We don’t exactly know. These drugs seem to modify the activity patterns in various areas of the brain.
There are some half-mathematical, half-neurological possible explanations. One is the generic observation that many things you can graph with a set of functions tends to form fractals when the functions are fluctuating around their critical point. The critical point is where the output of function nears zero, and often on one side of the critical point the output of the function is above zero, and on the other side it is below zero. E.g. if you draw a curved line that goes up and then goes down, the critical point is the peak of the line.
There have been studies where it’s been noted that the visual cortex activation patterns have a higher fractal dimensionality when subjects are exposed to psychedelic drugs. E.g. [this study](https://www.sciencedirect.com/science/article/pii/S1053811920305358).
Now the reason isn’t that the drugs themselves somehow produced fractals. Rather, it is that they disturb the ordinary function of the neural networks to a more random direction, meaning that the activation of those individual neurons fluctuates more around their critical point.
This sort of fluctuation around the critical point tends to produce fractal patterns, e.g. the [self-avoiding walk](https://en.wikipedia.org/wiki/Self-avoiding_walk) being a good example of this.
Now this is really just one hypothesis with some empirical and theoretical evidence for it. The truth is that we don’t know; but what we do know is that fractals are pretty common and many phenomena tend to produce fractals.
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