Fibonacci Clock
What is the minimum number of colored LED necessary to tell the time? The Fibonacci Clock is a unique timepiece that uses just five colored squares of different sizes to tell time within 2.5 minutes. Here's how it works.
Clock Layout
- The clock consists of five squares whose sizes correspond to the first five Fibonacci numbers (1, 1, 2, 3, 5)
- These squares are arranged in a pattern that forms a rectangle, with the largest square (5) typically on one side. In our example, it will be on the right side.
Reading the Time
Reading the time requires you to do some quick mental calculations.
- Colors indicate function:
- Red squares represent hours
- Green squares represent minutes
- Blue squares represent both hours and minutes
- Black squares are inactive (not used for the current time)
- To read the hours: Add the values of all red and blue squares
- Example: If the 5-square is red and the 3-square is blue, the hour is 8
- To read the minutes: Add the values of all green and blue squares, then multiply by 5
- Example: If the 2-square is green and the 3-square is blue, the minutes are (2+3) × 5 = 25
Some Limitations
- Hours are displayed in 12-hour format (1-12)
- Minutes are displayed in 5-minute increments (0, 5, 10, 15, etc.).
- The clock can only display certain minute values due to the limited combinations possible with the five Fibonacci squares. We actually round the actual minute to the closest 5-minute value so the number see on the display is always within 2.5 minutes of the actual time. For most particle household clocks this a good compromise.
This clever design creates a visually interesting timepiece that requires a bit of mental arithmetic to read, making it both decorative and intellectually engaging.
It will take you a bit of time to get used to doing the math. After a while is will become easier.