Thursday, September 29, 2016
Agents are placed at random on the image, then follow their paths until they go off-screen.
Below, an agent’s color is affected by the pixel brightness, and the range of angles is more narrow.
Created with Processing
Saturday, November 21, 2015
Monday, October 19, 2015
Having you been noticing a gradual increase in the popularity of Spirograph toys recently?
Maybe it’s just me; my kids’ manual coordination has developed enough that they’re just now able to work the gears on their own. I’ve seen a couple recent iterations of the traditional setup for sale – it looks like the new “Cyclex” toy by Spirograph reduces the required dexterity, though without the ability to mix and match gears the patterns all look pretty similar.
I noticed this set for sale and appreciated the mathematically accurate name.
For the last few months I’ve had fun playing with “Wild Gears,” designed by Aaron Bleackley and manufactured through Ponoko, a laser cutting service. Wild Gears come in a variety of versions, including the Compact Gear Set that my kids and I have been enjoying. The laser cut precision makes for very smooth motion, and the clear acrylic makes it easy to see your design progressing underneath. They’re a bit pricey, but Aaron’s working on simplifying the designs to reduce cutting cost, along with other improvements in Version 2.0 – check out his Kickstarter.
My favorite feature is the ability to nest different gears, allowing you to produce designs that lack some of the symmetry of spirograph patterns – not all nestings will do this, so it’s often a surprise to see what turns up.
Monday, July 13, 2015
Waiting in the car for a ferry the other day, I found I had two long nails and a little magnet for some reason, and came up with this balanced configuration:
At first I thought it was funny that there was less than 1 nail to the left of the balance point, and more than one to the right, but then I recalled this old lever formula:
Can we figure out how far down the nail the balancing point is? Call it x, and let’s say each nail has a length of 1 and mass of 1…
Saturday, April 18, 2015
I visited my son’s first grade class the other day, and brought along a branch I found in our yard debris pile. The kids didn’t take long to realize the big branch was made from smaller branches, which were made from still smaller branches. After establishing that a self-similar shape like that is known as a fractal, we set about making our own using a template I made. (The template has two equilateral triangles with vertices and midpoints marked, just to get everyone started)
For this “Sierpinski gasket” fractal activity, I wanted them to follow these steps:
1. connect the midpoints of a white triangle’s sides
2. color the triangle you created in step 1.
3. Go to step 1.
At the end we taped their triangles together in progressively larger groups of three. Judging by the results, not everyone grasped the iterative process, but they seemed to have fun with the idea, which is arguably more important.