Abstract
Fractals which represent many of the sets in various scientific fields as well as in nature is geometrically too complicate. Then we usually use Hausdorff dimension to estimate their geometrical properties. But to explain the fractals from the Hausdorff dimension induced by the Euclidan metric are not too sufficient. For example, in digital communication, while encoding or decoding the fractal images, we must consider not only their geometric sizes but also many other factors such as colours, densities and energies etc.. So in this paper we define the dimension matrix of the sets by redefining the new metric.
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References
R. Cawley & R.D. Mauldin,Multifractal decompositions of Moran fractal, Adv. in Math.92 (1992), 196–236.
K. J. Falconer,Fractal Geometry, John Wiley & Sons (1990).
M. Munroe,Measure and Integration, Addison-Wesley (1971).
M. Reyes & C.A. Rogers,Dimensionprint of fractal sets, Mathematika41 (1994), 68–94.
L. S. Young,Dimension, entropy and Lyapunov exponents, Ergodic theory & Dynamical System 2 (1982), 109–124.
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This paper was partially supported by Korean Research Foundation, 1997.
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Kim, T.S. Dimension matrix of the G-M fractal. Korean J. Comput. & Appl. Math. 5, 13–22 (1998). https://doi.org/10.1007/BF03008932
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DOI: https://doi.org/10.1007/BF03008932