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Temperature


The "temperature" of a curve Gamma is defined as

 T=1/(ln((2l)/(2l-h))),

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

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References

Mendès-France, M. "Entropie, dimension et thermodynamique des courbes planes." In Seminar on number theory, Paris 1981-82 (Paris, 1981/1982) (Ed. M.-J. Bertin). Boston, MA: Birkhäuser, pp. 153-177, 1983.Pickover, C. A. Keys to Infinity. New York: Wiley, pp. 164-165, 1995.

Referenced on Wolfram|Alpha

Temperature

Cite this as:

Weisstein, Eric W. "Temperature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Temperature.html

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