The Fractal Picture of Health and Wellbeing
By Guy C. Van Orden, PhD
Guy C. Van Orden is a professor of psychology at the University of Cincinnati. He received his PhD in Psychology from University of California San Diego in 1984. His current research interests are complexity theory and nonlinear methods applied to problems of cognition and action. For more information about Guy Van Orden's research, please visit his University of Cincinnati faculty page.
A healthy heart beats in an aperiodic rhythm, not too regular or repetitive, and not too random or chaotic. The healthy rhythm lives between those extremes, exhibiting a pattern of fractal variability. Loss of fractal variability signals heart disease, pathological dynamics of the heart. In congestive heart failure, for example, the heartbeat is overly regular, corresponding to a low fractal dimension. And in atrial fibrillation, the heartbeat is overly random, corresponding to a high fractal dimension (Goldberger, 1996; Goldberger, Amaral, et al., 2002; Havlin, Amaral, et al., 1999). Many dynamical diseases have this common form, a departure away from healthy fractal variability and toward a loss of complexity in the dynamical unfolding of a system's behavior across time (Glass & Mackey, 1988).
Fractal rhythms appear widely at multiple levels of analysis in healthy physiology (Bassingthwaighte, Liebovitch, & West, 1994) including brain physiology and also in measurements of a healthy person's behavior. As concerns behavior, fractal behavior has been observed in perceptual learning, postural sway, and the timing of perceived reversals of a reversible Necker cube. It is found in motor performances such as spacing and timing of rhythmic movement and the phase relation between rhythmic movements. It is found in tapping, human gait, and repeated measurements of simple reaction time. It appears in controlled cognitive performances including mental rotation, lexical decision, visual search, repeated production of a spatial interval, repeated judgments of an elapsed time, simple classifications, and variation in word naming by skilled readers, an automatic cognitive performance. And finally it is present in variation of ratings of self-esteem and in mood ratings by bipolar patients (Gilden, 2001; Riley & Turvey, 2002; and Van Orden, Holden & Turvey, 2003, are reviews).
Moreover, just as for heart physiology, recent behavioral and brain findings suggest that fractal variability is a signature of cognitive health and wellbeing. And deviations from the aperiodic rhythm are deviations from health and wellbeing. For example stress, epilepsy, manic-depressive disorder, aging, and neurodegenerative disorders such as Parkinson's and Huntington's disease are all associated with deviations from the healthy fractal pattern (West, 2006). To these we may add major depressive disorder, which is associated with an increase in fractal dimension of EEG recordings (Linkenkaer-Hansen, Monto, et al., 2005), and attention deficit and hyperactivity disorder, which is associated with a decrease in fractal dimension in cognitive behavioral tasks (Gilden & Hancock, 2007).
Patterns and Paradox
One way to see the pattern of healthy variation is in its spectral portrait, illustrated in the Figure. The Figure presents behavioral data, about 8000 trials of simple reaction times taken in one sitting, and the wavy aperiodic rhythm of variation from trial to trial across these data points is common to behavior and physiology. The spectral portrait below the trial data graph is derived by artificially reducing the aperiodic rhythm into multiple periodic component frequencies, usually sine waves. One can artificially segregate component waves of variation yielding rapid, higher frequency oscillations plus intermediate frequency oscillations plus low frequency oscillations. Axes have been adjusted in the Figure to make the illustrated sine waves visible.
Figure 1: Spectral Portrait of Fractal Behavior
Emergent properties of the fractal pattern dictate the relationship between amplitudes and frequencies, and the remarkable finding is the lawful scaling relation between amplitudes and frequencies of variation (on log scales). The amplitude of oscillation across blocks of hundreds or thousands of trials finds its value on the same line that captures amplitudes for oscillations with periods of tens, dozens, or scores of trials. The line itself, the red line in the spectral plot, defines the scaling relation in which amplitude of variation scales with frequency of variation. One can derive other pictures of the scaling relation with other fractal tools, but the spectral portrait is most commonly presented.
The scaling relation in repeated behavioral measures implies that each measurement is part of a common larger pattern that includes all other measurements. This fact can appear paradoxical. For instance, collect more data and you collect more of the aperiodic fractal wave. The amplitude of variation grows with the number of trials in the experiment. As an experiment increases in length from a few dozen to a few hundred to a few thousand trials the amplitude of variation increases proportionally (on log/log scales). Thus variability in human data has no characteristic amount and no preferred scale, which runs against the grain of what we are usually taught about data in courses on experimental design and analysis (Liebovitch & Shehadeh, 2005).
Most standard analyses assume that individual data points are distinct from one another, but they are not distinct if they are part of a larger fractal pattern. The fractal pattern entails long-range dependence-each data point depends on every other data point, as though some unseen hand is stitching together data points across a laboratory context of measurement. The paradox may run as deep as that confronted by quantum physicists. For instance, a measurement that appears both as a datum and as part of a larger fractal wave is not unlike the well-known electron that is both particle and wave (Van Orden, Kello, & Holden, in press). In psychology these paradoxes fuel spirited debate (e.g., Thorton & Gilden, 2005; Wagenmakers, Farrell, & Ratcliff, 2005; Van Orden, Holden, & Turvey, 2005). In physics scientists eventually accepted that quantum phenomena cannot be distinguished from their contexts of measurement, which some physicists take to mean that measurements themselves are emergent (Laughlin, 2005).
