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 :)