Footsteps of pi
Imagine you have a compass.
Now, instead of the 4 cardinal directions, mark the compass with 10 evenly-divided indications.
You and I are going to play a game. You are standing on a plane, and in front of you is a ball.
I am going to tell you a number. Push the ball with enough force to impart a 1 meter-per-second change in velocity in the direction matching the number’s annotation on your compass.
For example, if I gave you the number 7:
Now, I’ll give you some more numbers. Rather than an absolute change in direction, you will push the already-rolling ball, adjusting its current velocity.
7, 0, 3
I’m going to give you more numbers. Many more.
What does the path of the ball look like when I tell you 580,000 digits of pi?
I originally created this image in early 2020 to impress and woo my now-girlfriend, who I adore.
The colors are arbitrary, and have no deeper meaning. I picked a simple strategy to iterate colors and liked the result aesthetically, so stuck with it.
This image would look different if you interpreted pi in a different base. There’s nothing unique about base-10 in this context, it’s just what I used.
Here are some more irrational numbers expressed in this way: