Powers of Complex Points

power numerator

8

power denominator

3

grid size

10

color scheme

BeachColors

plot style

points

cells

lines

A Gaussian integer is a complex number of the form

a+bi

, where both

a

and

b

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,

n/d

(a+bi)

, where

n

is the power numerator, and

d

is the power denominator.

With "points", hovering your pointer over a point will show the original

a+bi

value on top, and a rounded

n/d

(a+bi)

on the bottom.

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

a

value and a horizontal line for each

b

value. When the power is changed, these lines join the corresponding mapped points and so intersect at

n/d

(a+bi)

values.