Temperature

The ``temperature'' of a curve $\Gamma$ is defined as

$$T\equiv {1\over\ln\left({2l\over 2l-h}\right)},$$

where $l$ is the length of $\Gamma$ and $h$ is the length of the Perimeter of the Convex Hull. The temperature of a curve is 0 only if the curve is a straight line, and increases as the curve becomes more ``wiggly.''

See also Curlicue Fractal

References

Pickover, C. A. Keys to Infinity. New York: Wiley, pp. 164-165, 1995.