A three dimensional fractal in 3D

The video below is a fractal. It is also three dimensional. It has also been rendered from two different locations very close to each other. Therefore, you can also see it in three dimensions.

If you're not used to using YouTube's 3d capabilities then don't worry, this guy has a tutorial video explaining how to see the full three-dimensionality of the video without the need for glasses. It's just like magic eye in reverse, basically (though I'm not sure how good it is for your eye muscles).

If you liked that you should read the description of how the Mandelbulb was discovered. The Mandelbulb was made by people looking for a three dimensional analogue of the well known Mandelbrot set. If you don't know what the Mandelbrot set is, first watch this video, then read about what you just saw at Wikipedia.

None of the Mandelbulb, or the Mandelbrot set or the 3d fractal (a Mandelbox) shown above were designed by a human mind. All of the complexity found in the images comes about from defining structures in two or three dimensional space as the set of points that are or are not solutions to relatively simple mathematical algorithms. For example, the algorithm describing the Mandelbrot set can be described in just one line:

"... the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial \(z_{n+1} = z_n^2 + c\) remains bounded".

All of the complexity you can see in the entire ten minutes of the Mandelbrot set video I linked to above is defined in that one simple sentence.

Twitter: @just_shaun

Cinema verité - biology style

Animations of scientific principles are becoming more and more popular as a way of condensing complex data into an easily accessible format, particularly in the field of biology. Nonetheless, a recent article in Nature has raised a number of interesting points about how the visualisation of biological processes should not be taken lightly. Biology is unnervingly complex and there is still much that we don't understand - how are we to know how much of an animation is based on actual data and how much is just 'filling in the gaps'? This is not limited to the layperson - humans are very visual creatures and we are more easily swayed by pictures than words, experts are no exception. This is not new, journals have included idealised representations of biological processes for decades, but the advancement in computer animation has opened the door for more sophisticated animations that may imply a more thorough understanding where one does not exist. 

That said, I don't believe that researchers actively seek to mislead when presenting their findings in animated form, rather that they have to take the necessary steps to complete the movie - inherently requiring some artistic licence. And, for the most part, the bits being filled in are done so with reasonable scientific assumptions in mind and are not wild fantasy. The medium is an exciting one, and one that will hopefully play a significant role in not only disseminating scientific understanding, but also help to further research by highlighting gaps in our understanding. We must, however, always be vigilant when interpreting these animations as they are exactly that - animations - and not actual footage of molecular biology.

An excellent example of biological animation is the 'Inner Life of a Cell' video by a group in Harvard. I love this video, which depicts the events that occur upon the activation of T cell, and is pretty accurate in that almost everything show is backed up by real evidence. The 'motor protein' kinesin at 3:40 is particularly impressive because its mechanism of 'walking' along microtubules is backed up by extensive structural and biochemical studies, yet it just looks so much like a drunk guy who's been pulled over by the police and is trying to walk in a straight line! If you get the chance, I really recommend watching the video and reading the article mentioned above. Enjoy!

The human machine: circuits and wires

The previous post in this series can be found: here.

In the first post of this 'human machine' series, I explained how 'energy' (that abstract entity) is processed and used by our bodies in order to converted the chemical energy in our food into the work energy required to keep us ticking over nicely. I discussed in this how we are all actually powered by electrical circuits that buzz along in the internal membranes of our cell's power stations, the mitochondria. Better yet, not only are we powered by currents of electrons, familiar to us as standard electricity, but also by currents of protons, and so are actually working off energy being extracted from two forms of electrochemical potential. We're pretty sophisticated machines!

The work energy generated by these processes is used in myriad ways, but one very important one is the creation of another electrical current that is the foundation of everything you've ever done and every thought you've ever had: the neuronal action potential. This is the electrical signals that run along the neurons in your brain and body in general, constantly relaying information back and forth throughout the whole complex machine. Without it we would be like plants, with one part of our bodies completely unaware of what's happening to the rest of it, and animal life as it is familiar to us would be entirely impossible. Most people have, I expect, heard of the notion of electrical signals running throughout our bodies (it's why the machines built the Matrix, right?), but few will actually know what that means. In today's post I'm going to be talking about what neuronal signals actually are, and so explain why being hit by lightning is a bad thing but being defibrillated (like in ER) can be a good thing.