Experiments at ivanwlam.com

You may not notice it, but every one of the twenty-five motifs above is different. I’m experimenting with form and pattern of basic geometry.

The concept is simple. Start with a certain amount of points. Then, starting at one point, count the next 1 point, and connect the points with a line. Repeat until all the points are connected fully. Then, repeat the entire process by counting 2, 3, 4 points and so on until the pattern repeats.

Here is a sample of what I came up with.

I did this up to the 18-point series.

Then I thought about completing each series all the way around, which repeats the pattern.

I started to notice a larger pattern near the bottom, where there are more points and intersections. And I wonder what it would look like it I continued the existing series for a longer duration. Technically, if you have four points and you count five points in one direction, it’s as if you have counted only one point. So it’s “logical” to continue the series this way. Click here to see it at 100%.

I skipped one square because if you have four points and count to 4, you’re back to where you’re started, and you can’t connect to anything. Technically, it could be indicated by just points, but oh well.

Then I figured I should let the patterns stand alone without the grid, but for some reason, I like it with the grid. Here is the image at 100%.

Maybe the grid looks good in this smaller scale, but it’s probably cleaner if I had continue the series down to 50, 100, or 200 points.

I really like this series because it’s a very logical and beautiful iteration of natural patterns in geometry. There was no human manipulation involved, other than setting up the unbiased rules of the game, and let the “program” run itself. I haven’t thought of a practical use for this, but I’m sure to revisit it someday.

Notes: 12/20/07.