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watching
https://yewtu.be/watch?v=-RdOwhmqP5s Newton's Fractal
and
https://yewtu.be/watch?v=C5Jkgvw-Z6E
ive had a thought, polynomial roots (in other words the amount of solutions in which x^n = 0 for a ..... ) can be thought of as strange attractors for algorithms like the one that produces newtons fractal.
It is very striking that the fratal pattern which arises from the real world phenomenom of 3 magnetic fields influencing a magnetic pendulum to fall one of three wells, is is strikingly similar to the newtons fractal pattern born from a root finding algorithm.
What this seems to mean is that in a dynamically complex system with three or more potential attractors (or roots) a point must make a decision at each iteration to either move definitively towards one attractor, or have the possibility of moving towards any of them (undecidability) but never just two, or less than the total set of attractors. The point *has* to eventually end up somewhere
There is a visual difference of course, the physical example with magnetic fields appears mores like a runny mixed paint thing, while the newtons fractal is more like rigid braids or "blobs on blobs on blobs". But The connection is there.
In iterative processes that approach definitive values (often some irrational number), unpredictibility and variation exist due to the infinite precision the universe calculates with. No matter how many decimal places one uses, there is always some level of uncertainty in the measurement. A small difference inherent micro-details presented as fractal overlaping. Any small movement in starting positions ultimately lead to different outcomes. This is the hallmark of chaos theory.
It is interesting to see how fractals pop up so frequently where you least expect them in both physical processes and abstract ones purely imaginary. This reveals a hidden connection between the two which is fascinating.