6174 : Visualizing Kaprekar's process
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Figure 1: A visual graph of the Kaprekar process. Every four-digit number is a point on one of the circles. Every iteration outlined by Kaprekar is a path. At the center is the number 6174 (indicated by the red dot).
1. Kaprekar's Process
- Pick a 4-digit number, using at least two different digits.
- Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.
- Subtract the smaller #number from the bigger number.
- Go back to step 2. and repeat.
The above process will always reach its fixed point, 6174. Thus spake D.R.Kaprekar (1905-1986) – school teacher, recreational number theorist and Indian mathematician.
I have created a visual graph of this process. Every four-digit number
is a point on one of the circles. Every iteration outlined by Kaprekar
is a path. His algorithm might be mechanical but the patterns emerging
from it are anything but. At the center is the number 6174
(indicated by the red dot) to which all others are inexorably
drawn. This plot itself was generated algorithmically using a
combination of Python, TikZ, and \(\LaTeX\).