3D printed blooming Fibonacci zoetropes

Stanford design prof John Edmark, as part of his artistic residency at Autodesk, created these 3D printed "blooming" Fibonacci-sequence zoetropes, which seem to grow, writhe, and pulse as they're spun before a camera shooting every 1/4000 of a second.

Edmark's created an Instructable detailing his process, if you want to try your hand at it!

The placement of the appendages on these sculptures is critical to the success of the animation effect. The positions are based on a specific phyllotaxy (i.e. leaf order) used by nature in a number of botanical forms, including pinecones, pineapples, sunflowers, artichokes, palm trees, and many succulents.

The photo above shows just such a succulent. I have numbered the leaves from youngest to oldest. If you follow the numbers in sequence you will find that each leaf is approximately 137.5º around the core from the previous leaf. 137.5º is a very special angle, called the golden angle, based on the golden ratio. When that angle is used by nature as a growth strategy it leads to the formation of spiral patterns. If you were to count the number of spirals in these patterns you will find that they are always Fibonacci numbers (e.g. check out the spirals on these pinecones).

In designing the sculptures, I used essentially the same method employed by nature. I placed the appendages one-at-a-time starting from the top-center, positioning each appendage 137.5º around the center from the previous appendage and also a little further out and/or down.

So when I animate these sculptures by spinning them with a strobe light (or video camera) I am, in a sense, recreating the process that I used to make them in the first place. Below are two stop-motion animations of some of my earlier work with Fibonacci spirals. You may these helpful in gaining a better intuition about how this animation technique operates.

Fibonacci Zoetrope Sculptures

via JWZ)