Papers

DETERMINATION OF FRACTAL DIMENSION OF THE CLASSICAL TRIADIC CANTOR SET AND STOCHASTIC CANTOR SET USING MONTE-CARLO SIMULATION AND COMPARISON WITH ANALYTICAL SOLUTION (Pages : 5 - 8)

A. NOBI, M. B. HOSSAIN, M. ZAMIL SULTAN, M.F. KIBRIA AND M. SAZZADUR RAHMAN

Fractal dimension of the classical triadic Cantor set is determined using Monte Carlo simulation in which an interval [0, 1] is fragmented into three equal parts and the middle one is deleted every time from each segment. Fractal dimension of the triadic Cantor set was found 0.630. The fractal dimension of stochastic Cantor set in which the interval is fragmented into three equal parts but deleted randomly, varies from 0.65 to 0.68 at probability 1 and increases with decreasing probability. In addition, a general comparison of the fractal dimensions of the stochastic Cantor set in different probabilities is presented in this study.Download


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