Abstract
The main exhibit in this paper is a stack of Cantor dusts that have identical fractal dimensions but differ violently from each other. Some look clearly fractal, while others look to the unassisted eye as filled intervals (they are said to be of low lacunarity), and others seem to reduce to the end points of a hollowed interval (they are said to be of high lacunarity). One of several quantitative measures of lacunarity is put forward, and the impact of low lacunarity fractals on modeling of nature is discussed.
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References
Evertsz, C.J.C. and Mandelbrot, B.B: Multifractal Measures. Appendix B to Chaos and Fractals by H-O. Peitgen, H. Jurgens and D. Saupe. New York, Springer, 1992, pp 849–881.
Family, F. and Vicsek, T.: Dynamics of Fractal Surfaces, Singapore: World Scientific, 1991.
Gefen, Y., Meir, Y, Mandelbrot, B.B., Aharony, A: Geometric Implementation of Hypercubic Lattices with Noninteger Dimensionality by Use of Low Lacunarity Fractal Lattices. Phy. Rev. Lett 50: 145–148, 1983.
Mandelbrot, B.B.: The Fractal Geometry of Nature. New York, W. H. Freeman, 1982.
Mandelbrot, B.B.: Plane DLA is not self-similar; is it a fractal that becomes increasingly compact as it grows? Physica A 191 95–107, 1992.
Peebles, P.J.E.: Principles of Physical Cosmology. Princeton University Press, 1983.
Pietronero, L.: The Fractal Structure of the Universe, Physics Reports 213 (No.6) 311–389, 1992.
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© 1994 Springer Basel AG
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Mandelbrot, B.B. (1994). A Fractal’s Lacunarity, and how it can be Tuned and Measured. In: Nonnenmacher, T.F., Losa, G.A., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8501-0_2
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DOI: https://doi.org/10.1007/978-3-0348-8501-0_2
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