lattice - and are characterised by "local" interactions.
## BroadeningIn more recent times there has been some interest in similar cellular systems which are aperiodic - or are spatially non-uniform.One possibility is that the term "cellular automata" could be broadened to include these new systems. Another is that a new category be proposed that includes these dynamical systems. I propose the name "local automata".
## For broadeningThe word "cellular" does not immediately suggest a system of cells where all the cells are necessarily identical - and consequently its current technical use is misleading and counter-intuitive.The term "cellular automata" was created before there was any significant understanding of the importance of non-uniform cellular automata - and before aperiodic tilings were well-known. If the term had been assigned in more modern times, it seems likely that aperiodic tilings would not have been neglected in the definition. The current usage doesn't "carve nature at the joints". The non-uniform and aperiodic systems under discussion share so much with cellular automata that it makes little sense to place them in a separate category.
Those involved in working with discrete non-uniform
cellular systems generally call them "non-uniform
cellular automata". Similarly those developing
discrete aperiodic cellular systems call give them
names like "cellular automata on a quasi-crystal" and
"cellular automata on Penrose tiles". They do this
In fact non-uniform cellular systems are all cellular
automata under today's definition A broadening of the term would simply be a reflection of modern usage.
## Against broadeningThe proposed redefinition no-longer results in a clear division between dynamical systems which are cellular automata and those that are not. Being a cellular automata becomes a matter of degree - since practically all discrete systems exhibitsome degree of
locality - in that the maximum distance a signal
travels in any time step is rarely the same as the
maximum distance between any two components.It makes the term "cellular automata" less specific - and thus less useful - just to include a few rare cases that hardly anybody is interested in anyway. Practically everyone deals with local, uniform systems. The term should reflect the most common usage.
The term is too-well established by historical usage to
think about changing it at this stage - and attempts to
do so would just cause confusion. The term "
## Okaay... but what do you
I am in favour of broadening the term. |