Fibonacci64 is a beautiful 86mm circular disc with 64 RGB LEDs surface mounted in a Fibonacci distrubution. Swirling and pulsing like a colorful galaxy, it’s mesmerizing to watch. It exists at the intersection of art, math, science, and geometry.

It consists of 64 RGB LEDs, arranged into a circular Fermat’s spiral pattern.

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In disc phyllotaxis, as in the sunflower and daisy, the mesh of spirals occurs in Fibonacci numbers because divergence (angle of succession in a single spiral arrangement) approaches the golden ratio. The shape of the spirals depends on the growth of the elements generated sequentially. In mature-disc phyllotaxis, when all the elements are the same size, the shape of the spirals is that of Fermat spirals—ideally. That is because Fermat's spiral traverses equal annuli in equal turns. The full model proposed by H Vogel in 1979[2] is

r = c \sqrt{n},
\theta = n \times 137.508^\circ,

where θ is the angle, r is the radius or distance from the center, and n is the index number of the floret and c is a constant scaling factor. The angle 137.508° is the golden angle which is approximated by ratios of Fibonacci numbers.[3]

Source code: https://github.com/jasoncoon/esp8266-fastled-webserver/tree/fibonacci64

3D printed case with paper diffuser: https://www.thingiverse.com/thing:4128167

3D printed case with 3mm black LED acrylic diffuser: https://www.thingiverse.com/thing:4154087

Fermat's spiral. (2015, October 24). In Wikipedia, The Free Encyclopedia. Retrieved 02:45, February 24, 2016, from https://en.wikipedia.org/w/index.php?title=Fermat%27s_spiral