Fractals
Patterns that repeat themselves across scales — and what that may mean for what we hear in the consulting room.
A fractal is a pattern that resembles itself at different scales. We think, for instance, of a romanesco — each protrusion is a smaller version of the whole. Or of a tree: a branch has a form reminiscent of a smaller tree, and a twig of a smaller branch. In this way, what is large appears to repeat itself in the small, and the other way round.
The mathematician Benoît Mandelbrot coined the word in 1975. He observed that elementary geometry (straight lines, smooth circles) fits most of nature rather poorly: the English coastline, a lightning flash, the branchings of the lung. These are all rougher and more self-similar than the geometry of the schoolbook. He gave it a name: fractal, from the Latin fractus — broken, irregular.
What does this have to do with mental health care?
We would say: less than some enthusiasts would wish, and perhaps more than was until recently surmised. There are several observations to which the idea offers footing.
First: heart-rate variability is fractal. Between two successive heartbeats there is a small variation, and that variation has a pattern that repeats itself across shorter and longer time scales. In healthy people this pattern is rich; in serious conditions it flattens. Something comparable is occasionally seen in physiological measures in depression and anxiety — the natural "noise" becomes flatter, less fractal.
Second: there are indications that in psychic functioning, too, patterns at different time scales hang together. The rhythm of a difficult hour, a difficult day and a difficult week sometimes — not always, but sometimes — show kindred forms. That is a rich idea for one who looks at time series. It would explain why a momentary measurement sometimes already tells one something about the larger whole.
Caution is in order
Fractals are appealing to write about precisely because they are so elegant and recognisable. That makes it tempting to see more in them than there is. Far from every time series that looks fractal actually is so mathematically. Much noise is simply noise. The claim "psychic problems are fractal" is larger than we can make good on.
For us it is above all a useful lens. One who compares patterns across scales sometimes sees connections that vanish in an average. One who looks at the variation in daily measurements — not only at the mean, but at the structure of the fluctuations — sometimes sees something shifting before the means move.
An honest summary
Fractals form, to our minds, a beautiful idea from mathematics and biology that may help us in mental health care to take patterns at different time scales seriously. It is no explanation for everything, and no passing fashion. We see it chiefly as an invitation to look at our data differently: not only at what is average, but also at how it fluctuates and whether those fluctuations carry any structure.