Effect of asynchronous updating on the stability of cellular automata
Finally, Section 3.4 addresses ontological issues ranging from the sense in which CA count as modelling portions of reality, to the bold philosophical conjecture of some scientists, who claim that the physical world itself may be, at its bottom, a discrete, digital automaton. Think of an automaton as a one-dimensional grid of simple elements (the cells).Each of them can only instantiate one of two states; let us say that each cell can be turned .that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields.Firstly, CA are (typically) spatially and temporally .At each time unit, the cells instantiate one of a finite set of states.They evolve in parallel at discrete time steps, following state update functions or dynamical transition rules: the update of a cell state obtains by taking into account the states of cells in its local neighborhood (there are, therefore, no actions at a distance).Let us make the two following assumptions: : a student will wear the hat in the following class if one or the other—but not both—of the two classmates sitting immediately on her left and on her right has the hat in the current class (if nobody wears a hat, a hat is out of fashion; but if both neighbors wear it, a hat is now too popular to be trendy). The global, emergent behavior of the system supervenes upon its local, simple features, at least in the following sense: the scale at which the decision to wear the hat is made (immediate neighbors) is not the scale at which the interesting patterns become manifest.This example is a paradigmatic illustration of what makes CA appealing to a vast range of researchers: and the micro-macro interplay have such an important role in science and philosophy (see the entries on supervenience and emergent properties; for a sample of scientific applications, see Mitchell 2009: 2–13; Gell-Mann 1994: Ch.
Each box stands for a student wearing (black) or not wearing (white) a hat. The evolutionary pattern displayed contrasts with the simplicity of the underlying law (the “Hat rule”) and ontology (for in terms of object and properties, we only need to take into account simple cells and two states).Much has been said over the course of philosophical history about each of these.Yet inevitably it has been informed only by current intuitions about how things are supposed to work.Sections 2.2–2.3 explain the classification of one-dimensional CA proposed by Stephen Wolfram.Section 2.4 introduces the Edge of Chaos hypothesis, a key CA-related conjecture in complexity theory.