Embedded Julia sets

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When zooming past minibrot islands in the Mandelbrot set (and similar) going deeper towards another minibrot, sometimes the structure of the filaments takes the appearance of a Julia set corresponding to the location relative to the parent island. For quadratic functions like [math]z \to z^2 + c[/math] or the Burning Ship, the embedded Julia set appears around half way along the zoom path between the parent island and the island at its center.

Original Page by Claude