Scaling

The underlying theme of the similarity dimension is the repeated subdivision of an object into smaller replicas of the original. Such subdivision is a form of scaling. Scaling here means to enlarge or reduce the representation of an object or pattern according to a fixed proportion or ratio, using facsimiles of the original. Chaos analyses almost always reduce or "scale down" the object, rather than enlarging it. The idea is to find out how certain results change as the length of the measuring device becomes smaller and smaller.
Suppose we take a straight line and chop it up equally into four identical smaller pieces. Each new piece is a miniature facsimile of the original line. In particular, each miniature replica is one fourth the size of the original. As represented by any one of these replicas, the original line then has been scaled down by a ratio of one fourth. The scaling ratio is the relative or fractional length of each new little piece.