I was sitting in a bagel shop on Saturday with my 9 year old daughter. We had brought along hexagonal graph paper and a six sided die. We decided that we would choose a hexagon in the middle of the page and then roll the die to determine a direction:
1 up (North)
2 diagonal to the upper right (Northeast)
3 diagonal to the lower right (Southeast)
4 down (South)
5 diagonal to the lower left (Southwest)
6 diagonal to the upper left (Northwest)
Our first roll was a six so we drew a line to the hexagon northwest of where we started. That was the first “step.”
After a few rolls we found ourselves coming back along a path we had gone down before. We decided to draw a second line close to the first in those cases.
We did this about 50 times. The results are pictured above, along with kid hands for scale.
Last Monday we celebrated a “Scientific Marathon” at Royal Botanic Garden in Madrid, a kind of mini-conference to talk about our research. I was talking about the relation between fungal spore size and environmental variables such as temperature and precipitation. To make my presentation more friendly, I created a GIF to explain the Brownian Motion model. In evolutionary biology, we can use this model to simulate the random variation of a continuous trait through time. Under this model, we can notice how closer species tend to maintain closer trait values due to shared evolutionary history. You have a lot of information about Brownian Motion models in evolutionary biology everywhere!
Another place that this is useful is in describing stock market movements in the short run.