Generalized Digit Parity

start

0

spread

200

start base

2

base spread

50

color scheme

DarkBands

This Demonstration shows fractal patterns in the generalized digit parity of natural numbers.

The concept of binary parity can be generalized for non-negative integers

n

and for all positive integer bases

b>2

by the definition:

sumofdigitsofninbaseb(modb)

. Plotting these results in two dimensions

(n,b)

produces beautiful fractal patterns. This Demonstration explores a subset of these patterns by allowing the setting of starting values and ranges for

n

and

b

.