July 28, 2011 — Christopher Carlson, Technical Communication & Strategy
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.
July 1, 2011 — Yu-Sung Chang, Technical Communication & Strategy
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.
June 30, 2011 — Jon McLoone, International Business & Strategic Development
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).
June 8, 2011 — Jon McLoone, International Business & Strategic Development
Back in 1988 when Mathematica was just a year old and no one in my university had heard of it, I was forced to learn Fortran.
My end-of-term project was this problem: “A drunken sailor returns to his ship via a plank 15 paces long and 7 paces wide. With each step he has an equal chance of stepping forward, left, right, or standing still. What is the probability that he returns safely to his ship?” I wrote a page or so of ugly code, passed the course, and never wrote Fortran again. Today I thought I would revisit the problem.
We can code the logic of the sailor’s walk quite easily using separate rules for each case. Firstly, if he is ever on the 16th step or already on the ship, then he is safely on the ship the next time.
June 1, 2011 — Andrew Moylan, Technical Communication & Strategy
Recently I found myself reading about “subitizing”, which is the process of instinctively counting small sets of items in a fraction of second. For example, try quickly counting a few of these:
The Wikipedia article indicates that you can nearly always correctly count four or fewer items in a small fraction of a second. Above four, you start to make mistakes. I wanted to test this claim in Mathematica (using myself as the test subject). I decided to create a simple game in which small groups of items are momentarily displayed on the screen, after which players estimate how many they saw.
December 17, 2010 — Christopher Carlson, Technical Communication & Strategy
Write a simulation of spherical particles coalescing under gravitational attraction. Limit the approach distance by a secondary repulsive force that acts over short distances. Produce an animation of the dynamic system starting with 15 particles in randomized positions.
Formulate your solution in 140 characters or less.
Sound challenging? A 138-character solution was Stephan Leibbrandt’s winning entry in the Mathematica One-Liner Competition that was a part of this year’s Wolfram Technology Conference.
December 14, 2010 — Ed Pegg Jr, Editor, Wolfram Demonstrations Project
Editorial note: A future post will explore some of the contributions to the visual arts and media facilitated by Mathematica.
The year 1982 saw a lot of important movies: Blade Runner, E.T.: The Extra-Terrestrial, Poltergeist, Star Trek II: The Wrath of Khan, The Thing, Mad Max 2: The Road Warrior, Pink Floyd The Wall, First Blood, Conan the Barbarian, Fast Times at Ridgemont High, The Dark Crystal, and TRON.
I used Mathematica functionality to turn the TRON logo into something you can manipulate. You can download my notebook to play with the logo. (Mathematica Home Edition could be used to do this as well.)
October 29, 2010 — Jon McLoone, International Business & Strategic Development
With Halloween approaching, I thought that I would plumb new depths in frivolous uses of Mathematica by making some scary pumpkin movies. Woooo!
If your nerves can take the sheer horror of it all, turn the lights down and dare to read on…
October 19, 2010 — Darren Glosemeyer, Lead Statistics Developer
As a society, we seem to love data. We slice it, dice it, aggregate it, and analyze it. It tells us about the people, places, and things around us and around the world. It informs public policies and the public.
It’s easy to take for granted official statistics collected and presented by government agencies or statistics collected by non-governmental curators, because data seems to be everywhere, but it’s important to remember that it takes a huge amount of work to collect that data and provide it in a usable form. World Statistics Day is a good time to remember that hard work and the impact information from the collected data has on our daily life.
October 5, 2010 — Ed Pegg Jr, Editor, Wolfram Demonstrations Project
I recently was asked about Fibonacci Day. I think I replied “What is Fibonacci Day?” Then the person explained it. November 23 is 11/23. Or 1, 1, 2, 3—the start of the Fibonacci sequence.
Other yearly math-related days I found were Pi Day (3/14), Foursquare Day (4/16), Pi Approximation Day (22/7, in European format), Opposite Day (12/21), and Mole Day (6:02 10/23).
A lot of these seem a bit arbitrary. I thought I might be able to do better, so here’s what I came up with for the month of September.