Uniform Degree

The distribution of a finite number of points in a polygon is referred to as a pattern in this book. Aggregation and uniformity are two typical opposite features of a pattern. Based on the uniform degree defined in this context, a pattern with uniform degree zero, like a periodic orbit, is the most aggregate pattern and the uniform degree of any chaotic orbit must be greater than 0. For any segment of a chaotic orbit, it may behave in either an aggregate or a uniform way. However, its average uniform degree is invariant, which is the reason for measuring chaotic behaviour by the uniform degree. Based on this, the word “chaometry” has been invented, meaning the measurement of chaos. The uniform degree of the pattern generated by a distribution function F in a polygon is abbreviated as the uniform degree of a distribution function, denoted by L_F.