A theorem of Lamé, Dixon, and Heilbronn states that the average number of iterations of the classical GCD function is

$\frac{12~\mathrm{ln}(2)}{\pi^2} \mathrm{ln}(\mathrm{max}(x, y))$

and the maximum is given by

$\lceil \mathrm{ln}(N \sqrt{5}) / \mathrm{ln}((1 + \sqrt{5}) / 2)\rceil - 2$

- Show maximumStair step upper bound
- Show averageSmooth middle surface
- Show iterationsSpiky surface in the middle