Is the Mandelbrot set computable?

Hertling, Peter GND

We discuss the question whether the Mandelbrot set is computable. The computability notions which we consider are studied in computable analysis and will be introduced and discussed. We show that the exterior of the Mandelbrot set, the boundary of the Mandelbrot set, and the hyperbolic components satisfy certain natural computability conditions. We conclude that the two{sided distance function of the Mandelbrot set is computable if the hyperbolicity conjecture is true. We formulate the question whether the distance function of the Mandelbrot set is computable also in terms of the escape time.

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Hertling, Peter: Is the Mandelbrot set computable?. Hagen 2003. FernUniversität in Hagen.

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