Posts Tagged ‘Mathematics’
Fun real-life demonstration of solitons.
In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed.
In 2011, Solitons were the topic of one of the Review Courses at the African Institute for Mathematical Sciences in Muizenberg, South Africa.
Lecturer: Patrick Dorey
Music: Kaninzadi by the Mendes Brothers
Licence: Creative Commons Attribution Share Alike
This awesome visualization of a Mandelbrot by makc3d set lets you zoom in and out of it super fast (it is pre-rendered). I love it because it really gives you a mindblowing sense of scale invariance if you get the zooming speed right. Nothing like a cool viz to get a good feel for abstract concepts and the Mandelbrot set is so beautiful! It’s one of those iconic science images of my upbringing.
How to display scientific data in a way that both inspires and respects the science? Not that science is ugly, but it’s definitely not trivial. Some images captivate us naturally, some, less so.
One of the biggest challenges is probably to display abstract, mathematical things with properties as obscure as fractional dimensions. This was first achieved a few decades ago with the beautiful fractals. Seeing fractals was one of the things that made me go study science. I would drool over Julia sets and admire the details of computer-generated mountain ranges.
Now, those same fractals are being imaged in three dimensions – and how beautiful they are!
These are called Mandelbulbs. Here is one example.
The guys who did this spent a couple of years working on the problem. In fact, it is really difficult. Most attempts would render something pretty but it wouldn’t be fractal. That is, you couldn’t zoom in indefinitely and keep seeing structure. Several people tried, building on each others’ attempts and eventually they came up with a solution. It seemed to work. They looked closer, and yes, it did work… almost.
But now, how to visualise it? This is new mathematics. You can’t just feed it into some 3D rendering software to produce an image of. It’s like asking Google to translate between R’lyehian and Klingon.
So the Mandelbulbians, in true geek fashion, wrote their own ray tracing routines and this is what resulted in these breathtaking images. Sheer eye candy. Our eyes love it, our brains have no idea what’s going on.
It doesn’t get much more obscure when it comes to understanding what this means, but it is really beautiful! This is visualisation at its best.