Radius of Gyration

A function quantifying the spatial extent of the structure of a curve. It is defined by

$$R_g={\sqrt{\int_0^\infty r^2p(r)\,dr}\over 2\int_0^\infty p(r)\,dr},$$

where $p(r)$ is the Length Distribution Function. Small compact patterns have small $R_g$.

References

Pickover, C. A. Keys to Infinity. New York: Wiley, pp. 204-206, 1995.