Footsteps of pi
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![](pi_580k.png)
Imagine you have a compass.
![](compass_standard.png)
Instead of the 4 cardinal directions, mark the compass with 10 evenly-divided indications.
![](compass_base10.png)
Let’s play a game together. You’re standing on a plane, and in front of you is a ball.
I’m 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:
![](walk_7.png)
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
![](walk_7_0_3.png)
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?
![](pi_580k.png)
Addendum
I originally created this image in early 2020 to impress and woo my now-girlfriend✱, who I adore.
✱ Note
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 special about base-10 in this context, it’s just what I used.
Here are some more irrational numbers expressed in this way:
![e to 400k digits](e_400k.png)
e to 400k digits
![phi to 400k digits](phi_400k.png)
phi to 400k digits