Purchase this article with an account.
E. G. Anjos, M. B. M. Mendonca, F. Orefice; Retinal Vessels, "To Be or Not To Be" Fractal? Log-Log Plots Are Invalid Paradigms of "The Fractal Geometry of Nature". Invest. Ophthalmol. Vis. Sci. 2010;51(13):6441.
Download citation file:
© ARVO (1962-2015); The Authors (2016-present)
"Everything is fractal", one could conclude from the thousandsof articles daily devoted to prove the "fractality" of almostall kind of phenomena. Accordingly, recent articles state thatthe retinal vasculature is fractal because log-log graphs ofsize in function to scale fit to a straight line, indicatingcompliance with a power law. Likewise, such fit to a straightline on log-log graphs has been used as a paradigm of "fractality"in different areas of knowledge. The aim of this study was totest the value of the log-log graphs as a paradigm of "fractality".
The log-log graphs of size in function to scale for the retinalvasculature of thirty normal subjects were compared with thesimilar graphs for non-fractal images and for pictorial representationsof well-known fractals. The range of scales used was 2 to 468pixels (about 2 decades) for vasculature images with 936 x 936pixels, the same range of scales utilized in the vast majorityof articles concerning fractal geometry of natural objects andphenomena.
Similar fit to a straight line and similar local slopes variabilitywas observed for the three groups of images, as showed in figs1and 2.
Compliance to power laws as tested by examining the log-loggraphs, within the range of scales largely utilized in the scientificliterature, having no value to prove "fractalness" and no valueto refuse "fractalness", have no value as a paradigm for testingthe "fractality" of the retinal vasculature and of no finiteset. Almost all scientific literature concerning fractal geometryof natural objects and phenomena are based in an invalid paradigm.
This PDF is available to Subscribers Only