Multifractal cascade dynamics

Following up on this post, and the earlier post linked therein, see "Scaling in executive control reflects multiplicative multifractal cascade dynamics." Front. Physiol., 19 April 2012.Damian G. Stephen^1*, Jason R. Anastas² and James A. Dixon^2,3,4

 

"Self-organized criticality (SOC) purports to build multi-scaled structures out of local interactions. Evidence of scaling in various domains of biology may be more generally understood to reflect multiplicative interactions weaving together many disparate scales. The self-similarity of power-law scaling entails homogeneity: fluctuations distribute themselves similarly across many spatial and temporal scales. However, this apparent homogeneity can be misleading, especially as it spans more scales. Reducing biological processes to one power-law relationship [monofractal] neglects rich cascade dynamics. We review recent research into multifractality in executive-function cognitive tasks and propose that scaling reflects not criticality but instead interactions across multiple scales and among fluctuations of multiple sizes. [...]

"Executive control is a general phenomenon of biological systems whose explanation lies in generic principles of complexity, rather than specifically cognitive mechanisms (Van Orden, 2010). However, the evidence of scaling in executive control does not point simply to SOC-like dynamics. Like many other aspects of living systems (Ivanov et al.,2001; Plotnick and Sepkoski, 2001; Ihlen and Vereijken, 2010), executive control is better understood through multiplicative multifractal cascade dynamics."