[IMSAI Guy] tore apart a device with a wireless network card and decided to investigate what was under the metal can. You can see the video of his examination below. Overall, it was fairly unremarkable, but one thing that was interesting was its use of an antenna on the PCB that uses a fractal design.
You probably know fractals are “self-similar” in that they are patterns made of smaller identical patterns. The old joke is that the B. in Benoit B. Mandelbrot (the guy who coined the term fractal) stands for Benoit B. Mandelbrot. You can think of it as akin to recursion in software. Antennas made with fractal patterns have some unusual and useful properties.
Continue reading “Teardown Locates Fractal Antenna”
Francesco de Comité is an Associate Professor in Computer Science at the University of Sciences in Lille, France, where he researches the 2D and 3D representation of mathematical concepts and objects. He’s presented papers on a variety of topics including anamorphoses, experiments in circle packing, and Dupin cyclides. His current project involves modeling and 3D printing sea shells. He’ll be presenting a paper on the topic at Bridges Conference in July. You can find his projects on Flickr as well as on Shapeways.
Hackaday: One of your recent projects involves creating fractal patterns and warping them into biologically-correct sea shell shapes, which you then print.
FdC: Modeling seashell shapes is an old topic–Moseley, 1838, D’Arcy Thompson beginning of 20th century. A seashell can be defined as a curve turning around an axis, while translating in the direction of this axis (i.e. on a helicoidal trajectory), and growing in size at the same time. This was modeled for computers in the ’60s by David Raup.
Drawing patterns on seashells was described by Hans Meinhardt using a model of chemical reactions (activator-inhibitor), in the same spirit as Turing’s work on morphogenesis. Combining these two works, and using 3D printers instead of 2D renderers, we can build realistic seashells, either by copying existing shells, or inventing new ones. A 3D model is not just a juxtaposition of a huge number of 2D views: manipulating 3D models can help you understand the object, find details, and so on.
I was curious to see if making a 3D seashell was possible. Moreover, I show that this can be done with simple tools — well, except the 3D printer.
Continue reading “Interview: Francesco de Comité Makes Math Visually Awesome”
One way to get around limitations in computing resources is to throw more computers at the problem. That’s why even cheap consumer-grade computers and phones have multiple cores in them. In supercomputing, it is common to have lots of processors with sophisticated sharing mechanisms.
[Henk Verbeek] decided to take 80 inexpensive PIC32 chips and build his own cluster programmed in — of all things — BASIC. The devices talk to each other via I2C. His example application plots fractals on another PIC32-based computer that has a VGA output. You can see a video of the device in action, below.
Continue reading “80-PIC32 Cluster Does Fractals”
Think not of what you see, but what it took to produce what you see
Randomness is all around you…or so you think. Consider the various shapes of the morning clouds, the jagged points of Colorado’s Rocky Mountains, the twists and turns of England’s coastline and the forks of a lightning bolt streaking through a dark, stormy sky. Such irregularity is commonplace throughout our natural world. One can also find similar irregular structures in biology. The branch-like structures in your lungs called Bronchi, for instance, fork out in irregular patterns that eerily mirror the way rivers bifurcate into smaller streams. It turns out that these irregular structures are not as irregular and random as one might think. They’re self-similar, meaning the overall structure remains the same as you zoom in or out.
The mathematics that describes these irregular shapes and patterns would not be fully understood until the 1970s with the advent of the computer. In 1982, a renegade mathematician by the name of Benoit Mandelbrot published a book entitled “The Fractal Geometry of Nature”. It was a revision of his previous work, “Fractals: Form, Chance and Dimension” which was published a few years before. Today, they are regarded as one of the ten most influential scientific essays of the 20th century.
Mandelbrot coined the term “Fractal,” which is derived from the Latin word fractus, which means irregular or broken. He called himself a “fractalist,” and often referred to his work as “the study of roughness.” In this article, we’re going to describe what fractals are and explore areas where fractals are used in modern technology, while saving the more technical aspects for a later article.
Continue reading “Fractals Among Us”
What’s better than spending hours and hours with CSS
trying to get images and text to center properly? Not [Jim], but he did notice that
Most fractals are recursive, and CSS rules can be applied to HTML objects that have already have rules applied to them. It’s not quite recursion, because there’s no way to dynamically generate HTML with CSS. However, with just a few tags, [Jim] can generate one level of a Pythagoras Tree. This method requires placing tags in the HTML for every level of the tree, greatly limiting the cool factor. That’s easily remedied by a few CTRL+Cs and CTRL+Vs.