Can randomness alone tune the fractal dimension?

Details Can randomness alone tune the fractal dimension? Can randomness alone tune the fractal dimension?

2002-01-16

arxiv.org/abs/cond-mat/0201273v1

Physics

Condensed Matter

Statistical Mechanics

6 pages 2-column RevTeX, Two figures (presented in the APCTP International Symposium on Slow Dynamical Processes in Nature, No

Scientific paper

10.1016/S0378-4371(02)01242-6

We present a generalized stochastic Cantor set by means of a simple {\it cut and delete process} and discuss the self-similar properties of the arising geometric structure. To increase the flexibility of the model, two free parameters, $m$ and $b$, are introduced which tune the relative strength of the two processes and the degree of randomness respectively. In doing so, we have identified a new set with a wide spectrum of subsets produced by tuning either $m$ or $b$. Measuring the size of the resulting set in terms of fractal dimension, we show that the fractal dimension increases with increasing order and reaches its maximum value when the randomness is completely ceased.

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