Irreducible Gaussian Fractions
Move the sliders to see the irreducible fractions for Gaussian integers in the given range and with specified zoom level in the complex plane.
An irreducible fraction is a fraction such that and have no common factor. This definition applies to ratios of ordinary integers as well as to Gaussian integers, which are of the form , where and are integers and . By rationalizing the denominator, such complex fractions can be put in the form , where and are real fractions; are the numbers plotted.
Heavily based on code by Michael Trott in The Mathematica GuideBook for Graphics New York: Springer-Verlag, 2004.