Registered: Oct 2003
Posts: 103

I was trying to find a good way to visualize addition.

As an extension of counting, one can make a picture of two blobs of black cells merging into a single blob. But it is more challenging to find a good graphic for addition using the rules of arithmetic.

The rules of arithmetic are a good example of computational reducibility. Adding two blobs of size n and m together, where n>m, takes m steps. Adding binary numbers using the rules of arithmetic takes at most Log[2,n] steps.

The attached graphic shows an example of addition using the usual rules, and the result is in the center column, here highlighted in green and blue. What is not so obvious is that the column left of center contains the carry values from the previous step. The rule diagram shows that this rule is one dimensional except for the cell containing the carry values.

One nice thing about this picture is that it shows addition as a process, which could continue indefinitely, like the computations found in NKS.

I'd be very interested if someone could find a better picture. It would also be very interesting if one could find a completely one dimensional rule.

Todd Rowland has attached this image:

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