Musings on Chaos

                         Chaos Theory, Spirals, Dynamism, and other Strange Attractors.  What does it all have to do with Art? 

In a famous paper written in 1963, Ed Lorenz stated  that simple systems of three differential equations can have complicated attractors. The Lorenz attractor, with its butterfly wings reminding us of sensitive dependence is the "icon" of chaos.  Lorenz showed that his attractor was chaotic, since it exhibited sensitive dependence. Moreover, his attractor is also "strange," which meant that it was a fractal.

Before Chaos (BC?), the only known attractors were fixed points, periodic orbits and invariant tori also called quasiperiodic orbits.  The famous Poincaré-Bendixson theorem states that for a pair of first order differential equations, only fixed points and limited cycles can occur.  Thus when a third random point is introduced into the equation, and interdependence ensues, the outcomes are infinite, and ultimately the fractal is formed.  A control parameter is a constant in an equation for which we get to choose the value.  Set the parameter's value at a certain number, and a system will evolve in a certain way. Set the parameter's value at a different number, and all chaos may break loose. Thus, the parameter is king, and it dictates whether or not a system travels the chaotic route.

Thee fractal is thee spiral of life:

If we are built from Spirals while living in a giant Spiral,

 then is it possible

that everything we put our hands

on is infused with the Spiral? 

                What is the spiral anyway?

     The Golden Spiral is a mystical shape that is an

                                      absolute in both abstract mathematics and chaotic               

                                      nature. It was first discovered by Phythagoras, a failed                                                              

                                      Greek messiah and mathematical cult leader in the 5th

                                      century B.C. 

                                      The spiral is derived via the golden rectangle, a unique

                                      rectangle which has the golden ratio. When squared, it

                                      leaves a smaller rectangle behind, which has the same

                                      golden ratio as the previous rectangle. The squaring

                                      can continue indefinitely with the same result. No other

                                      rectangle has this trait. 

                                      When you connect a curve through the corners of

                                      these concentric rectangles, you have formed the

                                      golden spiral. The Phythagoreans loved this shape for

                                      they found it everywhere in nature: the Nautilus Shell,

                                      Ram's horns, milk in coffee, the face of a Sunflower,

                                      your fingerprints, our DNA, and the shape of the Milky

                                      Way.

                What is Chaos Theory?

                          Chaos Theory can be generally defined as the study of  forever-changing

                          complex systems. Discovered by a meteorologist in 1960, chaos theory contends that

                                     complex and unpredictable results will occur in systems

                                     that are sensitive to small changes in their initial

                                     conditions. The most common example of this, known

                                     as the "Butterfly Effect," states that the flapping of a

                                     butterfly's wings in China could cause tiny atmospheric

                                     changes which over a period of time could effect

                                     weather patterns in New York, thousands of miles away.

                     In other words, it is possible that “one” very small occurrence somewhere can produce 

                     unpredictable and sometimes drastic results by triggering a series of increasingly  

                     significant events somewhere else.

                                     Although chaotic systems appear to be random, they

                                     are not. Beneath the random behavior patterns emerge,

                                     suggesting, if not always revealing, an order.

                                    Chaos Theory can be used to model other highly complex systems, including

                                     everything from population growth to epidemics to arrhythmic heart palpitations.    

                                    When applying chaos theory, it is revealed that even something as seemingly

                                    random as a dripping faucet has an order behind it.

Chaos: by definition is an effectively unpredictable long time behavior arising in a deterministic dynamical system because of sensitivity to initial conditions.  Mathematically, chaos can be achieved by the simple iteration of certain equations.  The recipe for chaos in the real world, however, is still in theory stage. Chaologists propose several possible causes of chaos:  

                                  1.  The value of a control parameter is increased to a point

                                       where chaotic behavior sets in.

                                  2.  The nonlinear interaction of two or more separate physical

                                       operations.

                                  3.  Ever-present environmental noise affecting otherwise

                                       regular motion. 

Change, flux, and movement:  Can we create the synergy?

Chaos begins with logic, the formalization of a mathematical  equation.  Art, too, begins with logic. Formalize the rules of logic into a mathematical formula, plot the result, and you will have created an order, a creation in itself.  Add to this self-similar design, the element of human consciousness, and you will have created art, art that changes the viewer, art that changes the creator. 

Effects on my art:

I have been interested in Chaos Theory since the mid 1980’s.  I feel that my constant meanderings and experimentations in thought related to Chaos, has had a significant impact on my art.  If not in a stylistic manner, at the very least philosophically.  I have always maintained a duality in my life, one of order and one in which I allow chance to guide me.  I believe creating art has a way of forcing me to work with order: the canvas, brushes, colour, etc, but chance is ultimately what guides me in the composition, the choice of colour, and the final result.  Like any dynamical system, I take a systematic approach to the creation of the stretcher, the stretching of the canvas, and the plotting of anticipated results (the sketch), but when it is done, the element of human consciousness is what has taken over.  That is the element that cannot be plotted, that is the element of Chance.  

Are we really ready to bridge the chaos?