A Random Walk with Pi
- 12:12 pm |
We’ve gotten really good at generating big datasets. From what we search for on Google to all the stuff we do on Facebook, we generate a lot of data. And there have in turn been a proliferation of methods of visualizing big data, slicing and dicing it and providing meaning to it.
But what’s the mother of all big datasets? The digits of π. Of course, the number of digits in π is infinite, but over the years, as computers have become more powerful, we know many more of them than ever before.
But it’s one thing to say that I can download trillions of digits of π and another to make some sort of sense out of all of these digits. Into this steps a team of researchers from Australia, Lawrence Berkeley National Laboratory, and Simon Fraser University with some elegant visualizations of π. In a recent paper, they used a classic method of visualizing large strings of numbers: the random walk.
A true random walk is the path described by a sequence of randomly generated numbers. For example, if we have a string of -1′s and 1′s, then one way to describe this is by using time as the x-axis, and the y-axis as the cumulative sum of numbers so far. This yields a nice little sawtooth shape.
Alternatively, you can do a random walk on a plane, with each digit describing the direction and distance being moved. In the case of π and the method used by these researchers, they used color to designate additional information. For example, here color is used to designate time, with the blue being earlier in the sequence and the further along the spectrum is later in the sequence:
Clearly, π is more “random” than other numbers, such as some of the ones below:
The rest of the paper is full of lots of other figures, as well as calculations of the fractal dimensions of the random walks from different numbers. Go check it out and enjoy some visualizations of one of the oldest big datasets.