Fractals
Patterns that repeat themselves at different scales, and what that might mean for what we hear in the consulting room.
A fractal is a pattern that resembles itself at different scales. A romanesco is a lovely example: each floret is a smaller version of the whole. A tree works in the same way: a branch is reminiscent of a smaller tree, and a twig of a smaller branch. What is large thus repeats itself in the small, and vice versa.
The mathematician Benoît Mandelbrot coined the word in 1975. He observed that the classical geometry of straight lines and smooth circles fits poorly with many forms in nature, such as the coastline of Britain, a flash of lightning or the branching of the lungs. These are rougher and more self-similar than textbook geometry. He called them fractal, after the Latin fractus: broken, irregular.
What does this have to do with mental health care?
In our view, less than some enthusiastic advocates hope, and perhaps more than was thought until recently. There are a few observations for which the idea offers something to hold on to.
First, heart rate variability shows fractal properties. The time between two successive heartbeats varies slightly, and that variation has a pattern that repeats itself on shorter and longer time scales. In healthy people this pattern is rich; in serious illness it can flatten. Something similar is sometimes seen in physiological measures in depression and anxiety: the natural "noise" becomes flatter and less fractal.
Second, there are indications that in psychological functioning, too, patterns on different time scales are related. The course of a difficult hour, a difficult day and a difficult week sometimes, though far from always, shows related shapes. For those who work with time series, this is a fruitful idea. It might explain why a snapshot sometimes already says something about the larger whole.
Caution is in order
Fractals are attractive to write about, precisely because they are so elegant and recognisable. For the same reason it is tempting to see more in them than is there. By no means every time series that looks "fractal" is fractal in the mathematical sense. A great deal of noise is simply noise, and the claim that psychological problems are fractal goes further than the current evidence allows.
As far as we are concerned, it is above all a useful lens. Comparing patterns at different scales sometimes reveals connections that are lost in an average. And looking at daily measurements not only for the average but also for the structure of the fluctuations sometimes shows something changing before the averages shift.
In closing
Fractals are, in our view, an elegant concept from mathematics and biology that can help us in mental health care to take patterns on different time scales seriously. The concept does not explain everything, but it is also more than a passing fashion. We see it mainly as an occasion to look at our data in a different way: not only at what is average, but also at how it fluctuates and whether those fluctuations show a structure.