# Math You Can Wear: Fibonacci Spiral LED Badge

Fibonacci numbers are seen in the natural structures of various plants, such as the florets in sunflower heads, areoles on cacti stems, and scales in pine cones. [HackerBox] has developed a Fibonacci Spiral LED Badge to bring this natural phenomenon to your electronics.

To position each of the 64 addressable LEDs within the PCB layout, [HackerBox] computed the polar (r,θ) coordinates in a spreadsheet according to the Vogel model and then converted them to rectangular (x,y) coordinates. A little more math translates the points “off origin” into the center of the PCB space and scale them out to keep the first two 5 mm LEDs from overlapping. Finally, the LED coordinates were pasted into the KiCad PCB design file.

An RP2040 microcontroller controls the show, and a switch on the badge selects power between USB and three AA batteries and a DC/DC boost converter. The PCB also features two capacitive touch pads. [HackerBox] has published the KiCad files for the badge, and the CircuitPython firmware is shared with the project. If C/C++ is more your preference, the RP2040 MCU can also be programmed using the Arduino IDE.

For more details on beautiful RGB lights, we’ve previously presented Everything You Might Have Missed About Addressable LEDs, and for more details on why they can be so fun to wear, check out our Hackaday Badgelife Documentary.

(Editor’s note: HackerBox makes and sells kits, is run by Hackaday Contributor [Joseph Long] IRL.)

# Unique Clock Keeps Time The Fibonacci Way

You say your binary clock no longer has the obfuscation level needed to earn the proper nerd street cred? Feel like you need something a little more mathematically challenging to make sure only the cool kids can tell the time? Then this Fibonacci clock might be just the thing to build.

Granted, [TecnoProfesor]’s clock is a somewhat simplified version of an earlier version that was nigh impossible to decode. But with its color coding and [Piet Mondrian]-esque grids, it’s still satisfyingly difficult to get the time from a quick glance. The area of the blocks represents the Fibonacci sequence 1, 1, 2, 3, 5, and adding up which blocks are illuminated by the RGB LEDs behind the frosted front panel. That lets you tally up to 12 intervals; for the minutes and seconds, there are indicators for the powers multiples of 12 up to 48. Put it all together and you’ve got a unique and attractive graphical time display that’s sure to start interesting conversations when the mathematically disinclined try to use it. Check out the video below as the clock goes from 12:28:01 to 12:28:46. We think.

If this doesn’t scratch your itch for obfuscated clocks, we’ve got plenty of them. From random four-letter words to an analog digital clock to an epic epoch clock, we’ve got them all.

# Fibonacci Clock Is Hard To Read, Looks Good

Artists have been incorporating the golden ratio in their work for many hundreds of years, and it is thought that when proportions are in line with this ratio, it tends to be more aesthetically pleasing. With that in mind, the clock that [Philippe] created must mathematically be the best looking clock we’ve ever featured, even if it is somewhat difficult to tell time from it.

The clock is made up of squares which represent the first five numbers of the Fibonacci sequence. The squares are backlit with LEDs, which will illuminate red for the hour, green for the minute, and blue representing the overlap of hours and minutes. Simply add up the red and blue squares to get the hour, and add the green and blue squares to get the minutes. The minutes are displayed in 5 minute increments since there aren’t enough blocks though, so you’ll also have to multiply. Confused yet? If not, it turns out that there are several ways to display certain times using this method, any of which can be randomly selected by the clock. [Philippe] reports that there are 16 different ways to represent 6:30, for example.

The clock is driven by an ATmega328P and is housed in a wooden case. There are schematics and code available on [Philippe]’s site if you want to build your own, there are detailed descriptions of how to tell time with this clock. You’ll probably need those. If you like getting confused by clocks, you might also like this one as well.