Can randomness alone tune the fractal dimension?

M.k Hassan and J Kurths

Physica A: Statistical Mechanics and its Applications, 2002, vol. 315, issue 1, 342-352

Abstract: We present a generalized stochastic Cantor set by means of a simple 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.

Keywords: Cantor set; Statistical physics; Fractal; Self-similar; Randomness and complexity; Scaling (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:315:y:2002:i:1:p:342-352

DOI: 10.1016/S0378-4371(02)01242-6

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