### Details

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.

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]

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

### Specifications

• Size: 3.39 x 3.39 x .063 inch (86 x 86 x 1.6 mm)
• 2 layer printed circuit board
• FR4 substrate
• Green SMOBC (solder mask over bare copper)
• HASL (Hot Air Solder Leveling) Finish
• Designed in the USA

Parts

Includes only the printed circuit board with LEDs, does not include parts that are required to assemble and run it (microcontroller, power supply, wires, etc).

Parts that are not included, but are required to assemble and use:

• Microcontroller (Arduino, ESP8266, ESP32, etc):
• Power supply, or run off of USB power from microcontroller.
• Wires, connectors, crimp tool, etc.
• Soldering iron, solder, etc.

Parts I used in my builds (also not included):

### Code

Open source example firmware and web application: https://github.com/jasoncoon/esp8266-fastled-webserver/tree/fibonacci64

### 3D Printed Case

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

### Assembly Instructions

Note: Double-check the position, alignment, and orientation of each component very carefully before soldering!

If you’re new to soldering, I highly recommend reading through a good soldering tutorial, such as the ones by Adafruit and SparkFun.

Note: Pictures are of the larger Fibonacci256, but the instructions are identical.

1. Find a clean spot on your soldering workspace. I used a piece of heavy card stock. Carefully place the board with the LEDs facing down and the bottom of the board facing up.
2. I used 90 degree header pins to allow connecting and disconnecting jumper wires easily. I used small female headers to keep them level while I soldered.