Modular arithmetic has long been known to produce interesting patterns of values for various kinds of numerical arrays.
The term numerical carpet refers to the results of initializing an array of numbers, applying a rule to each element that involves neighboring values, reducing the results by a specified modulus, and assigning a color to each resulting number. The patterns that result often resemble carpets with geometrical motifs; hence the term.
The original idea and its further development are described in this report.
An Icon application has been developed to assist in designing numerical carpets. There is a user's manual and the code itself is available.
The examples given on the following pages were produced by the application mentioned above. They tend toward less-traditional numerical carpets in order to give some idea of what is possible.
Although not shown on these pages, mirroring a carpet horizontally and vertically often produces more interesting results than the carpet alone.
numerical carpets, part one