What is the Golden Ratio?

Brett Berry

5217

Golden ratio, and its siblings are everywhere :). If you take for example a given number m>0, and for each n between 0 and m and sum up all the remainders from Euclid’s g.c.d algorithm of m versus n, normalize the result (divide the sum obtained by m), plot in [0,1]x[0,1] all the values, you get a fractal. Which peaks at 1/phi.

http://mathticks.blogspot.ro/2011/01/discrete-connections-part-ii.html