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- W2007667989 abstract "Fractal objects which, by definition, are objects that have scale-invariant shapes and fractional scaling dimensions (fractal dimension) with magnitudes related to the complexity of the objects, are ubiquitous in nature. In particular, many biological structures and systems have fractal properties and therefore may be well studied and modelled using fractal geometry. In the box counting algorithm, one of several different approaches to calculate the fractal dimension, one determines, for several values of?, the number of boxesN(?) with side length? needed to completely cover the studied object. IfN(?) andr are found to be related by the power law relationshipN(r) ~r ?D, whereD is the scaling dimension, and ifD is a non-integer, then the object is fractal andD is the fractal dimension.In certain circumstances in which one may need to calculate the fractal dimension of a three-dimensional fractal from a two-dimensional projection (e.g. an X-ray), a new mathematical relationship may be utilized to obtain the actual dimensionD; it readsD=?log[1?(1?R 2? D p) R ]/logR + 3, whereD p is the fractal dimension of the two-dimensional planar projection of the object andR is the box size used in calculating the box-counting dimension.Fractal dimension calculations have been found to be particularly useful as quantitative indices of the degree of coronary vascularity and the degree of heart interbeat interval variability. Fractal growth models such as diffusion limited aggregation (DLA) can be used to model artery growth.To sum up, fractal geometry is very useful in studying and modeling certain scale-invariant biological structures or systems which may not be easily described with Euclidean shapes." @default.
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- W2007667989 date "1995-06-01" @default.
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- W2007667989 title "Analysis and modeling of biological systems using fractal geometry" @default.
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- W2007667989 doi "https://doi.org/10.1007/bf02228815" @default.
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