Boundary of Mandelbrot Set is Self-Similar

Theorem

Let $M$ be the Mandelbrot set.

Then the boundary of $M$ in the complex plane $\C$ is self-similar.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Mandelbrot set (B. B. Mandelbrot, 1980)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Mandelbrot set (B.B. Mandelbrot, 1980)