What Do the Fractal Patterns Mean?
Fractal data force us outside of the comfort zone of standard statistical thinking, to the windy cliff above uncharted territory. For instance, no one yet knows exactly why fractal behaviors are ubiquitous or what they tell us in each case. A few clues have surfaced however. Fractal behavior is unlikely to refer to a single source for example (Duarte & Zatsiorsky, 2000). Rather, it reflects system properties of temporal coordination, how the system coordinates real-time activity within organ systems and across organ systems and in the macro-activities of an organism (Kello, Beltz, Holden & Van Orden, 2007). This coordination appears to be a form of allometric control. In this way of thinking the stability and control of hierarchical biological systems results from nested systems "i.e., organelles into cells, cells into tissue, tissues into organs, etc." (West, 2006, p. 313).
Dynamical diseases illustrate the crucial importance of coordination. The key then to understanding dynamical disease and perhaps human behavior is to understand the way component processes interact, the basis of flexible adaptive coordination. Component processes must work together across their different spatial scales and must coordinate their changes despite different intrinsic timescales of change. Flexible coordination is integral to health and wellbeing, and the loss of complexity in dynamical disease is the loss of the flexible coordination among processes that must adapt and work together. Thus, for example, loss of stability or complexity in the interaction among organ systems, and their consequent rapid decline, may be the basis for the otherwise baffling multiple organ dysfunction syndrome in critically ill patients (Buchman, 2006).
In all likelihood then, fractal behavior tells us about coordination of component processes in the minds and bodies of living organisms. It is tantalizing in this respect that the common fractal signature of healthy functioning is found widely in natural systems that self-organize their behavior, that self-organization actually predicts the ubiquitous fractal signature (e.g., Bak, 1996; Solé & Goodwin, 2001). Self-organization requires a particular kind of interaction to coordinate the processes that must work together. The precise form of this interaction balances competitive and cooperative processes to create an optimally adaptive and flexible working configuration or critical state, hence the technical term self-organized criticality. The interaction that yields critical states has been worked out for simple physical systems and serves as a working hypothesis for more complex biological and cognitive behavior. The name for this kind of interaction among component processes is interaction-dominant dynamics. The key fact of interaction-dominant dynamics is that system components change each other's dynamics to coordinate their collective behavior (Jensen, 1998).
Recent progress in systems neuroscience has converged on similar ideas about self-organization of central nervous system activity (e.g., Freeman & Holmes, 2005; Kozma, Puljic, et al., 2005; Sporns, Chialvo, Kaiser, & Hilgetag, 2004). Perhaps the day is not too far off when a more fully elaborated hypothesis of self-organization will explain ordinary coordination and control of cognitive and motor activity (Gibbs & Van Orden, 2002; Gilden, 2001; Kugler & Turvey, 1987; Riley & Turvey, 2002; Turvey & Moreno, 2006; Van Orden et al., 2003), including anticipation of changes in the environment (Kloos & Van Orden, in press; Raichle & Gusnard, 2005), and intentional behavior (Juarrero, 1999; Van Orden & Holden, 2002).
Prospects at Hand
In a new book, West (2006) argues that the emerging fractal picture of physiology and behavior will replace standard ways of thinking about living systems and lead to innovations in diagnosis and treatment. Whether or not this dramatic change in our thinking will occur, there is a present need for better methodological tools for empirical studies and a wider understanding of the tools that already exist and what they can tell us about cognition and behavior.
A more complete and integrated understanding of the fractal patterns that nature presents to us will require new nonlinear tools with which to examine fractal phenomena. Presently one usually relies on a single measure that corresponds explicitly or implicitly to the fractal dimension of variability in behavior. The fractal dimension or its equivalent is estimated using linear tools that are effectively cobbled together to converge on a reliable estimate. These important tools have successfully established the presence of fractal variability in behavioral and physiological phenomena, as well as departures from fractal variability, but they are limited in their scope and may not fully address the complexity of fractal phenomena. However, better nonlinear tools exist that may soon be available to study fractal behavior (Thomasson, Hoeppner, Webber, & Zbilut, 2001; Thomasson, Webber & Zbilut, 2002).
The other need I mentioned is for a wider understanding of existing tools and an expanded study of human behavior as a complex system. To meet this need, for example, The Society for Chaos Theory in Psychology and Life Sciencesruns tutorial workshops at its annual meetings. Also the National Science Foundationrecently supported preparation of Contemporary Nonlinear Methods for Behavioral Scientists: A Webbook Tutorial that can be downloaded from the NSF website of the Social, Behavioral and Economic Science Directorate, program in Perception, Action and Cognition. My own recent efforts, with those of my colleagues, have gone to creating an Advanced Training Institute in Nonlinear Methods for Psychological Sciencesponsored by the American Psychological Association. The next workshop will be held June 11-15, 2007, at the University of Cincinnati (please see The Nonlinear Methods webpage for more information).
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