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- Title
Scale invariance in percolation theory and fractals.
- Authors
Éntin, M. V.; Éntin, G. M.
- Abstract
The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot transformation, leading to a fractal behavior of the percolation probability in the complex plane. The hierarchical chains of impedances, reducing to a nonlinear mapping of the impedance space onto itself, are studied. An infinite continuation of the procedure leads to a fixed point. It is shown that the number of steps required to reach a neighborhood of this point has a fractal distribution. © 1996 American Institute of Physics.
- Subjects
SCALING laws (Statistical physics); PERCOLATION theory; FRACTALS
- Publication
JETP Letters, 1996, Vol 64, Issue 6, p467
- ISSN
0021-3640
- Publication type
Article