We are accustomed to thinking of the dimensionality of space as being an integer number. Distance along a line is measured in one dimension, as position on a piece of paper is measured in two dimensions, and a point in space is measured in three dimensions. For IBM mathematician Benoit Mandlebrot, space can have fractional dimension in the study of fractals. Fractal plots can be seen in generated images in motion pictures and they find practical applications in the modeling of blood vessels and turbulence. Blood vessels form a fractal space. Mapped out, they fit in a three-dimensional space but they take up relatively little volume in our bodies. Like the population growth plots seen in chapter 13, the pattern of blood vessels seems infinitely repeatable as large arteries branch into increasingly smaller capillaries. However, there is a lower limit to the size of blood vessels while a mathematical model of a fractals repeats forever as we magnify its fractal space.
KeywordsComplex Plane Affine Transformation Iterate Function System Fractal Space Complex Point
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