A.K. Rochmatulloh, U.Z. Fawziah, S. Feranie, F.D.E. Latief
A self-similarity relationship to the fractal dimension of 3D pigeon-hole rock models has been obtained by applying the box-counting fractal dimension. Self-similarity is a characteristic of fractals which shows that fractals consist of similarly shaped parts at each scale and produced the same 3D fractal dimension. 3D pigeon-hole models with self-similarity principle in structure and substructure (level 0, 1, 2) were constructed. Nine 3D rock models were generated with the size of 210 × 210 × 210 pixels and porosity of 30%. For each complexity levels (0, 1, 2), the grains were varied to have a size (radius) of 6-10 pixels, 11-15 pixels, and 16-20 pixels. The average correlation coefficient of 3D fractal dimension results obtained for 3D pigeon-hole model similar with 3 different range of radius for level 0, 1, 2 is 0.921. Based on the level of pigeon-hole produced on the model, the fractal dimension is increases as level increases, and it is found consistent in each radius range. The avarage correlation coefficient of 3D fractal dimension obtained for 3D pigeon-hole model for level 0, 1, 2 in three diferent radius range is 0.990. Based on the radius range on the model, the fractal dimension is decreases as radius range increases, and it is found consistent in each level of pigeon-hole. As a conclusion, based on these result 3D pigeon-hole model can be considered as fractal rock model based on its self-similarity both in similary structure and substructure and its fractal dimension and grain shape model that close to rock grains. Regardless of the random distribution of the grain position, and the grain overlap condition in the modeling scheme. © 2019 Published under licence by IOP Publishing Ltd.
Physics Department, Faculty of Mathematics and Natural Sciences Education, Indonesia University of Education, jalan Dr. Setiabudi No 299, Bandung, 40154, Indonesia; Physics of Earth and Complex Systems, Faculty of Mathematics and Natural Science, Bandung Institute of Technology, Jalan Ganesha No. 10, Bandung, 40132, Indonesia
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