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Computation & Analysis

The Mathematica One-Liner Competition

Your assignment: Write a simulation of spherical particles coalescing under gravitational attraction. Limit the approach distance by a secondary repulsive force that acts over short distances. Produce an animation of the dynamic system starting with 15 particles in randomized positions. Formulate your solution in 140 characters or less. Sound challenging? A 138-character solution was Stephan Leibbrandt's winning entry in the Mathematica One-Liner Competition that was a part of this year's Wolfram Technology Conference.
Christopher Carlson, Senior User Interface Developer, User Interfaces
Computation & Analysis

The Legacy of TRON

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.)
Ed Pegg Jr, Scientific Information Editor, Scientific Information Group
Best of Blog

Automatic Physical Units in Mathematica

I just published a Mathematica package that provides an alternative, richer implementation of units and dimensional analysis than the built-in units package. You can get it here. Aside from being a really nice extension to Mathematica, it is also an interesting case study in adding a custom data "type" to Mathematica and extending the knowledge of the built-in functions to handle the new "type". First I have to explain the point by answering the question, "What's wrong with the built-in units package?" Well, there is nothing actually wrong with it, it just doesn't apply Mathematica's automation principles. It can convert between several hundred units and warn if a requested conversion is dimensionally inconsistent. But give it an input like... and it does nothing with it until you specify that you want the result in a specific unit. The core reason is that it doesn't teach the system, as a whole, anything about units, or even that the symbol "Meter" is any different than the symbol "x". All of the knowledge about units and Meter in particular is contained in the Convert command.
Jon McLoone, Director, Technical Communication & Strategy
Design & Visualization

Navigating the Blenheim Maze

I read Jon McLoone's recent "aMazeing Image Processing in Mathematica" post with some interest. It showed how to import an image of a maze, and then use image processing functions in Mathematica (some new to Version 8) to draw paths through the maze. What fun! I then observed, to my dismay, that there was no way to determine a "good" path. Frankly, I was disappointed. I decided that there must be ways to do this in Mathematica. One approach would involve forming a graph. We would have vertices at points where the maze path forks, and we would make weighted edges from approximated distances between these vertices. New functionality in Mathematica supports these graph methods. Unfortunately I am not yet familiar with it.
Daniel Lichtblau, Symbolic Algorithms Developer, Algorithms R&D
Education & Academic

How to Win at Coin Flipping

Let's flip a coin, over and over. Beforehand, the players each pick a sequence of flips. The sequence that occurs first wins. With HH vs. TH, HH will win if the first two flips are HH and will lose if any of those flips are tails. HH vs. TH has a 1/4 vs. 3/4 possibility of winning. Phrased a different way: Suppose I offer a bet on a series of coin flips. One of these bets would be bad for you. Which one? The odds of the event occurring are given at the end. (The second bet is the bad bet to take.) HTT appears before TTT. If it does, I give you $1. If not, you give me $4. (7/8) HHT appears before TTT. If it does, I give you $1. If not, you give me $3. (7/10) THH appears before HHT. If it does, I give you $1. If not, you give me $2. (3/4) HTH appears before THH. If it does, I give you $1. If not, you give me $1. (1/2) This is the strange world of Penney's game. Here is a table of odds and facts for various 3-flip games. Calculating these odds can be both tedious and mathematically demanding—a natural job for Mathematica or Mathematica Home Edition.
Ed Pegg Jr, Scientific Information Editor, Scientific Information Group
Education & Academic

Conrad Wolfram’s TED Talk: “Stop Teaching Calculating, Start Teaching Math”

"We have a real problem with math education right now," is how Conrad Wolfram starts his TEDGlobal 2010 talk in Oxford, in which he reasons through what's wrong, why, and how we can fix it. Central to Conrad's argument is the role of calculating—that for the mainstream subject it's not an end in itself, but a means to an end, and therefore should be wholeheartedly computer based. As he puts it, "Math ≠ Calculating, Math >> Calculating". He's optimistic about what's possible. "We have a unique opportunity to make math both more practical and more conceptual simultaneously," and to get people to "really feel math". Couldn't agree more? Dramatically disagree? Let us know. PS: If you would like to get involved, check out and join computerbasedmath.org.
Wolfram Blog Team
Announcements & Events

Programming with Natural Language Is Actually Going to Work

I love computer languages. In fact, I’ve spent roughly half my life nurturing one particular very rich computer language: Mathematica. But do we really need computer languages to tell our computers what to do? Why can’t we just use natural human languages, like English, instead? If you’d asked me a few years ago, I would […]

Stephen Wolfram
Announcements & Events

The Free-Form Linguistics Revolution in Mathematica

With the release of Mathematica 8 today, the single most dramatic change is that you don’t have to communicate with Mathematica in the Mathematica language any more: you can just use free-form English instead. Wolfram|Alpha has pioneered the concept of specifying computations with free-form linguistic input. And with Mathematica 8, the powerful methods of Wolfram|Alpha […]

Stephen Wolfram
Announcements & Events

Mathematica 8!

Mathematica 8 is released today! It’s a huge and important release. With dramatic breakthroughs—and major broadening of the whole scope of Mathematica. After 8 versions and 22 years most software systems have decayed to slow and lumbering development. But not Mathematica. In fact, with Mathematica it’s quite the opposite. As the years go by, Mathematica […]

Stephen Wolfram
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