July 30, 2014 — Wolfram Blog Team
Kenzo Nakamura uses Mathematica to create Escher-inspired mathematical art. His trademark piece, Three-Circle Mandala, depicts a large circle covered by three smaller, repeating circles that form a Sierpinksi gasket.
When Nakamura began using Mathematica, he didn’t originally intend to use it for his artistic endeavors. He found the program by chance at a seminar while looking for the right tool to help him write his master’s thesis.
Now, in addition to using Mathematica for technical and operations research, Nakamura uses it to create Mathematica-derived visual illusions. Although his works are static drawings, their infinite properties create the illusion of movement.
Watch Nakamura discuss using Mathematica to create his drawings, and see a few of his creations.
(YouTube in Japanese)
July 22, 2014 — Wolfram Blog Team
Photography by Tracy Howl and Paul Clarke
Has our newfound massive availability of data improved decisions and lead to better democracy around the world? Most would say, “It’s highly questionable.”
Conrad Wolfram’s TEDx UK Parliament talk poses this question and explains how computation can be key to the answer, bridging the divide between availability and practical accessibility of data, individualized answers, and the democratization of new knowledge generation. This transformation will be critical not only to government efficiency and business effectiveness—but will fundamentally affect education, society, and democracy as a whole.
Wolfram|Alpha and Mathematica 10 demos feature throughout—including a live Wolfram Language generated tweet.
May 30, 2014 — Wolfram Blog Team
Donald Barnhart is a self-proclaimed mad optical scientist and independent business owner. He’s been developing optical design and analysis software in Mathematica since 1991, he’s the creator of the popular Optica software package, and he’s the developer of the first successful high-resolution holographic instrument that measures three-dimensional velocity fields in fluids.
Now Barnhart has another invention to add to his list of accomplishments: a totally new kind of photo album called the SlideOScope.
July 20, 2012 — Michael Trott, Chief Scientist
(This is the first post in a three-part series about electrostatic and magnetostatic problems involving sharp edges.)
Mathematica can do a lot of different computations. Easy and complicated ones, numeric and symbolic ones, applied and theoretical ones, small and large ones. All by carrying out a Mathematica program.
Wolfram|Alpha too carries out a lot of computations (actually, tens of millions every day), all specified through free-form inputs, not Mathematica programs. Wolfram|Alpha is heavily based on Mathematica, and many of the mathematical calculations that Wolfram|Alpha carries out rely on the mathematical power of Mathematica. And while Wolfram|Alpha can carry out a vast amount of calculations, it cannot carry out all possible calculations, either because it does not (yet) know how to do a calculation or because the (underlying Mathematica) calculation would take a longer time than available through Wolfram|Alpha. So for a detailed investigation of a more complicated engineering, physics, or chemistry problem, having a copy of Mathematica handy is mandatory.
But there is also the reverse relation between Mathematica and Wolfram|Alpha: Wolfram|Alpha’s knowledge, especially its data knowledge, allows it to carry out investigations and calculations that can substantially increase the power of pure Mathematica. And all of this is because Wolfram|Alpha’s knowledge is accessible through the WolframAlpha function within Mathematica.
August 26, 2011 — Maryka Baraka, Marketing Content Manager
Now that the Computable Document Format (CDF) is officially released, the real fun has begun. At least for me. Whether or not you plan to start using CDF in your own work anytime soon, you’ve got to admit, it’s pretty cool. From publishing textbooks and making complex information easy to understand to recreational games and everyday blogging, CDF truly makes it possible to communicate ideas in a more participatory way—as adopters of the format have already proven.
It has been exciting to see the tremendous interest in CDF following last month’s launch. Although CDF is a new advancement, it’s clear that the possibilities it presents resonate with authors and readers alike, and hence with publishers as well.
May 17, 2011 — Wolfram Blog Team
Ever wondered how to grill the perfect steak? Or how well dunking food into an ice bath stops the cooking process? Nathan Myhrvold used Mathematica to answer these questions, and many others.
Myhrvold, the first chief technology officer at Microsoft, has had a longtime interest in cooking and has a background in science and technology. When he started using new techniques like sous vide, in which food is slowly cooked in vacuum-sealed bags in water at low temperature, he discovered that many chefs don’t know much about the science behind cooking. He decided to change that with a massive cookbook that was released in March. In 2,438 pages, Modernist Cuisine covers a wide range of cooking techniques and their scientific backgrounds, including heat transfer and the growth of pathogens. (It has recipes, too.)
March 17, 2011 — Jon McLoone, International Business & Strategic Development
There is an old word game where you try to get from one word to another through connections with other words. For example, you might get from “cold” to “stationary” via the word “frozen”, since “cold” and “frozen” are synonyms and “frozen” and “stationary” are synonyms, albeit for different meanings of the word “frozen”.
I thought of this game when I started to learn the new graph theory functions in Mathematica 8. We can think of the words in the English language as the vertices of one large graph and the synonym connections between them as the graph edges. If you do that, it looks like this:
So let’s see if we can generally solve this synonym chain problem.
March 1, 2011 — Andrew Moylan, Technical Communication & Strategy
In the previous post in this series, we looked at how to model a stabilized inverted pendulum using the control systems design features in Mathematica 8. We were quickly able to simulate a linearly controlled cart-and-pendulum system, and show that it is stable against some fairly large perturbations.
But what about a double (or triple or quadruple… ) pendulum? A general n-link pendulum is depicted below. In this post we’ll see how to derive the equations of motions for this system, find out whether we can stabilize it with a linear control scheme, and produce some animations of the results.
January 19, 2011 — Andrew Moylan, Technical Communication & Strategy
Can you balance a ruler upright on the palm of your hand? If I concentrate, I can just barely manage it by constantly reacting to the small wobbles of the ruler. This challenge is analogous to a classic problem in the field of control systems design: stabilizing an upside-down (“inverted”) pendulum.
One of the best things about Mathematica is that it makes specialist areas like control systems accessible to non-specialists. This lets you freely combine and develop new ideas without needing to be an expert in everything. It also makes Mathematica a great platform for learning and exploring new areas.
Using the new control systems features (one of several new application areas integrated into Mathematica 8), I’ve been experimenting with models of stabilized inverted pendulums. I’m no expert in control theory, but you’ll see that one doesn’t need to be.
October 7, 2010 — Jon McLoone, International Business & Strategic Development
Mathematica has always had the most complete collection of special functions available. You might think that by now there were no more to add, but the next release of Mathematica will add another five. You might also think that any that are left to add are too obscure for you to care about. They are getting fairly obscure, but you should still care.
Let’s look at one of them: Owen’s T function.