TAILIEUCHUNG - Stephen Wolfram - A New Kind Of Science Episode 3

Tham khảo tài liệu 'stephen wolfram - a new kind of science episode 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Starting from Randomness The Emergence of Order In the past several chapters we have seen many examples of behavior that simple programs can produce. But while we have discussed a whole range of different kinds of underlying rules we have for the most part considered only the simplest possible initial conditions so that for example we have usually started with just a single black cell. My purpose in this chapter is to go to the opposite extreme and to consider completely random initial conditions in which for example every cell is chosen to be black or white at random. One might think that starting from such randomness no order would ever emerge. But in fact what we will find in this chapter is that many systems spontaneously tend to organize themselves so that even with completely random initial conditions they end up producing behavior that has many features that are not at all random. The picture at the top of the next page shows as a simple first example a cellular automaton which starts from a typical random initial condition then evolves down the page according to the very simple rule that a cell becomes black if either of its neighbors arc black. What the picture then shows is that every region of white that exists in the initial conditions progressively gets filled in with black so that in the end all that remains is a uniform state with every cell black. 223 STEPHEN WOLFRAM I A NEW KIND OF SCIENCE n 3BBQiL3Bisi A cnllular automaton that m olvws to a simp unrform state when started been ary random mt sal condition Thn ru o m this case was first shown on page 24 and e numbix 254 in the sdhenw described on page 53 It specifies that a cell shculd become deck whenever either of 8 neighbors IS alreed Wack. The pictures below show examples of other cellular automata that exhibit the same basic phenomenon. In each case the initial conditions are random but the system nevertheless quickly organizes itself to become either uniformly white or uniformly black. .

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