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King of the swingers: photographer builds giant pendulum to make amazing art King of the swingers: photographer builds giant pendulum to make amazing art
(about 4 hours later)
The following contraption is a prototype of a drawing machine that was fashionable in the 19th century. It’s a pendulum holding a funnel full of sand that once swung leaves an intricate trail on the paper below.The following contraption is a prototype of a drawing machine that was fashionable in the 19th century. It’s a pendulum holding a funnel full of sand that once swung leaves an intricate trail on the paper below.
Hugh Blackburn, a Scottish mathematician at Cambridge university, came up with the idea in the 1840s. He was amazed at the gorgeous looping patterns it produced.Hugh Blackburn, a Scottish mathematician at Cambridge university, came up with the idea in the 1840s. He was amazed at the gorgeous looping patterns it produced.
His machine works by creating two competing swings. First you pull the ring marked r so that it swings forward and back. Then you swing the bob below it from side to side. The swings combine with each other to create swirling designs called Lissajous figures.His machine works by creating two competing swings. First you pull the ring marked r so that it swings forward and back. Then you swing the bob below it from side to side. The swings combine with each other to create swirling designs called Lissajous figures.
The patterns are so stunning that machines like Blackburn’s Y-shaped pendulum were made commercially in the Victorian era. They became known as “harmonographs”, since the variation in images results from the variation in harmonies between the different swings.The patterns are so stunning that machines like Blackburn’s Y-shaped pendulum were made commercially in the Victorian era. They became known as “harmonographs”, since the variation in images results from the variation in harmonies between the different swings.
Many types of harmonograph have been manufactured over the last 150 years. Blackburn’s Y-shaped pendulum with falling sand was quickly superceded by other designs that used a stylus writing on paper.Many types of harmonograph have been manufactured over the last 150 years. Blackburn’s Y-shaped pendulum with falling sand was quickly superceded by other designs that used a stylus writing on paper.
Yet in some cases, Blackburn’s original design remains the simplest and most effective harmonograph. Just ask Paul Wainwright, a photographer in Atkinson, New Hampshire, who spent two years building an enormous Y-shaped pendulum out of wood and metal in the barn at the back of his house.Yet in some cases, Blackburn’s original design remains the simplest and most effective harmonograph. Just ask Paul Wainwright, a photographer in Atkinson, New Hampshire, who spent two years building an enormous Y-shaped pendulum out of wood and metal in the barn at the back of his house.
Paul’s pendulum looks more like a wrecking ball than an art-making machine. As can be seen below, the top half of the Y is a wooden triangle hanging from the ceiling. The bottom half is a chain holding a metal weight.Paul’s pendulum looks more like a wrecking ball than an art-making machine. As can be seen below, the top half of the Y is a wooden triangle hanging from the ceiling. The bottom half is a chain holding a metal weight.
The metal bob does not contain sand. The black cladding underneath it contains a light source, which draws out the Lassajous figures and which Paul photographs from below.The metal bob does not contain sand. The black cladding underneath it contains a light source, which draws out the Lassajous figures and which Paul photographs from below.
I’ll take you through what he does. Paul first pulls the bob up to the side, where he attaches it to a magnet.I’ll take you through what he does. Paul first pulls the bob up to the side, where he attaches it to a magnet.
Then he lies on the floor, 7ft below the bob, and points his camera upwards.Then he lies on the floor, 7ft below the bob, and points his camera upwards.
He switches on the light source on the bob - an array of LEDs in black housing. He switches off the magnet remotely, launching the bob on its swing. He switches on the light source on the bob – an array of LEDs in black housing. He switches off the magnet remotely, launching the bob on its swing.
Finally, he switches off the lights in the barn and begins to take the picture.Finally, he switches off the lights in the barn and begins to take the picture.
I wrote about Blackburn’s Y-shaped pendulum in my book Alex Through the Looking-Glass (called The Grapes of Math in the US), but had never seen one in action before I saw Paul’s machine. I assumed they had become obsolete in the early 20th century. I was thrilled when I saw the pictures he produced. Here are a few.I wrote about Blackburn’s Y-shaped pendulum in my book Alex Through the Looking-Glass (called The Grapes of Math in the US), but had never seen one in action before I saw Paul’s machine. I assumed they had become obsolete in the early 20th century. I was thrilled when I saw the pictures he produced. Here are a few.
Paul says he gets the best images when the period – that’s the length of time it takes for a full swing – of the north/south swing and the period of the east/west swings are multiples of each other.Paul says he gets the best images when the period – that’s the length of time it takes for a full swing – of the north/south swing and the period of the east/west swings are multiples of each other.
The image above is when there is a 1-1 ratio. And the one below is 2-1.The image above is when there is a 1-1 ratio. And the one below is 2-1.
Yet what makes the images really striking is the small changes in period and loss of energy in the pendulum, which have the effect of shading in the pattern with lines.Yet what makes the images really striking is the small changes in period and loss of energy in the pendulum, which have the effect of shading in the pattern with lines.
The precision of the images is stunning - they look computer generated. In fact, the apparatus is about as low-tech as you can get. The precision of the images is stunning – they look computer generated. In fact, the apparatus is about as low-tech as you can get.
You can look at more examples at Paul’s website and also buy prints. He is a professional large format black and white photographer who specialises in landscapes and buildings. The pendulum project is just a hobby.You can look at more examples at Paul’s website and also buy prints. He is a professional large format black and white photographer who specialises in landscapes and buildings. The pendulum project is just a hobby.
Good work Paul!Good work Paul!
For more details on Paul’s pendulum, watch his short video:For more details on Paul’s pendulum, watch his short video:
If you have made any mathematical art and want it featured here please send me an email.If you have made any mathematical art and want it featured here please send me an email.
You can follow me on Twitter at @alexbellos, and on Facebook.You can follow me on Twitter at @alexbellos, and on Facebook.