The Swingograph


In the 1950s a schoolfriend and I experimented with recording the motion of a compound pendulum on photographic paper. I still have some of the results, an example appearing in the first image below.

In the 1970s we were in Hamleys toy store and bought a toy consisting of a pen drawing patterns on a swinging platform that reminded me of those earlier experiments. This time I was able to work out exactly what was happening and made a much larger version which gave years of enjoyment to our children, their friends and later, our grandchildren. A picture of it appears below.

In 2013, after having the "Swingograph" out for visiting grandchildren I decided it would be an easy matter to write a program to simulate the patterns on the computer. That program has evolved to do significantly more than its mechanical counterpart and some of the results are presented in the remaining pictures below. I call these "Swirlygrams"

pattern from the 1950s
The mechanical version and a typical pattern drawn

How it Works

The platform in the mechanical version can swing as a pendulum in the forward and backward direction (X swing) and the side to side direction (Y swing). The X and Y swing periods can be slightly different and can start out of phase with each other depending how the platform is launched initially. There can also be a twist motion which is designed to have almost the same period of oscillation as the other two, Each of these motions will decay with time. For the E-version these three oscillations can set to any values of Amplitude, Period and Phase to produce an unlimited range of swirling patterns. The rates of slowing down can also be adjusted. The resulting patterns can be expressed mathematically as shown on the right. While the pattern is developing the colours of the line can be changed for added effect.

The E-version has two additional motions added, a second X oscillation and a second Y oscillation. The mathematical equations shown don't include these. In most of the patterns shown in the gallery (patterns 1 to 20) these extra motions are not active.

Nov 2018 - I've added a second gallery of more recently produced patterns. What I can't share on this website is the pleasure one gets from seeing a pattern as it is drawn on the computer screen. I find myself saying "that's so beautiful". The choice of colouration is also a significant factor in adding beauty. Another feature that's difficult to share is the third dimension (Z axis). This has no effect in what is displayed in the single image. But I can display the pair of images as would be perceived by each eye and this can be viewed as a 3-dimensional object. They can be viewed either with a special viewer that enables each eye to see only its appropriate image, or simply by looking at the pair cross-eyed, if you know that trick. Seeing a 3-dimensional image unfolding gradually as it's plotted in front of your eyes is quite an experience.