# Powers of Complex Points

Powers of Complex Points

A Gaussian integer is a complex number of the form , where both and are integers. The set of Gaussian integers mapped as points in the complex plane is a square grid. Much more complicated patterns form when the numbers are raised to a power instead, , where is the power numerator, and is the power denominator.

a+bi

a

b

n/d

(a+bi)

n

d

With "points", hovering your pointer over a point will show the original value on top, and a rounded on the bottom.

a+bi

n/d

(a+bi)

With "cells", the Voronoi region corresponding to a point is displayed.

With "lines", actual straight lines are shown when the power is 1, giving a square grid with a vertical line for each value and a horizontal line for each value. When the power is changed, these lines join the corresponding mapped points and so intersect at values.

a

b

n/d

(a+bi)