With a little math, sculptures can come to life. It’s hard to be anything but mesmerized by Stanford professor John Edmark’s writhing, wriggling 3D-printed sculptures. No, those sculptures aren’t alive, though your eyes may deceive you. The secret to this eye-massaging video is actually Edmark’s creative application of Leonardo Fibonacci’s famous sequence of numbers.

#### Fibonacci Everywhere

In mathematics, the Fibonacci sequence, or Golden Ratio, is a series of numbers in which every subsequent number in a series is the sum of the previous two (i.e. 1, 1, 2, 3, 5, 8, 13…). You’ve probably seen the Fibonacci spiral in a math textbook, which is created by connecting the opposite corners of squares whose side lengths are successive Fibonacci numbers. Not familiar? Then simply look around. The Golden Ratio is manifest in lots of places in nature, from the arrangement of sunflower seeds to the shapes of galaxies. The Golden Ratio is so ubiquitous in nature, math, art and science that it’s often considered a fundamental characteristic of the universe. Keep this in mind as we dissect Edmark’s video.

#### Animating the Inanimate

To make his sculptures come alive, Edmark placed them on a platform rotating at 550 revolutions per minute. He videotaped the sculptures at 24frames per second with an incredibly fast shutter speed (1/4,000th of a second). The camera was synchronized with the rotating platform and it snapped a photo every time the sculpture turned 137.5 degrees. This sync-up is key, because 137.5 degrees is the golden angle, or an angle that divides a full angle into a Golden Ratio. In nature, points separated by 137.5 degrees in tightly bound spirals — like those seen in a pine cone — produce interlocked spirals winding in opposite directions. In an Instructable post, Edmark explained how the illusion works:

Each petal on the sculpture is placed at a unique distance from the top-center of the form. If you follow what appears to be a single petal as it works its way out and down the sculpture, what you are actually seeing is all the petals on the sculpture in the order of their respective distances from the top-center.

When you see the beauty of Edmark’s pulsating sculptures, it’s no wonder the Golden Ratio underlies the structure of so many things in our world.