Monday, December 29, 2014

Brain Activity and Julia Sets

If one accepts the brain as a closed-loop network, then plotting its activity as a whole one would assume to spot something fractal. One would expect pictures of the brain's activity to resemble, for example, something like Julia Sets. Julia Sets, in principle, are the same attempt to map complex dynamics out to some kind of topology.

We know from Julia Sets that it is of no use to investigate parts of them in a topologic fashion. What can be investigated is the character of the sets as a whole (Do they consist of snowflakes? Are they connected? How distributed are they? Does they contain attractors? What kind of symmetry can be observed?).  Considering dynamic fractals one might add (Do they transition between these states over its lifetime? How long does the wave last? How does the spatial expansion of its boundary change?).

When considering fractals, those centers ore nodes are simply attractors within these complex dynamics. They possess no meaning of their own outside this particular rendering, and even more imporant, they possess no topological meaning at all. In those brain images, many centers could be just as transitory, dependent on the thought activity that just brought them by, without particular topological meaning outside of these waves.

Maybe we have to turn the typical orientation of the Julia and Mandelbrot sets upside down to continue thinking. Or it is only another attempt at confusing popular art.

Fractal Imges by John Tsiombikas, Retrieved from
Brain Images by Scott Williams, Retrieved from