## Quick Reference

An example of a curve having fractal dimension. Starting with an equilateral triangle, the middle third, *PQ*, say, of a side is replaced by the two lines *PR* and *RP* so that *P*, *Q*, and *R* form the vertices of a smaller equilateral triangle, with *R* outside the original enclosed region. This process is repeatedly applied to each line segment. The resulting ‘curve’ is the snowflake curve and has infinite length but encloses a finite area. Its fractal dimension is defined to be ln 4/ln 3, since each ‘edge’ of the curve contains four copies each of 1/3 size.

**Snowflake curve.** This is an example of a curve with fractal dimension ≠ 1.

*Subjects:*
Probability and Statistics.