Table of Contents

Details

Fibonacci32 is a beautiful 86mm circular disc with 32 RGB LEDs surface mounted in a Fibonacci distribution. Swirling and pulsing like a colorful galaxy, it’s mesmerizing to watch.

It consists of 32 RGB LEDs, arranged into a circular Fermat’s spiral pattern.

Background

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: 86 x 86 mm x 1.6mm (3.39 x 3.39 x .063 inch)
  • 2 layer printed circuit board
  • FR4 substrate
  • Black SMOBC (solder mask over bare copper)
  • Lead Free HASL (Hot Air Solder Leveling)
  • Designed in the US by Evil Genius Labs
  • Assembled in the US by Cyber City Circuits

Code

Open source example firmware: https://github.com/evilgeniuslabs/fibonacci32-demoreel100

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.

Nano header pins

  1. Snap the header pins into sets of two, using side/flush cutters:

  2. We need five sets right now. Insert the long side of the header pins into the corners and side of the Nano outline, on the back of the PCB.

  3. Place the Nano onto the pins, but DO NOT solder the pins on the Nano yet.

  4. Hold the Nano in place as you flip the whole thing over.

  5. Solder the pins on the front side of the board.

  6. Using side/flush cutters, trim the pins close to the PCB.

  7. Flip the board back over and take the Nano off. Again, DO NOT solder the Nano on just yet.

Prepare the LEDs

  1. Insert two sets of pins into opposite sides of the gap in a breadboard. If you don’t have a breadboard, you can use the Fibonacci PCB for this instead.

  2. Place an LED PCB onto the pins, and solder them.

  3. Remove the LED PCB, and repeat for the rest.

Assemble the Fibonacci32

Note: Double-check the orientation of each LED very carefully before soldering! It is much more difficult to desolder and fix incorrectly placed LEDs.

The small black dot in the middle of each and every LED should point toward the outside of the main round PCB.

You can insert and solder the LEDs in any order. If you follow the order listed below, you can stop and test the LEDs at any point. It’s not a bad idea to test after each LED. If a mistake is made, or an LED has failed, it will be easier to fix the fewer LEDs have been assembled.

  1. We’ll start with L0, the first LED, in the enter of the main PCB.
  2. Align the V, G, I, & O markings on an LED PCB with the markings on the main PCB. Insert the LED PCB pins into the holes on the main PCB.
  3. Check the markings again, making sure they match.
  4. Double-check and make sure that the small black dot in the middle of the LED points toward the outside of the main round PCB.

  5. Hold the LED in place while carefully flipping the board over.
  6. Hold the PCB down while soldering the pins on the LED.
  7. Flip the board back over and repeat the steps above to check, recheck, insert, and solder each LED.
  8. Below is the order in which the LEDs should ideally be assembled:
  •     0
  •   13
  •   26
  •   31
  •   18
  •     5
  •   10
  •   23
  •   28
  •   15
  •     2
  •     7
  •   20
  •   25
  •   12
  •     4
  •   17
  •   30
  •   22
  •     9
  •     1
  •   14
  •   27
  •   19
  •     6
  •   11
  •   24
  •   29
  •   16
  •     3
  •     8
  •   21