1. FRACTALS, AVERAGE DISTANCE AND THE CANTOR SET.
- Author
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LEARY, CHRISTOPHER C., RUPPE, DENNIS A., and HARTVIGSEN, GREGG
- Subjects
- *
FRACTALS , *CANTOR sets , *SELF-similar processes , *BETWEENNESS relations (Mathematics) , *DISTANCES , *ARITHMETIC mean - Abstract
The average distance between points of a fractal is proposed as a natural measure of the way in which the points of a fractal are distributed. The average distance between points of the Cantor Set is found to be $\frac{2}{5}$, the average distance between points of the Cantor p-set is $\frac{p+1}{p+3}$, and the average distance between points of the Fat Cantor p-set is $\frac{2}{3(2-p)}$. A general formula for computing the average distance between points of a self-similar set satisfying the open set condition is found. [ABSTRACT FROM AUTHOR]
- Published
- 2010
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