Want To Play Fibonacci Pinball?
5 min readJan 10, 2023
A project and a thought experiment
Let’s build a pinball machine. You will need 10 finishing nails, 5 small cups, a wooden board, and a pinball (marble).
Bang the nails partway into the board in a triangular pattern:
- one nail in the top row,
- two nails in the second row,
- three nails in the third and so on, and
- with enough space for the pinball to fit between the nails.
To operate the machine, tilt the board and release the pinball so that it hits the top nail dead center. The pinball deflects either left or right with equal probability. It will then continue falling, hitting one of the nails in the second row, and deflecting either left or right around that nail with equal probability.
The result is that the pinball follows a random path, deflecting off one pin in each of the four rows of pins, and ending up in one of the cups at the bottom. The gray lines show many possible paths. The red line shows one of them.
