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How I Made Wine Glasses from Sunflowers

Eons ago, plants worked out the secret of arranging equal-size seeds in an ever-expanding pattern around a central point so that regardless of the size of the arrangement, the seeds pack evenly. The sunflower is a well-known example of such a "spiral phyllotaxis" pattern: It's really magical that this works at all, since the spatial relationship of each seed to its neighbors is unique, changing constantly as the pattern expands outwardly—unlike, say, the cells in a honeycomb, which are all equivalent. I wondered if the same magic could be applied to surfaces that are not flat, like spheres, toruses, or wine glasses. It's an interesting question from an aesthetic point of view, but also a practical one: the answer has applications in space exploration and modern architecture.
Announcements & Events

Launching the Computable Document Format (CDF): Don’t Compress the Idea, Expand the Medium

Today we launched our Computable Document Format, or CDF, to bring documents to life with the power of computation. CDF binds together and refines lots of technologies and ideas from our last 20+ years into a single standard—knowledge apps, symbolic documents, automation layering, and democratized computation, to name a few. Disparate though these might appear, they come together in one coherent aim for CDF: connecting authors and readers much better than ever before. The idea is to provide a knowledge container that's as easy to author as documents, but with the interactivity of apps—for CDFs to make live interactivity as everyday a way to communicate as spreadsheets made charts.
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Mathematica Q&A: Creating Movie Files

Got questions about Mathematica? The Wolfram Blog has answers! We'll regularly answer selected questions from users around the web. You can submit your question directly to the Q&A Team using this form. Here is this week's question: How can I create and export movies and animations in Mathematica? This is something we do often—just about every movie or animation on the Wolfram Blog is created in Mathematica.
Announcements & Events

Driving CUDA over the Grid

There are two great principles to Mathematica's parallel computing design. The first is that most of the messy plumbing that puts people off grid computing is automated (messaging, process coordination, resource sharing, fail-recovery, etc.). The second is that anything that can be done in Mathematica can be done in parallel. With this week's release of gridMathematica 8, which adds the 500+ new features of Mathematica 8 into the shared grid engine, one nice example brings together both ideas—and that is driving CUDA hardware, in parallel, over the grid.
Announcements & Events

Join Us for the 23rd Wolfram Technology Conference, Oct 19-21, 2011

“Every conference brings reunions with old friends and a chance to make new ones among the many attendees who use Mathematica in a wide variety of industries and application areas.” ---Sal Mangano, Author of Mathematica Cookbook If you are interested in the latest and future technologies that are shaping computation and algorithm-rich development… would like to keep current on how to most efficiently develop and deploy with Wolfram technologies… want to see how others are solving computation challenges across industries and fields… Then join us for the Wolfram Technology Conference 2011 from October 19 through 21 in Champaign, Illinois, USA. Just steps from Wolfram's headquarters, the conference will provide three days of pure productivity, featuring talks by Wolfram developers, users presenting real-world solutions, interactive workshops, developer kitchens, and the opportunity to exchange ideas with fellow Mathematica enthusiasts. This year’s conference schedule will feature even more interactive and hands-on sessions and will cover topics that include:
Computation & Analysis

Celebrating the Fourth of July with Mathematica Fireworks

What could be a better way to celebrate the Fourth of July than beautiful fireworks in the dark sky? And what could be a better way to create fireworks on your screen than using Mathematica? There are a few different ways to create firework "effects" on computers, but it would be a shame if we chose to use just graphical effects with Mathematica. Yes, we are going for the full-scale particle simulation. Here is the synopsis. We create a firework simulation. With a mouse click, we seed a number of particles on the screen. Each particle has a different initial velocity, and it will follow the projectile motion. The particles spend a limited time on the screen, in which their opacity will diminish gradually. There will be a few customizable effects—colors and trails.
Computation & Analysis

All Rational Approximations of Pi Are Useless

When I first learned about π, I was told that a good approximation was 22/7. Even when I was 12 years old, I thought this was utterly pointless. 22/7 agrees with π to two decimal places (so three matching digits): Since there are three digits to remember in 22 and 7, what have you gained? You have just as much to remember, but have lost the notion that π is “just over 3”. Is there a better rational approximation where we actually get out more digits than we put in? Here is a brief and rather low-brow investigation (and the chance to win something if you can do better).
Design & Visualization

Mission Mathematica: Making a Photo Booth App in Three Steps

Creating an interactive app could be a complex and painstaking task. Not with Mathematica. Here I will present how I created a photo booth program in three easy steps—mostly during my lunch breaks. Step One: Architecture The application will have four main stages. Stage one: We show live webcam images with different image effects applied (possibly multiple pages of them) as a preview, and let the user choose one. Stage two: The chosen image takes up the window, waiting for the user to click a button. Stage three: Count down. Stage four: Capture an image, apply the effect, and add it in a film strip. Repeat.
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Mathematica Q&A: Computing Freight-Container Check Digits

Got questions about Mathematica? The Wolfram Blog has answers! We'll regularly answer selected questions from users around the web. You can submit your question directly to the Q&A Team using this form. This week's question comes from Adri, an engineer: How can I calculate the check digit in freight container codes like MSKU3881107? We had to start with some quick research for this question: it turns out that freight (shipping) container identification is covered by the ISO 6346 standard (Wikipedia). Under ISO 6346, each container is labeled with an 11-digit code (four letters + seven numerals) in which the last digit is a "check" digit that is computed from the other 10 digits, according to a fixed rule. For example, in MSKU3881107, the final “7” is the check digit. The rule specified by ISO 6346 for computing the check digit is designed so most accidental changes or misreadings of a single digit in a code will also change the check digit. This means you can use the check digit to catch most such errors; whenever you see a code, you calculate the check digit yourself and see if it matches up with the one in the code.