Number Systems in 3D

The points are the set , which is the first approximation of the fractional part in the base- system with digits.

This is a natural generalization of ordinary numeration systems with complex bases, but this time we treat the space as ℝ⨯ℂ, where the first coordinate is along and the second is in the plane orthogonal to . Addition and multiplication are done component-wise using the coordinates, and , .