December 7, 2010 — Daniel Lichtblau, Scientific Information Group

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.

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November 10, 2010 — Jon McLoone, International Business & Strategic Development

Ever since I wrote the “Doing Spy Stuff with Mathematica” blog post, I have had a feeling that I am being watched. Time to build some office security using Mathematica Home Edition!

First, I am going to make use of an imminent new Mathematica command CurrentImage, which will import a real-time image from a video device. Let’s get some test images using the webcam on my laptop.

Imported real-time test image

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November 3, 2010 — Jon McLoone, International Business & Strategic Development

A little over a mile from the Wolfram Research Europe Ltd. office, where I work, lies Blenheim Palace, which has a rather nice hedge maze. As I was walking around it on the weekend, I remembered a map solving example by Peter Overmann using new image processing features in an upcoming version of Mathematica. I was excited to apply the idea to this real-world example.

Once back at my computer, I started by using Bing Maps to get the aerial photo (data created by Intermap, NAVTEQ, and Getmapping plc).

The maze is meant to depict a cannon with cannon balls below it and flags and trumpets above.

Aerial photo of the maze

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October 27, 2010 — Andrew Moylan, Technical Communication & Strategy

Practically everything I know about British art history would fit in one BBC documentary—the very BBC documentary I watched a little while ago.

I was intrigued to learn about the The Ambassadors, a sixteenth-century painting by Holbein. Among other things, this painting is famous for containing a human skull hidden in plain sight. Can you see it?

The Ambassadors

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September 1, 2010 — Jon McLoone, International Business & Strategic Development

I have a lot to study at the moment, as I learn how to use the technology that’s in our development pipeline. One of the first features I played with was so much fun I thought I would share it with you. You will be able to efficiently and easily texture map over any 3D image.

Texture mapping has all kinds of practical uses for improving visualization, but the first thing that I thought of was setting fire to a plot…

Importing a texture and creating the plot
The resulting textured plot

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September 8, 2009 — Doug McClintic, Commercial Account Executive

Are you a die-hard video gamer? Can you spend hours at a time sacrificing sleep to play your favorite real-time action console game? Or maybe you find yourself captivated by the amazing animation found in movies such as Pixar’s latest release, Up. Whatever your form of diversion, have you ever stopped to wonder what makes 3D games so realistic or how Pixar managed to animate thousands of balloons lifting Carl’s house? We at Wolfram Research have the inside scoop—it’s all about the math and physics.

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June 23, 2009 — Jon McLoone, International Business & Strategic Development

While tidying up after my kids once again, I found myself staring at the toy shown below and thinking of a conversation that I had had with an archaeologist Mathematica user a few days before. He had been interested in image processing of aerial photographs, but it occurred to me that image processing would also allow reconstruction of the musical secrets of this precious artifact that I had just uncovered in the remains of a lost toy civilization.

Well, this should be fun for 5–10 minutes. The toy is a music box, where you crank the handle to turn the drum that has pins on it to pluck the prongs to the left. Can I discover the tune, without having to move the parts?

Music box

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April 24, 2009 — Jon McLoone, International Business & Strategic Development

The “Droste effect” is when images recursively include themselves. The name comes from Droste brand cocoa powder, which was sold in 1904 in a box that showed a nurse carrying the same box which, in turn, showed the nurse carrying the box, and so on. The simplest form is to use a scale and transform on an image to place an exact copy within it, and then repeat. Take a look at this Demonstration using the original Droste box artwork. But much more interesting results can be achieved when you get complex analysis involved. M.C. Escher was the first to popularize applying conformal mapping to images, but with computers we can easily apply the same ideas to photographs, to get results like this:

A photograph conformally mapped in Mathematica

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December 1, 2008 — Theodore Gray, Co-founder, Wolfram Research, Inc; Founder, Touch Press; Proprietor,

It’s been possible since Version 6 of Mathematica to embed images directly into lines of code, allowing such stupid code tricks as expanding a polynomial of plots.

Mathematica allows you to embed images directly into lines of code

But is this really good for anything?

As with many extremely nifty technologies, this feature of Mathematica had to wait a while before the killer app for it was discovered. And that killer app is image processing.

Mathematica 7 adds a suite of image processing functions from trivial to highly sophisticated. To apply them to images, you don’t need to use any form of import command or file name references. Just type the command you want to use, then drag and drop the image from your desktop or browser right into the input line.

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May 2, 2008 — Theodore Gray, Co-founder, Wolfram Research, Inc; Founder, Touch Press; Proprietor,

You’ve probably seen examples of photo mosaics where each “tile” in the mosaic is a tiny photograph, selected so the overall brightness and color of the tiny photo averages out to the brightness and color needed for its position in the overall mosaic.

Following a suggestion by Ed Pegg, I suddenly found it impossible to imagine life without a photo mosaic of Dmitri Mendeleev, the principal inventor of the periodic table, made out of photographs of the elements.

It was convenient in this regard that I possess the world’s largest stock library of photographs of the chemical elements—about 2000 photographs of roughly 1550 different physical samples of the pure and applied elements—along with a photograph of Mendeleev and a bit of software called Mathematica. (You can see this library at; don’t forget to order a copy of my photo periodic table poster.)

You might think that creating photo mosaics is a standard task for which software, probably even free software, is available. And for all I know it is. But upon brief reflection I decided it would probably be faster and easier for me to write code to do this from scratch in Mathematica than it would be to find something to download and then figure out how to use it.

It turns out you can do a first pass at it with three lines of input.

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