Abstract mathematical principles are often obtuse ideas that don’t have any direct correlation to the real world. Indeed for the majority of the time I spent in university I had no idea how the concepts I was being taught could be applied in the real world, that was until the final unit where they showed us just how all these esoteric formulas and algorithms could be applied. However there are times when the real world and the land of pure mathematics cross paths and when they do the results can be quite amazing. Thus I present to you the Fibonacci Zoetrope:
The Fibonacci Sequence is one of the more commonly known mathematical concepts, one that can be seen often in nature. It can be used to approximate the Golden Spiral which everyone will readily recognise as the shape of a common sea shell. It also appears in sunflowers arising out of the fact that the interior of the flower is most efficiently filled in a Fibonacci like sequence, giving it an evolutionary advantage. The sculptures you see in the video above uses these same sequences to produce some rather interesting patterns which, when combined with a video camera, produce the illusion of motion that isn’t there.
The trick works due to the way modern cameras work, capturing individual frames at precise intervals. If you were looking at this in real life it would look like a blur of motion instead of the strange movement that you see in this video. However you would be able to see this with your own eyes if you used a strobe that pulsed at regular intervals, much like the modern Zoetropes do. Depending on the speed of the rotation and the image capture interval you’ll see very different kinds of motion and, if you time it precisely, it could appear to not move at all.
I really love these crossovers between art and science as they demonstrate some incredibly complicated ideas without having to dive into reams of proofs and scientific papers. The creation of the sculptures themselves is also a feat of modern engineering as some of those structures are simply not possible to create without 3D printing. I might lament not being as talented as the people who created this video but I think it’s for the best as otherwise my hose would be covered in all sorts of weird and wonderful sculptures inspired by random mathematical principles.