# What am I thinking?

If you see me with a slightly glazed look on my face, there’s a fair chance my brain has gone off to do some maths. Nothing super complicated, mostly stuff with triangles, I like triangles, but today it’s circles.

I got a new toy, a pixel stick to be exact. A pixel stick is a 6 foot long bar of 200 full colour range LEDs, attached to a handle that allows you to spin the stick if you want. You upload an image to it and then, while you take a long exposure, plays back the image one row at a time, ‘printing’ the picture onto the camera sensor as it goes. Of course, once I’ve played with something for 10 minutes, I have to try to work out what else I can do with it, and this was no exception.

Here is one of my first attempts, using an example image that came with the stick (patience is not my strongest characteristic). So, what else can you do? Well, as you’re probably aware, I like to do a bit of maths mixed in with the photography and, as I was lying in bed with nothing to do, I was running sine waves and things through my head. What happens if you rotate a sine wave around a central axis? As it turns out, you get a circle. And if you have four sine waves at regular intervals?

Surprisingly enough, you get a circle in each quadrant of the overall spinning circle, each with a diameter half of the original circle. I’ve tried to illustrate it to the left there. At the beginning, the sine wave moves quickly away from the centre, but the centre of the stick moves slowly, so it doesn’t make huge changes. As it gets to the edge, the rate of change of the distance from the centre is slower, but the outer edge of the stick moves quickly. The net effect is that, for each cycle of the wave, two circles are drawn in the ‘right’ quadrant of the pixel stick. So, adding three more staggered sine waves will give 3 more circles in the other three quadrants. If you ever needed an excuse to love trigonometry… then you’re probably not as sad as I am.

You end up with an image looking something like this, the rainbow is obviously in there because everything looks prettier in rainbow colours. I’m not going to be able to surprise you with how it comes out, because you’ve already skimmed to the pictures. I wasn’t really aiming to get four perfect circles intertwined, I wanted to see what it looked like repeating over and over. Here’s the end result, I hope you like it.