Tuesday, October 18, 2016

Fractal friends

I was working on a program to make branching curlicue designs, when my kids came in and asked how the pictures were made.  I explained that the computer follows directions based on the numbers you give it.  I changed the maximum angle that the curls could bend at each segment, and these cool shapes started popping up.

We noticed that some of the images looked like recognizable objects (like finding pictures in clouds), so we took some of our favorites into Photoshop and drew on them.  We found a spaceship...
 A mermaid...
 A jumping bear...
 And some birds on a wire

Here's the program if you want to look for your own fractal friends.

Thursday, October 13, 2016

Nelson's MagicTile

Magic Tile is a free program (possibly for Windows only) that provides a large number of Rubik's cube variations in different geometries.  Some of them are much simpler to solve than others, and viewing the different projections is fun in itself.  

Thursday, September 29, 2016

Slopefield face

What if you took a picture and used the brightness of each pixel to determine the angle that a little agent (a black dot) would travel? 

Agents are placed at random on the image, then follow their paths until they go off-screen.
Above, black pixels equated to East and white mapped to West.  There are lots of ways to set the angles. 

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

Flash cards

Here's a little program I wrote to help my son with his math facts.  It's a flash card program with sliders to adjust the range of values involved and the pause before it tells you the answer.  Let me know what you think.

Monday, October 19, 2015

Wild Gears!

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. 
hypotrochoid set
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

Balancing nunchucks

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

First grade fractals

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)
sierpinski fractal activity
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.
sierpinski fractal activity

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.