Why does the Mandelbrot shape show up in other fractals?

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In the pictures below, the Collatz map fractal includes parts resembling the Mandelbrot set. Why? Do other fractals do so?

The Mandelbrot set

From Wikimedia Commons

Part of the Collatz map fractal

From Wikimedia Commons

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1 Answer

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This resemblance, of which I see only a bit of, is likely due to the fact that both are fractals generated on the complex plane by convergence of non-trivial equations (to distinguish them form fractals like Sierpinski's Triangle/Sponge/Carpet or Koch's Snowflake that are generated geometrically); they both share similarities with Julia Sets. Since the fractals are self-similar, the nodules of similarity are likely to show up, and the human brain picks up patterns and highlights the similarities between patterns, making instances where the dynamics of the two fractals are vaguely similar stand out, even if the actual similarities are weak.

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