The Gaussian ring Z [i] = {a+bi | a, b ∈ Z) can have a geometric interpretation by complete residue classes. Using complex bases, a Gaussian integer z can be expanded by a radix representation. Those complex number which are expressed by the above e...
The Gaussian ring Z [i] = {a+bi | a, b ∈ Z) can have a geometric interpretation by complete residue classes. Using complex bases, a Gaussian integer z can be expanded by a radix representation. Those complex number which are expressed by the above expansion are classified in the complex plane. We differently color those number depending the power of B. In this process we get plenty of fantastic fractiles. As an application we have a criterion about the completeness for a digit system.