June 4, 2008 — Dillon Tracy, Web Intelligence

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:

Secret message revealed

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.

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May 22, 2008 — André Kuzniarek, Director of Document and Media Systems

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:

File > New > Demonstration

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March 19, 2008 — Kathryn Cramer, Scientific Information Group

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.

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March 5, 2008 — Jessica Paris, Demonstrations Project Administration

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.
Browse by topic on The Wolfram Demonstrations Project

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February 13, 2008 — Jeffrey Bryant, Scientific Information Group

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. Its 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
Broken Heart Tangram
A Rose for Valentines Day
A Rose for Valentines Day
Equations for Valentines
Equations for Valentines
Sweet Heart
Sweet Heart
The Polar Equations
of Hearts and Flowers
The Polar Equations of Hearts and Flowers
Cupid’s Arrow
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.

December 28, 2007 — George Beck, Scientific Information Group

I do love gadgets, linkages, clockworks, all that 19th-century cogs-and-wheels technology. So much easier to see than our 21st-century nanotubes and zillion transistors on a chip.

Sándor Kabai has written many Demonstrations illustrating such mechanisms. A few of his latest are:

Gyroscopic Joint TheStraightLine as a Roulette
Gyroscopic Joint Straight Line as a Roulette
Lemniscate Plotting Device Helicopter Tilt Control
Lemniscate Plotting Device Helicopter Tilt Control

What makes these interesting is that playing with the various parameters lets you vary both the geometric setup and the controls that make the mechanism go through its motion.

One in the same vein is from Stephan Heiss:

Mechanical Involute Gears

It shows how gears work. Amazing! You can vary the geometry to the point where the gears lock up and change gear ratios to get a really good understanding of what makes gears tick.

October 14, 2007 — Conrad Wolfram, Director of Strategic & International Development

My announcement last Thursday that you can publish almost any Mathematica notebook so it’s interactive in our free Player brings about much more of a change than you might first think.

In my Technology Conference talk, I explained how this new Publish for Player service removes one of the last hurdles to making new applications as everyday as new documents. And in turn that initiates a new era of communicating technical ideas.

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October 5, 2007 — Joe Bolte, Director of Consulting, Wolfram Solutions

The Demonstrations team has been very busy behind the scenes lately. Even though I work on The Wolfram Demonstrations Project every day, it amazes me to see that we’ve published nearly 2,000 Demonstrations already. And we’re working hard to add site features (many of which are user-suggested) at the same time.

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June 8, 2007 — Christopher Carlson, Senior User Interface Developer, User Interfaces

One of the challenges of developing Mathematica is resisting the urge to spend all my time playing with the graphics toys I create. A lot of what I do results in features so fun to explore that they jeopardize the further development of Mathematica. I’d like to point out a few of them in this blog, starting with a simple but profound change in the behavior of Mathematica graphics: direct graphics output.

In previous versions of Mathematica, the result of a Plot or other graphics command was the abbreviated form  - Graphics -  that represented the symbolic output. The actual graphical image itself was spit out like a watermelon seed as a side-effect of the evaluation and was not associated with the symbolic output.

In Mathematica 6, the output and the image are one and the same, behavior we call “direct output” to contrast it with the “side-effect output” of previous versions. This simple change in behavior underlies much of the interesting new functionality in Version 6.

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May 4, 2007 — Joe Bolte, Director of Consulting, Wolfram Solutions

Now that Mathematica 6 is out, I can finally talk about an amazing site we’ve built with it–The Wolfram Demonstrations Project.

The Demonstrations Project is a collection of interactive visualizations made using Mathematica 6. You can preview the Demonstrations on the web and download them to run in Mathematica or the free Mathematica Player.

We began the project last year, when Stephen Wolfram realized that the dynamic capabilities we were building into Mathematica 6 would allow users to create and share new interactive content much faster than ever before.

From an initial seed of a few dozen, the site has already grown to almost 1,300 Demonstrations, with more pouring in each day. And if you have Mathematica 6, making your own Demonstrations is as easy as completing and uploading an authoring notebook. Any Mathematica 6 user can participate.

The Demonstrations are all open-code, so you can even see how each one is built (usually with just a few short lines of Mathematica).

Take a few moments to explore the site. It’s grown so much that even someone like me–who works on it full time–is constantly surprised by what’s there. It has everything from interactive addition tables to molecular models and more.

Explore 3D graphics. Watch calculus being done. Create your own computer-generated art.

I can’t wait to see how the new methods of education, research, and collaboration that the site enables take form in this exciting publishing medium. The site’s features and the collection of Demonstrations that you’ll find there now are just the beginning.

I hope you enjoy what we’ve made, and that you’ll let us know any ideas you have about it.