Publications by Martin Stefan
High Jump World Records
In the image below you see a higher jumper using the modern-day Fosbury flop technique. Unlike athletes using older techniques like the scissors jump or the straddle technique so-called floppers go backwards over the bar backwards and land on their shoulders and back. But why is the proper technique so important if you want to become an Olympic g...
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Replicating the Axelrod Tournaments
Starting in 1980 American political scientist Robert Axelrod ran a series of computer tournaments. He invited fellow researchers to submit computer codes (written in Fortran or Basic) that would play a very special game against each other: The iterated prisoner’s dilemma. The results of the tournament turned out to be quite remarkable. Simple s...
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Fractals with R
In the images below you can see two fractal structures. The first is the famous “Koch snowflake” named after the Swedish mathematician Helge von Koch. The second is based on a “recursive tree”. Both of these structures are “self similar”. These means that they are based on a pattern that keeps on repeating itself in ever greater detai...
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The Traveling Salesman Problem
It’s one of the oldest problems in the field of optimization. A salesman wants to travel to a number of cities and then return back home. The million dollar question now is: How should he plan his route to minimize his time on the road? At first, this might sound like trivial problem. Why not just calculate the distance of every possible route ...
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Maze Generation (Part 1)
When generating a maze, you could start with an empty space and then randomly adding some walls. Would the resulting structure be any interesting? Well, maybe. Depending on the number of walls that you added, at least some areas of your maze will be impossible to reach, while other parts of the maze will constitute perfect loops. In the image bel...
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Toward A Better COVID-19 Map
About this map Numerous European health authorities have created interactive dashboards that visualize the COVID-19 situation in their respective countries. These maps are often very detailed and display the data on a regional or even local level. Pan-European maps, like the one of the European Centre for Disease Prevention and Control, are typic...
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Maze Generation (Part 2)
In the previous part of this series on maze generation, I explained how one can generate perfect mazes using the “recursive backtracking algorithm”. In this part, I will introduce two additional maze generating algorithms. The first is a randomized version of the “Kruskal algorithm” devoloped by Joseph Kuruskal. The second is a randomized...
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