Fractals look visually complex because the components extracted by our visual system cannot abstract sufficiently to compress them to their generator function.
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Replying to @Plinz
That's an over-broad generalization. The Koch curve generator is very easy to derive visually as is the Cantor dust generator. If you watch a Mandelbrot set progress through each iteration it too is easy to derive sequentially. But yeah, lotsa of fractals are hard to extract.
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