Estimate the shortest paths on fractal m-gons |
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| Authors: | Mohamed Mubarak |
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| Institution: | 1. School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW 2052, Australia;2. School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney, NSW 2006, Australia;3. School of Photovoltaic and Renewable Energy Engineering, University of New South Wales, Sydney, NSW 2052, Australia;1. School of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China;2. School of Mathematics and Statistics, Shandong Normal University, Ji''nan 250014, Shandong, China |
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| Abstract: | The self-similar sets seem to be a class of fractals which is most suitable for mathematical treatment. The study of their structural properties is important. In this paper, we estimate the formula for the mean geodesic distance of self-similar set (denote fractal m-gons). The quantity is computed precisely through the recurrence relations derived from the self-similar structure of the fractal considered. Out of result, obtained exact solution exhibits that the mean geodesic distance approximately increases as a exponential function of the number of nodes (small copies with the same size) with exponent equal to the reciprocal of the fractal dimension. |
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