I was reading on Complex Systems journal and found a paper where the author states that a cellular automaton can be viewed as a computer. In the introduction part:Cellular automata can be viewed as either computers or logical universes where computers may be embbed.What i am trying to understand is, is it always a given Cellular Automaton  is a computer ?  like Elementary Cellular Automata {ECA} rule 110 and rule 90, i know that rule 110 is universal which makes it a computer but what about rule 90 ... what about other ECA rules are they also computers ?Suppose we have a cellular automaton (x), how do we know that it is a logical universe (as stated by the author), how can we know if it is a logical universe where computers can be embedd in or not and how can we know if it is just a computer ?I know that logical universes are Cellular Automata, but what dimensions these universes should be to implement a computer easily, 1D like ECA or 2D like Conway's Game of Life ?
Are Cellular Automata always computers?
computation models;cellular automata
... is it always a given Cellular Automaton is a computer?...I interpret is a computer as being capable of universal computation or in other words being capable of simulating an arbitrary Turing machine.The answer is clearly NO; a trivial example is a CA that doesn't modify the input:0[0]0 -> 00[0]1 -> 00[1]0 -> 10[1]1 -> 11[0]0 -> 01[0]1 -> 01[1]0 -> 11[1]1 -> 1(rule 204)According to Wolfram's (qualitative) classification, only type-4 CAs exhibit a behaviour that can potentially be universal. But it is an informal statement (like many others in Wolfram's NKS) ... in order to say that a particular CA is/is not Universal you must prove it formally.For a more rigorous introduction to the argument I suggest you to read some research articles on the subject, for example: Kristian Lindgren, Mats G. Nordhal. Universal Computation in Simple One-Dimensional Cellular Automata. Complex Systems 4 (1990) 299-318Or - for a good, more general, introduction to computational universality - read Chapter 7: The Grand Unified Theory of Computation of the (IMO excellent) book:  Cristopher Moore, Stephan Mertens. The Nature Of Computation (2011)