While most of us think about mathematics as quite an ‘impractical’ science, it seems that almost everything around us is based on mathematical concepts and can be expressed in numbers. Even the beauty of seemingly amorphous and spontaneous life forms found in nature is actually much more structured and organized than you may think. In fact, amazing geometric patterns that can be observed in certain plants, such as sunflowers, pinecones and artichokes, are determined by the concepts known as Fibonacci Sequence and Golden Ratio.
Now, Stanford artist and inventor John Edmark has designed 3D printed spinning sculptures to demonstrate these mathematical concepts in action. The method used for arrangement of the appendages on the sculptures was inspired by the way nature creates geometric patterns in sunflowers, artichokes and pinecones. That is, their spiral shape follows the Fibonacci sequence – a series of increasing numbers.
The ‘Blooming Zoetropes’, as the artist calls his creations, are rotating at 550 RPM and appear to be infinitely and cyclically blooming, which produces a kind of hypnotizing optical illusion. To get this fascinating effect, Edmark captured a particular segment of the rotation on high speed camera. The video, which is filmed at 24 frames per second, is synchronized with the rotation speed of the sculptures – each frame shows the moment when the sculpture turns 137.5°, known as the ‘Golden Angle’.
“I employ precise mathematics in the design and fabrication of my work. I do this neither out of a desire to exhibit precision per se, nor to exalt the latest technology, but because the questions I’m trying to formulate and answer about spatial relationships can only be addressed with geometrically exacting constructions. Mathematical precision is an essential ally in my goal of achieving clarity,” Edmark writes in his artist statement.
Moreover, the artist shared the instructions for creating these amazing spinning sculptures on Instructables, so in case you have a 3D printer, you can make your own Blooming Zoetropes. Even if you don’t plan to, you will certainly enjoy this video demonstrating this mind-blowing optical illusion inspired by nature itself: