Animation of a 2D array of dots transforming into the Divisor Plot Pattern ....by JJ Ventrella


(requires Java)... Hit the refresh (reload) button on your browser to replay the animation.

The animation above demonstrates pattern formation arising from a straightforward transformation of a 2D array of dots, resulting in the Divisor Plot pattern (www.divisorplot.com).

At the start, all the rows of dots have the same spacing. During the transformation, the spacing between dots increases, but at differing rates among the rows. The top row doesn't expand at all, and the bottom row expands the most. The rate of expansion increases along the rows, from top to bottom. And this difference in expansion rate is linear.

The transformation stops when the amount of expansion in each row is equal to the ordinal number of the row. In other words, row 2 expands until it is 2 times as long as the original length; row 3 expands until it is 3 times as long as the original length; and so-on.