Pi in the Mandelbrot Set

An interesting thing is that pi can be computed from the Mandelbrot set, by counting the number of iterations required before point (−0.75, ε) diverges.

Discovered by David Boll in 1991, he computed the number of iterations required for the series to diverge for z = −3/4 + iε (-3/4 being the location thereof). As the series doesn't diverge for the exact value of z = −3/4, the number of iterations required increases with a small ε.

It turns out that multiplying the value of ε with the number of iterations required yields an approximation of π that becomes better for smaller ε.

If points with coordinates (−0.75, ε) are considered, as ε tends to zero, the number of iterations until divergence for the point multiplied by ε converges to π.

For example, for ε = 0.0000001 the number of iterations is 31415928 and the product is 3.1415928

**Sources**
* [Numberphile video featuring Dr Holly Krieger](https://www.youtube.com/watch?v=d0vY0CKYhPY)
* Gary William Flake, The Computational Beauty of Nature, 1998. p. 125.
* [Aaron Klebanoff, π in the Mandelbrot set, 2001](https://www.webcitation.org/66iUmBi3B?url=https://home.comcast.net/~davejanelle/mandel.pdf)
* [Mandelbrot set wikipedia page](https://en.wikipedia.org/wiki/Mandelbrot_set#Pi_in_the_Mandelbrot_set)

Also, this is probably the least efficient way to approximate the number pi.

I don't know if a coding challenge can be made on this topic, but it may inspire you for something else :)

Beginne damit, die Beschreibung des Issues und die darin zitierten Quellen über die Berechnung von π aus der Mandelbrot-Menge zu lesen. Das Issue nennt keine Dateien, Tests, keinen Einstiegspunkt und keine konkrete Programmieraufgabe, daher müssten Umfang und Kriterien für den Abschluss definiert werden, bevor mit der Implementierung begonnen werden kann.

Vom Indexierungsmodell aus dem Issue-Text verfasst.