Fractal patterns have been found in traffic flows, music, cardiology, electronics, meteorology etc etc. All fractals are made by positive feedback, no matter what the medium. They are neither stable nor static. They teeter at the edge of chaos. A minute touch and they may fly into wild gyrations, but equally a massive heave may fail to budge them. Prediction is far from assured. Determinists are uncomfortable with them.
Plasma science is well established, not least through the search for the cheap, clean energy of nuclear fusion. The search has failed so far because it involves an electrical process relying on ‘Z pinch’, a feedback process which, not surprisingly, is capricious. But Nature has mastered the art.