Irreducible Gaussian Fractions

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Move the sliders to see the irreducible fractions for Gaussian integers in the given range and with specified zoom level in the complex plane.
Contributed by: Eric W. Weisstein (March 2011)
Suggested by: Michael Trott
Open content licensed under CC BY-NC-SA
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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.
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