Carl Barratt, PhD, Department of Mechanical Engineering, University of New Haven, West Haven, Connecticut

"Chaos" is a scientific field dedicated to the study of systems whose behaviors are characterized by two distinctive traits: sensitivity of the system to small changes in its state, and "deterministic unpredictability." The first trait describes the situation whereby the smallest of disturbances can cause a dramatic change in how the system behavior evolves: the so-called "butterfly effect", whereby a butterfly flapping its wings in China can, in principle, precipitate a hurricane in Connecticut. An everyday example of a chaotic system is to be found in the game of pool: reproducing a sequence of collisions is for all practical purposes impossible no matter how precisely you place the balls initially. The second trait represents the well established fact that the behavior of systems - when in the chaotic regime - appears to be random and unpredictable even though the system itself is deterministic, that is, given the same initial conditions (e.g. initial placement of the balls on the pool table) it should in principle evolve in exactly the same way each time. Such superficial randomness has been studied at great depth over the last few decades and has been shown to hide within itself a very rich structure, an "order within the disorder". Furthermore, the remarkable dynamic behavior that we call "chaos" has been shown to be pervasive. It's everywhere. It is to be found in the beating of the heart, in the neuronal firings of the brain, the workings of our immune system, as well as in the flutter of airplane wings, and the whirls and eddies of turbulent flow. Chaotic dynamics is invoked to explain the evolution of epidemics, the dither of electronic systems, and it might even be able to quantify trends in the economy.

The aforementioned order within the disorder - as remarkable as it is counter intuitive - invariably manifests itself in the form of a chaotic attractor, a geometrical representation of the chaotic system dynamics. Furthermore, the geometry of such attractors is invariably (and again remarkably) "fractal," exhibiting self-similarity to all levels. Fractal geometry is itself a characteristic of so many everyday phenomena, for example a continental coastline, a cloud, a fern leaf, and a snowflake. By self-similarity we mean that as you zoom into the object you see structures that are similar to the original structure. Indeed, one can argue that the Universe itself exhibits fractal geometry: stars orbit galactic centers, planets orbit starts, electrons "orbit" atomic nuclei, the proverbial Russian dolls within dolls within dolls: each doll representing a scaled down version of the original doll.

The principles of chaos and fractal geometry have found an inspired artistic forum in the work of John Arabolos. Take a pile of sticks, haphazardly strewn, and record this randomness on photographic film. Take the image and introduce a line of symmetry, for example by mirroring it about a horizontal line. Then rotate the resultant image through ninety degrees, frame it, and stare at it. As you allow your gaze to linger, observe the appearance of structures, observe the emergence from the randomness of figures that seem familiar: ghostly apparitions, angels with wings, skeletons, mythical creatures, scary bugs... images with symmetries that Mother Nature has bestowed on all things organic. Move closer to the image and observe the emergence of other structures, some very similar - albeit on a smaller scale - to those you observe when standing afar. And all this "order within the disorder" came from where? From a haphazardly strewn pile of sticks.

The effect can only become more dramatic when the artist expands his algorithm by repeating the process of mirroring the original image. Again, out of the randomness emerge shapes, and more shapes, and more still...

Such is the artistic achievement of John Arabolos, dramatically illustrated by the works contained within this fascinating book. Enjoy the works for their beauty but let your gaze linger to draw from the picture the inner symmetries, those spooky fractal structures buried beneath the chaotic exterior of the original image.