Can anyone tell me what these 128 rules are in the following paragraph? Are they the rules dominating Conway's automaton or other kind of rules like the whole universe rules that could be summarized as a pack of 128 rules?
Context:
In 1970, the Cambridge mathematician John Horton Conway created a computerised miniature universe on a two dimensional grid containing evolving cells, and called it the ‘game of life’. The cells survive or die according to the existence of an optimum number of other cells. John Von Neumann has even shown such cellular automata capable of selfreplication, as in real life, and his analysis of the mathematics of self-production is so accurate that it can be applied to the structure of DNA itself.Cellular automata, as they are called, have been described as new life forms, existing in a state somewhere between order and chaos. Stephen Wolfram has pointed out the similarities in their behaviour patterns to those in non-linear dynamics and has gone on to classify them into four universality classes. The system starts with an array of cells in one or more dimensions, each with a colour code to denote the steps at which the pixels change and evolve, according to a rule of dependence based on the cells’ existing colours and those of their neighbours, and the complex interaction becomes visibly manifest in repeating shapes or patterns. There appear to be a maximum of 128 independent rules, out of which even a few form extraordinary complex patterns which can be mathematically measurable. Some patterns are so complex that they can even simulate a Turing machine, a universal computer, which can compute equations for any structure or process in the universe. Simpler mechanisms can explain therefore the emergence of the diverse morphologies of plants and animals – the geometries of flowers, the fractal branching patterning of trees and lungs and the Fibonacci spiralling of shells.
(Art and Science by Sian Ede)
Generally speaking, rules in cellular automata are counted by simple combination formulas, depending on the setup and on restrictions imposed on the automaton. Since the setup and/or restrictions are entirely absent in the passage you have quoted, it is impossible to give a precise answer to your question. This number 128 is certainly special to one particular setup that the author means to refer to, and this number 128 will have nothing to do with other setups.
So, rather than trying to guess at a cellular automaton setup that gives 128 rules, I'll given an example of simple setup and how to count its rules.
The setup will be a 1-dimensional cellular automaton based on subdividing the line at the integers, each cell being a unit length subinterval bounded by a pair of adjacent integers. At a given moment of time each cell is in one of two states, "on" or "off". At a the next moment of time the state of a cell is updated, using an update rule that works locally, by considering only the state of a given cell--call it the "central cell"---and its two neighboring cells, three cells in all. The possible states of these three cells form a set of size $2^3=8$: "on-on-on", "on-on-off", "on-off-on", "on-off-off", and four more. The update rule assigns a new state to the central cell depending solely on which of the eight possible 3 cell states holds, at the current moment of time, for the central cell and its two neighbors. Thus, each update rule is a function from the set of three cell states to the set $\{\text{on},\text{off}\}$. In this example that makes $2^8 = 256$ rules.
Added later: Maybe this example leads to $128$ rules by a consideration of symmetry: if we interchange the states "on" and "off" there is no essential change in the behavior of the cellular automaton, and so the number of essentially different rules coming from this example is $256/2=128$. However, this is somewhat doubtful because often one thinks only about initial states with a finite number of "on" cells, which would break the symmetry.