Editorial note: A future post will explore some of the contributions to the visual arts and media facilitated by Mathematica. The year 1982 saw a lot of important movies: Blade Runner, E.T.: The Extra-Terrestrial, Poltergeist, Star Trek II: The Wrath of Khan, The Thing, Mad Max 2: The Road Warrior, Pink Floyd The Wall, First Blood, Conan the Barbarian, Fast Times at Ridgemont High, The Dark Crystal, and TRON. I used Mathematica functionality to turn the TRON logo into something you can manipulate. You can download my notebook to play with the logo. (Mathematica Home Edition could be used to do this as well.)

With Halloween approaching, I thought that I would plumb new depths in frivolous uses of Mathematica by making some scary pumpkin movies. Woooo! If your nerves can take the sheer horror of it all, turn the lights down and dare to read on...

As a society, we seem to love data. We slice it, dice it, aggregate it, and analyze it. It tells us about the people, places, and things around us and around the world. It informs public policies and the public. It's easy to take for granted official statistics collected and presented by government agencies or statistics collected by non-governmental curators, because data seems to be everywhere, but it's important to remember that it takes a huge amount of work to collect that data and provide it in a usable form. World Statistics Day is a good time to remember that hard work and the impact information from the collected data has on our daily life.

I recently was asked about Fibonacci Day. I think I replied "What is Fibonacci Day?" Then the person explained it. November 23 is 11/23. Or 1, 1, 2, 3—the start of the Fibonacci sequence. Other yearly math-related days I found were Pi Day (3/14), Foursquare Day (4/16), Pi Approximation Day (22/7, in European format), Opposite Day (12/21), and Mole Day (6:02 10/23). A lot of these seem a bit arbitrary. I thought I might be able to do better, so here's what I came up with for the month of September.

I am a big fan of Randall Munroe's web comic strip xkcd. (Apparently I am not alone.) A while ago, Randall posted a strip with a self-referential chart of the amount of black ink in the image. If you have read my past blog items, you know I like recursive pictures. So I thought I would create a Mathematica version of this strip.

My mother has a theory: "The nicest weather is when you are at work, and then it rains on the weekend." Hearing this from her once again, I think it is time to expose her theory to the facts and prove her wrong. We'll start by setting up some tools to help retrieve and categorize the data in terms of the type of day. In the United Kingdom, the weekend is Saturday and Sunday.

The knockout stage of the 2010 FIFA World Cup is about to begin in South Africa. At the time of writing, every team has one group stage match remaining, and most teams still have a chance to finish in the top two places in their group and progress to the knockout stage (see the tournament schedule and group stage standings). There are different approaches to ranking world football teams. The most well known is FIFA's official world rankings, which are derived from points gained and lost in each match according to a heuristic set of rules that generally reward winning against higher-ranked opponents in more-important tournaments. A simple alternative with a more statistical basis is an Elo rating system (described in more detail below). A handy property of Elo rating systems is that they directly provide an estimate of the probability that a given team will perform better than another. We can use Mathematica with that to set up simulations of the knockout stage of the World Cup. This lets us estimate things like the chance of each team winning the tournament. We'll also generate some nice visualizations of the results, such as the following simulated knockout stage (based on the current top two teams in each group):