Just a couple of weeks ago we released Mathematica 7. This week we’ve made the Wolfram Demonstrations Project live with Mathematica 7. All the 4270 Demonstrations on the site run with Mathematica 7 (yes, we tested every single one of them, partly automatically, partly by hand). And we added 147 new Demonstrations that specifically make use of Mathematica 7’s features. Most of those Demonstrations were created internally within Wolfram Research, in a small frenzy of activity right around the actual release of Mathematica 7. I was involved in organizing this Demonstrations-fest. It’s very impressive how quickly it’s possible to create so much high-quality material with Mathematica. Of course, it helped that we were able to work directly with the key developers of much of Mathematica 7’s functionality—so people were often creating Demonstrations based on the very features they had implemented in the system. The new image processing system in Mathematica 7 was a particularly fertile source of Demonstrations. Charting, splines and vector visualization are other areas that have spawned all sorts of interesting Demonstrations. Here are a few of my personal favorites:

As the project coordinator for the Wolfram Demonstrations Project, I’ve seen a lot of new exciting features we’ve been working on come to fruition recently and I want to tell you about them. I hear from a lot of our users, and want to let you know that we are listening to you and working on features that will make communicating your ideas, sharing your work and learning about Demonstrations even easier. And trust me, even more features are coming! Here are some of the most recent updates we’ve made to the Wolfram Demonstrations Project.

Recent Demonstrations: Visual Encryption

When I was a kid, dinosaurs and secret codes were topics of surefire interest, since one was useful for eating your little sister and the other one for denying her the password to the clubhouse. I haven't noticed any Demonstrations about dinosaurs yet (I continue to keep an eye out), but interesting ones about cryptography turn up regularly, including a couple of neat recent entries on visual encryption: Michael Schrieber's Visual Encryption Pad and Paul van der Schaaf's Graphical Modulo-4 Image Encryption.

One cipher (if you can call it that) common in my kiddie code books involved printing a message in red stipple overlaid with a noise field of blue stipple. You could use the piece of red cellophane included in the back of the book to mask out the blue part and reveal the secret message. The Visual Encryption Pad Demonstration is the sophisticated cousin of this scheme, involving the overlay of a random bit mask (the key) with another bit mask of the same size (the message). Applying a set of rules to the combination of bits at a given pixel (in the case of this Demonstration, XNOR) reveals the message, which might look like this:

If your spies in the field don't have computers, and you are limited to passing around messages on microfilm or something, then the only bit-combination rule set you will be able to use is OR. And of course your messages are limited to one bit per pixel. The Graphical Modulo-4 Image Encryption> scheme, on the other hand, can encode more than one bit per pixel, even on physical media. Let me quote some snippets of the Demonstration's code and describe how they work, and then I'll discuss a couple of extensions that suggest themselves.

There are a lot of interesting features hidden “under the hood” of the Wolfram Demonstrations authoring notebook, and most of them are new to Mathematica 6. The authoring notebook acts as a stand-alone form, and not only represents a simple new way to standardize information for systematic deployment, but also offers a convenient basis for sharing these subtle but powerful new technical details. I’m excited by any new features that enhance the document creation process in Mathematica. As an 18-year veteran of the company, I’ve interacted with the notebook front end since Version 2, and have been contributing to the interface and documentation systems since Version 3. I’ve recently taken on new responsibilities for managing some of our web applications, particularly online forms for both internal business and external customer interactions, and I’m eager to insert notebook-based source material and Mathematica controller logic into these systems. We have already done so with the Wolfram Mathematica Documentation Center and the Wolfram Demonstrations Project. Of all these systems, Demonstrations are the most visible to our users from their starting point through administrative stages to ultimate deployment, so let’s dissect the Demonstrations authoring form to expose its hidden talents. If you haven’t done so already, you can open the authoring notebook from Mathematica’s File menu:

A week or so ago I made an Easter egg in Mathematica and emailed around a bit to see if I could get other people to try it, too. I consulted with my family, dared readers of my blog to send me Mathematica eggs and mentioned my egg to my friend science-fiction writer Cory Doctorow, who blogged it on BoingBoing. I also spread the idea around Wolfram Research. As someone with a small collection of ornamental eggs in a glass case in my living room, I am quite pleased with the results. Here’s how it came about: My kids are enthusiastic celebrators of holidays. They want to start decorating for Halloween in August, and decorating for Christmas as soon as the pumpkins and spider webs come down. Last week, I had bought a carton of eggs and a package of egg dye, and kept finding my kindergartner getting out the eggs or the dye without permission. So I’d promised that Thursday, absolutely, we would begin work on eggs. I have a copy of Michael Trott’s The Mathematica GuideBook for Graphics, and on Thursday afternoon, my fifth-grader was flipping through it, looking at the pretty pictures. He saw a picture in it and asked if I could scan in and print out a picture like that on a sticker for him to put on an Easter egg. I decided he had a point there: that one could and should decorate eggs with Mathematica. The example he’d chosen was more elaborate than I was willing to take on in 3D, but I decided to see what I could do while we boiled the eggs. I looked for something to work from and found the Ellipsoid Demonstration on the Wolfram Demonstrations Site. I adapted from that, using the mathematical description of an egg shape from Jürgen Köller’s website as my guide to egginess.

As the project coordinator of the Wolfram Demonstrations Project, I have an inbox that is overflowing with fantastic ideas from Mathematica users and coworkers for how to make the Demonstrations site even more user-friendly and easy to navigate. One of the most exciting new features we’ve implemented recently is the new topics page. In a few easy clicks, users can fine-tune their searches to browse topics ranging from Middle School Mathematics to the Solar System to Natural Forms and everything in between.

As an editor for the Wolfram Demonstrations Project, I see many new submissions every day. The amount of variety is sometimes staggering. Occasionally, we have events that trigger Demonstrations based on a theme, and Valentine's Day is one such event. What in the world do Demonstrations have to do with Valentine's Day? Take a look at some of the new set of Demonstrations that are available for this February 14. They include a puzzle, a parametric surface, an algebraic surface, two parametric curves and one that’s just plain fun. It’s amazing to see how mathematics can be applied to everyday topics (and matters of the heart), not just to classroom math or science.

Broken Heart Tangram

A Rose for Valentines Day

Equations for Valentines

Sweet Heart

The Polar Equations of Hearts and Flowers

Cupid's Arrow

Stay tuned for a blog post from Chris Carlson with details about how he “lovingly” created his "Sweet Heart" Demonstration. I’m looking forward to seeing what Demonstrations the next holidays might bring.