fibonacci sequence

5 Articles

Fibonacci Clock Looks Like Beautiful Modern Art

December 19, 2024 by 12 Comments

Don’t ask us why, but hackers and makers just love building clocks. Especially in the latter case, many  like to specialize in builds that don’t even look like traditional timepieces, and are difficult to read unless you know the trick behind them. [NerdCave] has brought us a pleasing example of such a thing, in the form of this gorgeous Fibonacci clock.

The build was inspired by an earlier Fibonacci clock that later became a Kickstarter project. Where that build used an Atmega328P, though, [NerdCage] landed on using a Raspberry Pi Pico W instead. The build throws the microcontroller board on a custom PCB, and sticks in inside an attractive 3D-printed enclosure. Black filmanet was used for the body, while white filament was used for the face of each square to act as a diffuser. Addressable RGB LEDs are used to illuminate the five square segments of the clock.

Obviously, you’re wondering how to read the clock. All you need to know is this. The first five numbers in the Fibonacci sequence are 1, 1, 2, 3, and 5. Each square on the clock represents one of these numbers—the side lengths of each square match these numbers. Red and green are used to represent hours and minutes, respectively, while a blue square is representing both. Basically, to get the hour, add up the values of red and blue squares, and to get the minutes, do the same with green and blue squares, but then multiply by 5. In the header image, the clock is displaying 8:55 PM… we think.

We’ve featured Fibonacci-themed clocks before, albeit ones with entirely different visual themes. Video after the break.

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DIY Core Rope Memory Z80 Demonstrator Generating A Fibonacci Sequence

October 16, 2024 by 14 Comments

We’ve seen a few retro products using core rope memory, such as telephone autodiallers. Obviously, we’ve covered the Apollo program computers, but we don’t think we’ve seen a complete and functional DIY computer using core rope memory for program storage until now. [P-lab] presents their take on the technology using it to store the program for a Z80-based microprocessor demoboard, built entirely through-hole on a large chunk of veroboard.

For the uninitiated, core rope memory is a simple form of ROM where each core represents a bit in the data word. Each wire represents a single program location. Passing a wire through the core sets the corresponding bit to a logic 1, else 0. These wires are excited with an AC waveform, which is coupled to the cores that host a wire, passing along the signal to a pickup coil. This forms an array of rudimentary transformers. All that is needed is a rectifier/detector to create a stable logic signal to feed onto the data bus.

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A black work mat holds a circular badge with 64 addressable LEDs in a spiraling shape akin to the center of a sunflower. The LEDs have a rotating rainbow spiraling around the circle with red touching violet on one end. The colors extend in bands from the center to the rim of the circle.

Math You Can Wear: Fibonacci Spiral LED Badge

June 14, 2023 by 8 Comments

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.)

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Unique Clock Keeps Time The Fibonacci Way

July 10, 2019 by 9 Comments

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.

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Fibonacci Clock Is Hard To Read, Looks Good

May 7, 2015 by 18 Comments

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.

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