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Powers of Complex Points

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power numerator
8
power denominator
3
grid size
10
color scheme
BeachColors
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.
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