Fractals

Abstract

It would be an understatement to say that order and disorder are controversial notions. Who could claim that as a child they have never been described as ‘untidy’ or ‘disorganised’, whilst attempting to find something that an incensed mother has requested? Does this not imply that order is merely a question of personal appreciation? Hardly so. An objective approach to the problem is to ask whether there exists a rule by which the position of each thing (or the instant of each event) could be predicted. If the answer is affirmative, then there is no doubt that there exists an order. For the person who knows or discovers this rule, the apparent disorder is instantaneously dispelled by an organising principle. However, the definition of what is called order does not end here. What the irate mother is expecting of her offspring is just that the rule should be simple. This is not really the case in the example chosen. It is a fairly safe bet that the rule is limited to some kind of three-dimensional geographical index (in terms of longitude, latitude, and altitude) of all the objects in the room. The rule would thus be just as long as a list of all the objects (or, in other examples, of the succession of events). No indeed, what we expect of an ordered situation is that the rule should be short to state and simple to apply. A third property is also desired: the rule should suffer few exceptions. What would be the point in knowing a rule if it were always being violated?