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Kaprekar Routine

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Created by Christopher Manning


Kaprekar’s constant is 6174. The Kaprekar Routine arranges four digits (zeros are appended to the number if it’s less than 4 digits) in descending and ascending order, subtracts those two numbers, and repeats the process until the difference is 0 (degenrate case) or 6174 (Kaprekar’s constant). The color is HSL with a scale of 0 to 300 in the domain of 1 to 7 (minimimum and maxium iterations to reach Kaprekar’s constant) for hue, 1 for saturation, and .5 for lightness.

I created this because I wanted to visualize Kaprekar’s constant in some way. This Wolfram MathWorld article on the Kaprekar Routine has a compelling image that is inspired by the cover of The Mathematics Teacher. From there, I decided to research some visualization techniques by recreating it with d3.js and adding some extra features (sorting, highlighting, and showing the routine).

I first heard of Kaprekar’s constant after looking at the Google New York office. Apparently, there are about one-half of Kaprekar’s constant Googlers there.