Science, maths and computers.
Process 6 by Casey Reas
Casey is computational artist and professor at the University of California, Los Angeles. He co-created the Processing programming language, which I’ve fallen in love with recently. It’s a free package with provides a powerful and simple graphical environment for all sorts of graphical simulations, and image generation. It’s just generally really fun to play with.
View more of Casey’s artistic work here.
Stare at this painting for a while. Regardless of what you perceive its artistic merit to be (“my little sister could do that…” some of you will no doubt be saying), you have to admit there is some strange aesthetic quality to it. It guides your eye from one focal point to another, giving your brain a plane of seemingly infinite detail to explore and it seems to - in some sense - resonate with your gaze. Artsy bullshit? Or science?
Jackson Pollock was a controversial figure. His work has been described as “mere unorganized explosions of random energy” and even “a joke in bad taste”. However it just so happened that his unconventional painting technique generated what a mathematician would instantly recognise as a fractals. We see fractals a lot in nature and mathematics and their most distinct feature is their display of self-similarity on many scales. Bronchi of a lung, branches of a tree and the Sierpinski triangle are examples of fractals (have a look and you’ll get a good idea).
If we zoom/enhance a portion (say, around a quarter) of the painting above, we get something that looks a lot like the original painting itself!
This is what is meant by self similarity - zoom in and you see the same thing again. We can quantify the ‘fractalness’ of an image by calculating its fractal dimension. Though I won’t go in to the maths here, it will suffice to say that while a 1D line has a dimension of D=1 and a 2D square has one of D=2, fractals can have non integer dimensions such as D=1.71, or anything!
Now, why does the Pollock look pretty? There have been interesting studies on how the human eye assess an image. In one, subjects were asked to look at pictures while their eye motion was tracked. It was found that the eye trajectories themselves were fractals! This makes sense. A 1-dimensional eye motion (below, left) does not give us enough information about a scene, however a fully 2-dimensional gaze (below, right: where the eye attempts to perform a full scan of every point in front of it) is way too much for the visual cortex to process at any instance. Instead, the eye has come up with a much more efficient method of looking - doing an intensive 2D scan of a small area before making a 1D leap to another area. The overall result (below, middle) is a kind of 1.5-dimensional fractal scan; it allows isolated ‘islands’ of detail to be put together by the brain to make a complete image!
It turns out that there is also a ‘resonance’ effect that occurs when viewing an image with a fractal dimension similar to that of the eye. Subjects were asked to view a series of computer generated fractal images and rate their aesthetic quality. It was found that images with a dimension of around 1.5 (same as the eye) had by far the most positive response. Furthermore, fMRI scans indicated that viewing such images activated regions of the brain associated with emotions such as happiness.
It is quite easy to analyse a Pollock painting and calculate its fractal dimension. You can kinda tell where I’m going with this… It turns out that his artwork does indeed possess a fractal dimension of around 1.5! Haters can hate, but science proves that Pollock is good. Who ever said that art was subjective?
Though it may be stretching it a little bit too far to attribute all of Pollock’s success to a mathematical quirk, there’s one thing for sure: Your little sister can’t do it.
Black ferrofluid and dye race through bubble structures, drawn through by the invisible forces of capillary action and magnetism.
It’s a truly incredible work of art/science.
Also, word for the day: ferrofluid. Use it in conversation, perhaps.
Magnet TV by Nam June Paik, 1965
This is really cool. Old CRT (cathode ray tube) televisions worked by scanning a beam of electrons across a phosphor screen. The horseshoe magnet on the top of this TV messes up any nice raster pattern the electron beams might have had to create these cool patterns.
Generative art piece visualising the brain.
Graph drawing by Ethan Hein
Lorenz attractor by pretendy
Mathematical Mountains is a collection of generative art pieces by Steve Brunton. These are bifurcation diagrams, which map the stable and chaotic dynamics of a system. Bifurcation essentially means changing a parameter of a system until one stable point forks (or bifurcates) into two. These forks get smaller and smaller and denser and denser until the system has no stable points at all an exhibits chaotic dynamics.