Determinism is a core characteristic of elementary cellular automata. Once the initial seed condition and ruleset are selected, the automaton runs and generates the same pattern time after time.
Another characteristic is that the outcome of many of the generated patterns can not be predicted ahead of time. While some of the rulesets, such as Ruleset 001, generate simple patterns that can be predicted, many of the rulesets generate complex or random patterns which cannot be predicted, i.e. there is currently no way to calculate the state of the cells in the 200th row of a pattern generated by a complex ruleset. The only way to determine the state of that row is to run the automaton. Taken together, this means that even before the pattern is generated, the state of cells is established. We may not be able to know the state of the 200th row until we run the automaton, but the states of those cells has been established by the rules of the system.
An idea that comes out of the study of cellular automata is that a simple-rule system is all that is needed to generate something as computationally complex as the universe. The next conceptual jump is that a simple-rule system such as an elementary cellular automaton is generating the complexity of the universe. The first proposition has been pretty much proven. The second proposition is conjecture. If this second proposition is accepted, the inevitable conclusion is that the universe is deterministic and the future is predetermined.
In very human terms, this means that life is guided by fate and the idea of free will has no meaning. Wolfram addresses this in A New Kind of Science by focusing on the unpredictably of simple-rule systems.
"For even though the underlying laws for this system are perfectly definite, its overall behavior ends up being sufficiently complicated that many aspects of it seem to follow no obvious laws at all.
"And indeed if one were to talk about how the cellular automaton seems to behave one might well say that it just decides to do this or that—thereby effectively attributing to it some sort of free will."
A New Kind of Science. p. 750
This way of defining free will is echoed in this paper by Seth Lloyd: "I argue that this intrinsic computational unpredictability of the decision making process is what give rise to our impression that we possess free will."
In short, they are saying that free will is the appearance of making a choice. Even though the outcome of the next step is already established, our inability to predict the outcome is what we call free will.
This definition does not seem to square with what the generally accepted meaning of free will. The first sentence of the Stanford Encyclopedia of Philosophy article states that free will "is a philosophical term of art for a particular sort of capacity of rational agents to choose a course of action from among various alternatives." If we, as rational agents, are able to choose a course of action, that means the outcome is not predetermined. Our actions do not originate from an appearance of unpredictability. They are unpredictable.
In elementary cellular automata, there are two alternatives — active or passive. Taken to extreme, the ability "to choose a course of action" suggests that rather than each rule in a ruleset generating the same active or passive state in the target cell each and every time, the state of the target cell is based on random selection like the flip of a coin. So if fate is characterized by a fully predetermined system, then free will is the expression of a fully randomized one.
This is an unsettling conclusion because it points to an existence where the state of things in the past have no effect on our actions now. In this state, there is only the appearance of order.
These become two sides of the same argument. In the first case, the state of any cell is pre-ordanined. In the second, even though the state is not ordained, the mechanism of choosing is pre-determined. This doesn't address the question of free will. A completely randomized mechanism lasks the essense of free will: the ability of a cell to choose its state, or at least have a direct influence over its state.
How, then, can free will enter into such a model as cellular automaton? Or, what is "agency" of free will and how does it work?