catscan4

$e-MATH$
The mathematical CAT scan

4. The Poker-chip CAT scan

The computations in my numerical simulation were done by hand except for the totals, but the graphics required Maple. A low-tech and even cruder but still illustrative simulation can be done with a checkerboard (for the grid) and poker chips (for tallying).

To keep the numbers reasonable we have to work with a small grid: 4x4. This is one quarter of a standard checkerboard. As ``objects'' we can take various letters of the alphabet, e.g.


0110  1000  1111
1001  1111  1000
1111  1001  1000
1001  1111  1111

For ``A'' the line totals will be (in the same order as before)

2222 0120 0222 0221 3223 1220 2220 0210
2222 2012 2222 1101 3223 1011 2222 2102
4444 1221 2221 2211 3223 1122 1222 1221
2222 2101 2211 1011 3223 1101 1122 1012

As before, applying the dual transform means adding up these 8 tables square-wise. A ``manipulative'' way to perform this addition is to set down a layer of poker chips for each table. At the end the heights of the stacks should be:

 8 15 15  8
15 10 10 15
15 17 17 15
13  9  9 13

and the ``A'' should be recognizable.

This simulation required 204 poker chips.