The Fractal Modelling of Evolution of the Organized Structures in Geology


Authors: Prudil V

Published in: Bulletin of Geosciences, volume 75, issue 4; pages: 427 - 431;

Keywords: banded rocks, box-counting method, fractal dimension, fractals L-systems,

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This is a study of fractal properties of banded rocks. The theory is based on the fact that the patterns formed by bands can be divided into more parts, each of which is to a certain degree a reduced copy of the whole unit. The variable which shows most about the shape properties of any fractal is called fractal dimension. The formulas for fractal dimension calculation are shown in the study. The so-called L-systems appear to be very convenient fractal types for natural structures modelling. Their construction is based on repetitional geometrical transformation of a single shape. There are four simple deterministic L-systems simulating the development of the bands. Calculated fractal dimension is related to the percentage of dark and light components in the banded rock profile. By using fractal geometry, it is possible to describe not only morphological properties of natural fractals, but also the spatial development of such natural structures can be simulated.