Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Characterizations of the structures generated in these classes are discussed. Three classes exhibit behaviour analogous to limit points, limit cycles and chaotic attractors. The fourth class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable.
Stephen WolframRelated topics
automaton cellular chaotic complex computation fall four simple three universal universality pointsRelated quotes
If we want to postulate a deity capable of engineering all the organized complexity in the world, either instantaneously or by guiding evolution, that deity must have been vastly complex in the first place. The creationist, whether a naive Bible-thumper or an educated bishop, simply postulates an already existing being of prodigious intelligence and complexity. If we are going to allow ourselves the luxury of postulating organized complexity without offering an explanation, we might as well make a job of it and simply postulate the existence of life as we know it!
Richard Dawkins
About mid-day, Kesselring telephones me and tells me that we shall probably have to wait three or four days before our large-scale counter-measures begin to get under way. Until then there can be no major shift of developments in our favour. Kesselring is nevertheless in good heart. He is assured and full of character in his estimate of the situation and there is not a trace of defeatism with him. He tells me also that the attitude of the civil population has somewhat improved under the influence of our propaganda.
Albert Kesselring
Complex organisms cannot be construed as the sum of their genes, nor do genes alone build particular items of anatomy or behavior by themselves. Most genes influence several aspects of anatomy and behavior-as they operate through complex interactions with other genes and their products, and with environmental factors both within and outside the developing organism. We fall into a deep error, not just a harmful oversimplification, when we speak of genes "for” particular items of anatomy or behavior.
Stephen Jay Gould
This great increase of the quantity of work which, in consequence of the division of labour, the same number of people are capable of performing, is owing to three different circumstances; first, to the increase of dexterity in every particular workman; secondly, to the saving of the time which is commonly lost in passing from one species of work to another; and lastly, to the invention of a great number of machines which facilitate and abridge labour, and enable one man to do the work of many.
Adam Smith
Virtually the entire inflow was therefore Asiatic, and all but three or four thousand of that inflow originated from the Indian subcontinent... It is by 'black Power' that the headlines are caught, and under the shape of the negro that the consequences for Britain of immigration and what is miscalled 'race' are popularly depicted. Yet it is more truly when he looks into the eyes of Asia that the Englishman comes face to face with those who will dispute with him the possession of his native land.
Enoch Powell