### Multiscaled randomness: A possible source of 1/*f* noise in
biology

#### Jeffrey M. Hausdorff and C.-K. Peng

Phys Rev E 1996;54:2154-2157
We evaluate the possibility that the 1/*f* fluctuations
observed in many biological time series result simply from the fact
that biological processes have many inputs with differing time
scales. We present a stochastic model whose output is the summation of
multiple random inputs (i.e., different regulatory mechanisms). We
derive the conditions under which the model reproduces the complex
fluctuations and 1/*f* scaling observed in biological
systems. Simulations demonstrate that if model parameters are
unconstrained, the likelihood of generating 1/*f* noise is quite
small. Thus, while the model can be used to generate 1/*f*^{
beta } noise with various scaling exponents, it is
unlikely that the 1/*f* behavior observed in many biological
systems is due *only* to the fact that these systems are
regulated by many different inputs acting on different time
scales.

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