FRACTALS, AVERAGE DISTANCE AND THE CANTOR SET
Authors:
- 1 September 2010
- journal article
- research article
- Published by World Scientific Pub Co Pte Ltd in Fractals
- Vol. 18 (03) , 327-341
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 [ ], the average distance between points of the Cantor p-set is [ ], and the average distance between points of the Fat Cantor p-set is [ ]. A general formula for computing the average distance between points of a self-similar set satisfying the open set condition is found.Keywords
This publication has 11 references indexed in Scilit:
- Clustering and conservation patterns of human microRNAsNucleic Acids Research, 2005
- Uses and abuses of fractal methodology in ecologyEcology Letters, 2004
- The Relative Success of Some Methods for Measuring and Describing the Shape of Complex ObjectsSystematic Biology, 1998
- Lacunarity analysis: A general technique for the analysis of spatial patternsPhysical Review E, 1996
- Spatial Point Pattern Analysis and Its Application in Geographical EpidemiologyTransactions of the Institute of British Geographers, 1996
- On the Minkowski measurability of fractalsProceedings of the American Mathematical Society, 1995
- Fractal dimension of vegetation and the distribution of arthropod body lengthsNature, 1985
- The Fractal Geometry of NatureAmerican Journal of Physics, 1983
- How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional DimensionScience, 1967
- Distance to Nearest Neighbor as a Measure of Spatial Relationships in PopulationsEcology, 1954