I saw a fun random walk program shared by Steven Strogatz yesterday:
Today I shared the program with the boys. It has 4 different types of random walks to explore. For each one I asked the boys what they thought would happen. At the end we looked at all 4 simultaneously.
Sorry that the starting videos are so blue – I didn’t notice that while we were filming (and didn’t do anything to fix it, so I don’t know why the last two vides are better . . . .)
Also, following publication, I learned the author of the program we were playing with:
Here’s the introduction and the first random walk – in the walk we study here, the steps are restricted to points on a triangular lattice:
In the next random walk, the steps were chosen from a 2d Gaussian distribution. It is interesting to hear what the boys thought would be different:
Now we studied a random walk where the steps all have the same length, but the direction of the steps was chosen at random:
The last one is a walk in which the steps are restricted to left/right/up/down. They think this walk will look very different than the prior ones:
Finally, we looked at the 4 walks on the screen at the same time. They were surprised at how similar they were to each other:
Definitely a fun project, and a really neat way for kids to explore some basic ideas (and surprises!) in random walks.