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Harmonograph - Part 2


I'm retired and living in Northamptonshire, so plenty of time for photography.
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Harmonograph - Part 2

20 Jan 2022 10:32AM   Views : 329 Unique : 194

Part 2 – Developing my Harmonograph

In Part 1 of this Blog I gave a bit of history and outlined some of the challenges I wanted to overcome in the project. In this part, I will outline the platform I have constructed and how it works.

This next variant of the machine is around 2 metres tall, and made out of oak, with hardpoint bearing screws and comprehensive adjustability. I built it as a ‘platform’ I can use to adapt and change and try new things. It is a good job I did this as it had some significant deficiencies, which I later corrected!


More Engineered Machine!
This is a view of the new machine in its initial configuration. It has a gimballed frame for the camera (lower platform) and an upper platform suspended on a simple gimbal with a weight that can be moved up and down to change the period. An example image is ‘Linen Fold’ – an attractive fine pattern, with slow decay…but still dominated by precession on the upper platform, which I couldn’t adjust.


Linen Fold

Another ‘schoolboy error’ (at least it seemed so for an optical scientist) was that the motion of the camera was very ineffective – it is always pointing at the centre of the gimbal frame, which is its centre of rotation… so if the LED was positioned there (which it almost is on the photo) it doesn’t move at all when you set the camera swinging! The corrections were fortunately quite easy; duplicate the gimbal frame for the upper platform, use this for the camera and put the light source on the lower platform.

Now I had a machine I could control, adjust, experiment and have fun with! Cooking on gas! It was also quite mesmerising to watch. Take a look at the video below:

The top platform has the camera and the lower one the LED light source. Both can swing in two dimensions. The period of each can be adjusted by moving the camera or LED platform up and down, with swing periods from over a second down to about half a second. The gimbals can also be fine tuned to add or remove ‘precession’ by adjusting the pairs of suspension screws differentially, which effectively shortens or lengthens the pendulum for one swing direction only. It is like the multiple strings in a piano for each note; they are not all exactly the same frequency, giving the tone depth and colour. However, too much detuning isn’t nice though, and the same is true in harmonograms! Typical exposure times are 4-5 minutes, although for some images I have used up to 30 minutes! In the configuration on the Video the lower platform is extended down by additional rods, to increase its swing period.

Adjusting the light level, ISO and exposure takes time and experimentation. I find that it is best with a stack of ND filters on the camera, as the LEDs are quite bright; this reduces the sensitivity to background light, as exposures can exceed ten minutes. Everything has to be set to manual, with no IS. Live view is also essential, and remote shooting is a real boon. Long exposure noise reduction also works really well, otherwise all the hot pixels show up! Best long exposure results were achieved with further measures to exclude light from the machine, cardboard cladding! My camera is an EOS R, which works brilliantly in this application. Patience is needed, as the long exposure noise reduction takes as long as the exposure. Any minor jogs, door closures or earth tremors will ruin the capture, and you don’t know what you will get until it appears on the screen. Sometimes a magic moment. Most times ‘in the bin’.

The simplest and easiest patterns are produced when the periods of the two platforms are almost the same; some precession is needed to give the patterns an interesting form; a minimal degree of detuning can also be attractive, as it causes the pattern to slowly rotate.


The musical aspect now becomes very clear – the most coherent patterns are produced when the two platforms are tuned close to the integer ratios from music, such as a major fifth (3:2), perfect fourth (4:3), minor third (6:5). The patterns become more intricate with the complex ratio tunings. For instance with minor third tuning, there will be 11 peaks in the pattern and 5 for a major fifth; adding precession folds the patterns, further increasing complexity. I have spent many hours timing the swing periods, adjusting, and retiming. For many of the forms, the tuning has to be right to a few parts in 1000, so patience is needed. Left overnight, the machine will be noticeably out of tune in the morning.


‘Convolution’ – tuned close to a major fifth, with a fairly high level of precession. I think this invites the viewer to mentally unfold and explore, seeking ways through the form.

For ‘Binding by the Light’ the platforms are precisely tuned to a 15:8 ratio, corresponding to a Major 7th. The pattern repeats 23 times moving round the form, giving the starburst effect. It seems evocative of something being tied up in a never ending ball of light, hence the title. I have reduced the LED current progressively through the exposure time of several minutes, giving the complex glow from the centre of the image, without burn out. I’m always taken aback when I look at this image, with its complexity, precision and symmetry. it is stunning as an A2 print!


'Blinding by the Light'
When the two platforms are tuned an octave apart (2:1), the patterns can be surprisingly beautiful and complex. This was just about the limit of tuning on the machine. Any increase would require a large hole in the ceiling ( I argued for this, but had to try and find other, more acceptable ways…)!


‘Entwined’ - this image was taken near octave tuning, with quite strong precession set to give the linen fold in the tails of the form. To me this was evocative of two futuristic forms or beings, entwined together, or maybe some deep sea creature from the Abyss.

Producing patterns like this I think hastened my effort to transition from ‘Technology’ just a bit further towards ‘Art’ – but it is up to you to judge! Prior to this, I wanted the patterns to be perfect, with no edge clipping or jogs, no noise and no highlight saturation (ie technology driven). Once I had control of the machine I could start to ‘compose’, trying to make the images tell a story or become more artistic or ethereal. More on this in Part 3! You can view many more of my images on my Smug Mug gallery here. I hope you are enjoying these blog posts - please leave comments, thoughts, requests, suggestions!


dudler Plus
18 1.9k 1929 England
20 Jan 2022 3:26PM
My first maths teacher, Mr Witcomb, taught me that plus and minus infinity meet up behind the blackboard... Similarly, physics and music meet up somewhere I don't understand and can't see, but the results seem to be delightful - including the visible form you have explored.

Keep going - the images are strange and lovely.
cooky Plus
18 6 6 United Kingdom
21 Jan 2022 12:12PM
The art is now coming through and there is so much to link the sciences with the arts - energy is a wonderful thing! Ridiculously creative and beautiful and from now on you will be known as EPZ's Dr Who!


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