About a year ago, we brought you an enchanting video featuring 3D-printed sculptures dubbed Blooms that seemed to come to life before your eyes. There were no magic or camera tricks at play, just good old-fashioned math courtesy of artist/lecturer John Edmark of Stanford University. Each solid sculpture began as a computer program written in Python that directed the 3D printing of these works of art, brought to life courtesy of a rotating turntable and a finely tuned strobe light. Edmark is back at it again with a new batch of psychedelic sculptures he calls Blooms 2.

Check out the hypnotic video from John Edmark below (via Colossal) and continue reading to find out just what the heck is going on:

Here’s how Edmark describes the math behind his illusion-inducing sculptures:

Blooms are 3-D printed sculptures designed to animate when spun under a strobe light. Unlike a 3D zoetrope, which animates a sequence of small changes to objects, a bloom animates as a single self-contained sculpture. The bloom’s animation effect is achieved by progressive rotations of the golden ratio, phi (ϕ), the same ratio that nature employs to generate the spiral patterns we see in pinecones and sunflowers. The rotational speed and strobe rate of the bloom are synchronized so that one flash occurs every time the bloom turns 137.5º (the angular version of phi). Each bloom’s particular form and behavior is determined by a unique parametric seed I call a phi-nome (/fī nōm/).

In plain English, the sculptures themselves (solid structures) appear to shift and undulate because our eyes are seeing different “faces” of the sculptures in sequence instead of the whole thing at once, much like how a movie is actually a sequence of still images played in sequence at high speed to trick our minds into perceiving motion. As for the golden ratio (roughly 1.618), it not only produces some stunningly beautiful visuals that appear almost organic thanks to numerous examples of this ratio found in nature, it’s also used to time the strobe light’s flash in order to sync up the rotation and pull off the illusion. It’s a perfect melding of mathematics, computer programming, art, and technology.

Do you plan to pick up one (or more) of these optical illusions for your own personal gallery? Be sure to let us know in the comments below!

Images: John Edmark