Abstract
Each stage of the generation process for a fractal curve adds more length to the curve. A fractal curve generated through an infinite number of steps will have infinite length. It was demonstrated in Chapter 2 that the length of different fractal curves grows from one generation stage to the next at different rates. The rate of growth of the length of the fractal curve is the distinguishing feature of the curve. The central concept is that length and the size of the instrument used to measure it are related. The relationship turns out to be a power law (Mandelbrot, 1983): (y) is proportional to (x)d (3.1)
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© 1996 Springer Science+Business Media New York
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Bovill, C. (1996). The Fractal Dimension. In: Fractal Geometry in Architecture and Design. Design Science Collection. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0843-3_3
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DOI: https://doi.org/10.1007/978-1-4612-0843-3_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6918-2
Online ISBN: 978-1-4612-0843-3
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