Disk and Box Dimensions: Selected Case Studies of Fractals with Ifs Codes

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Author(s) Salau, T. A.O. | Ajide, O.O.
Pages 234-247
Volume 1
Issue 5
Date May, 2012
Keywords Fractal, Fractal Dimension, IFS Codes, Monte Carlo
Abstract

Six (6) fractals with IFS were identified from literature. Algorithms (coded in FORTRAN) based on Monte Carlo approach was developed for disk and box count methods. Common factors to all studied fractals are seed value for random number generation (9876), start coordinates (1,0.5), transient solutions (1000), steady solutions (5000), total number of corresponding scale of examinations (20) and ten (10) trial times. The FORTRAN programme computes both transient and steady solutions of fractals with IFS, Estimated dimension and other relevant quantities of this study while graphs were plotted using Microsoft office Excel 2003. Programming for the disk overlay is less skill demanding than box overlay as experienced from this study. Estimated dimensions vary from transient to steady for cases. Dimension variation transient from lower dimension value to higher steady dimension value except for some cases investigated with box method. Estimated disk dimension was consistently on the lower side of actual dimension with absolute relative error (%) range of 0.5 to 19.6 for cases. Similarly 66.7 percent of estimated box dimensions were on the lower side of actual dimension with absolute relative error (%) range of 0.9 to 17.2 for cases. The average absolute error (%) for disk and box methods was 6.7 and 6.8 respectively. Actual dimension was sandwiched between estimated disk dimensions and box dimensions in 33.3% for cases. Preference can be given to use of disk count method for solving fractal dimension problems for its capability to estimate fractal dimension consistently and the fact that the method is averagely less error prone compared with box method.

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