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, periodictable.com

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, periodictable.com

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 periodictable.com; 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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June 29, 2007 — Theodore Gray, Co-founder, Wolfram Research, Inc; Founder, Touch Press; Proprietor, periodictable.com

A little hobby of mine is collecting and photographing the chemical elements. I have them all (except those that break the laws of man or physics). This is the photographic periodic table poster I sell:

The Periodic Table Poster by Theodore Gray

My poster and related imagery can be seen in several TV shows, and most recently staff at the venerable NOVA science series emailed asking for permission to use my poster image in an upcoming show about metals. They wanted to pan and zoom over it, starting wide and then focusing down onto a few individual elements.

I said, “Fine, but I have something I think you’ll like even better…. How about a video where every one of those samples is rotating in place?”

And here is that video.

What does any of this have to do with Mathematica? That video, and the more complex ones below, are directly output from Mathematica without any processing in traditional video editing tools.

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