Fractals and the analysis of growth paths |
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Authors: | Michael J Katz Edwin B George |
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Institution: | (1) Neurobiology Center and Department of Biometry, Case Western Reserve University, 44106 Cleveland, OH, USA |
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Abstract: | A simple practical method exists for classifying and comparing planar curves composed of connected line segments. This method
assigns, a single numberD, the fractal dimension, to each curve.D=log(n)/log(n)+log(d/L)], where:n is the number of line segments,L is the total length of the line segments, andd is the planar diameter of the curve (the greatest distance between any two endpoints). At one end of the spectrum, for straight
line curves,D=1; at the other end of the spectrum, for random walk curves,D→2. Standard statistics are done on the logarithms of the fractal dimension log(D)]. With this measure, trails of biological movement, such as the growth paths of the cells and the paths of wandering organisms,
can be analyzed to determine the likelihood that these trails are random walks and also to compare the straightness of the
trails before and after experimental interventions. |
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