Creating Digital Landscapes

Tim Chartier, a professor of mathematics at Davidson college, has put together some great resources on using mathematical algorithms and free computer software to create random-looking 2D and 3D landscapes.

In the following paper posted at the MAA’s Digital Library, Chartier outlines the basic ideas of fractal geometry and random number generation, and creates a simple computer program that will generate random-looking coastlines and mountain ranges:

http://mathdl.maa.org/mathDL/23/?pa=content&sa=viewDocument&nodeId=1795

And in a follow-up blog post, Chartier takes the process one step further by turning his 2D fractal island into a planet, using free ray-tracing software.

http://forum.davidson.edu/mathmovement/2011/07/10/a-random-planet/

After explaining how to produce the planet, Chartier challenges the reader to create and submit their own!

It’s easy to see some of the applications of this idea in computer animation and graphics, as well as perhaps in simulations.  A simple, innovative, and fun idea to explore!

By patrick honner, ago

Math, Music, and Crossword Puzzles

This is a nice profile on Dan Feyer, the winner of the 2010 American Crossword Puzzle Tournament.

http://www.nytimes.com/2010/12/07/science/07profile.html

Feyer, who is a music director in New York City, excelled at math as well as music in school.  This combination of talents, math and music, is not uncommon, and both of these skills sets seem to appear with great frequency among crossword puzzle enthusiasts.

Indeed, as the article points out, Jon Delfin, a 7-time winner of the tournament, is also a musician, and many other winners and crossword constructors are math and computer science types.  As one puzzler points out, the connection between math, music, and crossword puzzles is pattern finding.  In addition, the three fields also rely on the manipulation of symbols that often contain no inherent meaning themselves.

This all makes perfect sense to me.  I am an avid crossword puzzle solver, I have competed in the tournament many times, and I have even constructed several puzzles of my own, including this one that incorporates many mathematical ideas:

https://mrhonner.com/2011/06/02/crossword-puzzle-a-touch-of-math-2/

Unfortunately, constructing a good crossword puzzle takes as much time and effort as constructing a good math test!

By patrick honner, ago

NYT Presents: Jeterography

In celebration of Derek Jeter’s 3,000th major league hit, the New York Times ran a really cool infographic displaying the relative frequencies of where those 3,000 hits went.

http://archive.nytimes.com/www.nytimes.com/interactive/2011/06/15/sports/baseball/jeter-3000-hits.html

In addition to tracking where all of Jeter’s hits have gone, two graphics also compare his first 1,500 hits to his second 1,500 hits:  not surprisingly, the second 1,500 consists of fewer home runs and fewer hits to left field.  A similar graphic shows Alex Rodriguez’s hit patterns.

There are several other interesting data displays here, including year-by-year histograms for all 28 MLB players with 3,000 hits.

By patrick honner, ago
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