Galaxies, trees, and influenza cases have something in common: they tend to occur in clusters. The issue of how to model clustered spatial patterns is thus of interest to a variety of scientific disciplines.

Volume rendering, a new feature in Mathematica 9, provides an efficient way to visualize very large data sets. I first learned of this feature from reading Jeffery Bryant’s post on the Wolfram blog.

In our last post, we explored how Fourier transforms can be used in Mathematica to make a frequency filter for audio files. That post was primarily concerned with implementing the appropriate transforms (and, of course, paying homage to the amazing talent of Macklemore and Ryan Lewis).

The Heist by Macklemore and Ryan Lewis is a masterpiece. It is clearly the best album of 2012, and I suspect it will go down alongside classics like Illmatic, The Chronic, The Marshall Mathers LP, and The College Dropout.

One of my New Year’s resolutions is to make this blog more interactive. To do this, I’ll be using Wolfram’s computable document format (CDF). You don’t need Mathematica to interact with CDF files, but you do need a free player.

A couple of months ago, we wrote a post on how to use finite difference methods to numerically solve partial differential equations in Mathematica. Several readers have asked for more details about the method.

Art Heist Last week, burglars stole seven paintings from the Kunsthal museum in Rotterdam. The paintings included works by Picasso, Monet, Gauguin, and Matisse. The loot is likely worth hundreds of millions of dollars, but the loss of these great pieces surpasses anything that can be calculated as a monetary figure.

In today’s blog post, we’ll show you how to use Mathematica’s plotting features to visualize geospatial data. Baintha Brakk, aka The Ogre, is a mountain in the Karakoram range in northern Pakistan.

I love the elegant simplicity of programming in Mathematica. There is something undeniably beautiful about accomplishing something complex in a concise chunk of code. A famous Mathematica mantra is, “if you are using a For loop, you are probably doing it wrong.

In a recent blog post, The Economist discusses its “Sinodependency Index”, which measures the world’s economic dependence on China. This index was originally proposed in 2010. In today’s post, we will take a closer look at this index, and in the process, we will explore some of Mathematica’s finance-related capabilities.

In today’s post, we will explore numerical schemes for integrating stochastic differential equations in Mathematica. We will take an informal approach; for an in-depth treatment of stochastic differential equations, I recommend that you look at Stochastic Processes for Physicists by Kurt Jacobs and Modeling with Ito Stochastic Differential Equations by Edward Allen.

Mathematica’s NDSolve command is great for numerically solving ordinary differential equations, differential algebraic equations, and many partial differential equations. Most of the integration details are handled automatically, out of the user’s sight.

Today’s post will attempt to answer a provocative question: is the race for Olympic medal dominance getting more competitive? In the process of addressing this topic, we’ll learn how to directly import data from WolframAlpha into Mathematica.

You’ve probably heard of the traveling salesman problem: given a set of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?

Ecological models sometimes find very unexpected applications. Work on wolf territory modeling by Mark Lewis’s research group at the University of Alberta has been employed by researchers studying gang territories in Los Angeles.