Tag: real space renormalization
R. Hilfer, A. Blumen
in: Fractals in Physics
edited by: L. Pietronero and E. Tosatti
Elsevier Publishing Co., Amsterdam, 33 (1986)
submitted on
Thursday, July 11, 1985
We construct deterministic fractal lattices using generators with tetrahedral symmetry. From the corresponding master equation we determine the spectral dimension d and prove that d<2. Furthermore we extend our set of fractals (with d dense in [1,2]) by direct multiplication, thus obtaining fractals whose d are dense for all real numbers larger than or equal to 1 .
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R. Hilfer, A. Blumen
J.Phys.A: Math. Gen. 17, L783 (1984)
https://doi.org/10.1088/0305-4470/17/14/011
submitted on
Monday, July 9, 1984
We introduce and investigate new classes of Sierpinski-type fractals. We determine their fractal and spectral dimensions using renormalisation procedures and, for particular classes, we give these dimensions in closed form. The spectral dimensions densely fill the interval [1,2], allowing us to choose flexibly models for applications.
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R. Hilfer, A. Blumen
Journal of Physics A: Mathematical and General 17, L573-L545 (1984)
10.1088/0305-4470/17/10/004
submitted on
Friday, April 13, 1984
We present a family of deterministic fractals which generalise the d-dimensional Sierpinski gaskets and we establish their order of ramification and their fractal and spectral dimensions. Random walks on these fractals are renormalisable and lead to rational, not necessarily polynomial, mappings.
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