John Edmark is an inventor, designer and artist who teaches design at Stanford University in Palo Alto, CA. One of his latest creations is a series of 3D-printed sculptures designed with proportions corresponding to the Fibonacci Sequence. When Edmark's sculptures are spun at just the right frequency under a strobe light, a rather magical effect occurs: the sculptures seem to be animated or alive! The rotation speed is set to match the strobe flashes such that every time the sculpture rotates 137.5º, there is one corresponding flash from the strobe light. 

These masterful illusions are the result of a marriage between art and mathematics. Fibonacci's Sequence is defined as a recurrent relationship that can be expressed as  F_n = F_{n-1} + F_{n-2}...  where the first two digits of the sequence can be defined as F_1=1, and F_2=1. What this means is that the sequence starts with two 1's, and each following digit is determined by adding together the previous two. Therefore, Fibonacci's Sequence begins: {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...} etc. 

What makes the sequence so incredibly fascinating is its proliferation throughout nature, such as in the branching of trees, the arrangement of leaves on a stem, the flowering of baby broccoli, a nautilus shell, or even the spiral of galaxies; and that's just to name a few. You've probably seen Fibonacci's Sequence on countless occasions in your lifetime without even recognizing the pattern. One of the reasons that it appears in so many plants is because its particular arrangement of leaves along the stem allows for the most sunlight to hit each and every leaf. With its exposure to sunlight maximized, the plant then stands the best chance possible of properly photosynthesizing, growing stronger, and staying healthy. 

Regarding his sculpture series, Edmark states on his website: 
"While art is often a vehicle for fantasy, my work is an invitation to plunge deeper into our own world and discover just how astonishing it can be. In experiencing a surprising behavior, one’s sense of wonder and delight is increased by the recognition that it is occurring within the context of actual physical constraints. The works can be thought of as instruments that amplify our awareness of the sometimes tenuous relationship between facts and perception.

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 explores an interesting realm through his examination and representation of these ideas. The line between fact and perception can often become blurred, especially when considering something like artistic illusion: what you see is not always the same as what is really happening. While Edmark's spinning sculptures create the illusion that the objects are moving and morphing, the objects themselves are actually rigid forms and do not change in shape. This is a representation of what Edmark is referring to in his statement above when he mentions "the tenuous relationship between facts and perception." This relationship between perception and fact has been the subject of inquiry for philosophers, mathematicians, and artists alike for hundreds if not thousands of years, and Edmark's work does a fantastic job of illustrating its puzzling yet awe-inspiring nature. 

What did you think of the art? Were you familiar with Fibonacci's Sequence? Have you seen it manifest in an unusual place? Let us know your thoughts in the comments below.