Fibonacci48 x 14mm

Posted March 23, 2024


Table of Contents

Details

Fibonacci48 x 14mm is a tiny, beautiful circular disc with 48 RGB LEDs surface mounted in a Fibonacci distribution. Swirling and pulsing like a miniature galaxy, it’s mesmerizing to watch.

It consists of 48 XL-1010RGBC-WS2812B 1mm² RGB LEDs, arranged into a circular Fermat’s spiral pattern.

It has solder pads on the back that match the pinout of the TinyLily. It can be used by any microcontroller via the 5V, GND, and Data In pads. It also has a Data Out pad, for connecting more LEDs on the same data pin.

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: 0.55 x 0.55 x .063 inch (14 x 14 x 1.6 mm)
  • 2 layer printed circuit board
  • FR4 substrate
  • Black SMOBC (solder mask over bare copper)
  • HASL (Hot Air Solder Leveling) Finish
  • Designed in the US by Evil Genius Labs

Code

Open source touch demo: https://github.com/jasoncoon/fibonacci48x14mmDemo

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.

  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. VERY carefully check polarity before connecting 5V and GND.
  3. Either:
    • Solder wires to the pads on the edge of the Fibonacci PCB and connect them to your microcontroller.
    • Or:
    • Carefully align a TinyLily, or another controller with an identical footprint with the pads on the back of the Fibonacci PCB. Solder the pads.
  4. Each XL-1010RGBC-WS2812B can theoretically draw 15mA at full brightness, solid white color. 48 of them can theoretically draw 720mA. I’ve found tha is blindingly bright, and brightness should be drastically reduced to keep current draw and heat down.
  5. Keep an eye on the temperature of the PCB and especially the connectors. High temperatures can reduce the life of the LEDs. When possible, ensure air can flow, either passively (ventilation) or actively (exhaust fan).
  6. If using FastLED, I suggest using its power management to limit the maximum brightness to a reasonable amount, well under the maximum your power supply is rated for.