I guess this scenario sounds mildly scientific enough to analyse. So which countries does little Pi visit in his 2015 year long journey? And which countries would have never learned about the beauty of $\pi$? The following map provides the answer (red dot was the starting point)
Pi actually missed quite a few countries. From a total of 244 countries/territories/colonies, Pi did not visit 111. Even my home country Germany! It is interesting to see, how he "avoided" a big part of Europe and also some African Countries which are not that far from his point of departure.
Due to his weird traveling route, Pi did not only miss some countries but also visit several points more than once. The following map shows, how often he visited certain locations. The darker the color, the more often he was there.
The most frequently visited point by Pi was -100 Longitude and 43.5 Latitude: The Middle of Nowhere, South Dakota, USA. And he went there 57 times... It also becomes apparent, why he missed so many countries. He was sailing around quite a lot on the seven seas. So at the end, was Pi just a Pirate?
Yes, i admit this scenario is a bit whacky. But mathematically still quite interesting. For example the world consisted of 259200 reachable locations in my example. A random walk with 736036 steps could have visited each location almost 3 times! There is a lot more interesting stuff behind this scenario, which I will talk about in later posts.
This post was also quite interesting from a visualizational point of view. I guess without the help of the R package rworldmap
stackoverflow thread, this post wouldn't have been possible.