A week or so ago my older son did a short project on random walks out based on a page in Patters of the Universe:

Returning to Patterns of the Universe

By coincidence that week Kelsey Houston-Edwards’s new video was about random walks. So, we watched her video after that project:

Today my younger son is sick and wasn’t up to participating in a project. So, I thought it would be fun to revisit the random walk project and dive in a little deeper since my older son was a little more familiar with that topic.

I started by asking him what he remembered about random walks from the prior project and from the PBS Infinite Series video. One thing that he remembered is that 2d random walks do tend to return to where they started, but 3-d ones tend not to.

We started looking at specific random walks by studying a 1-dimensional random walk. We created a random walk by rolling dice and didn’t get quite what we were expecting, but that result led to a fun conversation:

In the last video we got more even numbers than we were expecting, so we decided to continue on to see if the walk would return to 0. Obviously we kept rolling even numbers . . . .

Next we moved on to studying a 3d random walk (and, of course, now rolled lots of odd numbers ðŸ™‚ )

We created the 3d random walk with snap cubes and it was pretty neat to see the shape that emerged from the dice rolls.

Despite the unexpected outcome with the even and odd rolls this was a fun project. I’d like to think a little more about how to make some random walk 3d prints. My guess is that those prints would be really fun to share with kids.