I was curious if it would be possible to use statistical analysis to investigate whether human movement was random. The American physicist Leonard Mlodinow in The Drunkard’s Walk (2008)suggests that our path is governed by randomness, but I had begun to suspect that this was false, and realized I had a few million GPS points from my studies that I could use to test it.

To do this I developed a variation of a box-counting algorithm in *processing* in which a matrix is projected onto the landscape and a count is made of how many GPS points fall into each cell of the matrix. The next step was to make a histogram (a diagram which shows the frequency of a variable’s occurrence within a set) by taking every cell of the matrix and placing them into bins with all other cells with the same amount of points. The amount of cells with the same amount of GPS signatures are then counted and this is plotted as a graph showing the distribution of the data. To test this I ran the algorithm on the GPS data I collected from over 367 people for my Masters of Architecture Thesis. A diagram illustrating the algorithm is below:

What the histograms of the GPS data I collected in Rome, Mississauga, and Waterloo show is that the distribution of people across a landscape follows an inverse relationship best described by the equation:

## y=1/(x^k)

Where “y” is the number of points a person visits, “x” is amount of time spent at a specific point, and “k” is a value which allows the curve to best fit the data. From these histograms below, we see that people spend a lot of time at a small set of points (long low tail to the histograms at right) and small amounts of time at a large amount of points. This distribution shows that people have tendencies towards certain regions of space.

If human movement is random then we would not expect there to be any tendency towards a small number of specific regions of space and we would see what is called a standard distribution, more familiarly known as a ‘bell curve’. Based on these histograms: human movement is not random and fits within a “power law” relationship. Therefore, based on my analysis: human movement is far from random. More rigorous analysis is required however.