Fractals- the Interface Between Chaos and Order

Fractals are more than just hippie psychadelic velvet poster art (although that medium has captured great exemplars!). Fractals are mathematical constructions which have completely changed how we approach understanding the world around us. In my formative artistic years, I saw the world through fractal tinted glasses- my philosophy was pervaded by fractal references. Perhaps knowing a bit more will change your perspective as well! There was a time when I saw everything in terms of fractals and it completely chagned the way I related to the world about me....

The development of fractals led the way to a new type of mathematical thinking in which we were able to interact and understand irrational numbers. Most interestingly of all is how pervasive these numbers turned out to be in our lives- in nature, in us.

A teeny bit of background: Fractals were discovered by Benoit Mandelbrot which is also the name of the most famous fractal. They are generally formed from simple equations, (in the case of the Mandelbrot fractal, Z = Z² +  C) that are ‘iterated’ (fed back into itself) many many times (1000’s of times). Each result can be plotted to a point on a graph and given a color value and thus is born the fractal imagery.

The crazy thing about them is that they are unpredictable- you can have an idea of what is going on, of what will happen next, but you can't be certain...and yet, they are describable- we can make images and interact with them in a way that without this type of thinking in simply not posisble. Fractals are a system where chaos becomes understandable (to the varying extents to which this is possible).

Some fractals help animators program realistic fur or water ripples, others help researchers understand complex behaviors, while some are purely for beauty's sake, like the ones I'm showing here, courtesy of Phidelity.

Fractals became an extremely insightful way of perceiving our world and inevitably spun off corresponding philosophy, which is the more pertinent use for me of this topic. From first truly appreciating fractals in my life during my movement practices, I soon moved on to other ways of integrating fractal thinking into my life.

These are soe of the qualities of fractals:

• Internal harmony- every part is a representation of the whole
• Unpredictability- small changes can have tremendous and unforeseen consequences to the system (think weather patterns)
• Regularity- periodic movement
• Holistic- it moves as a whole
• Integrated- all parts combine to form the expression
• Balanced- in its entirety, energy movement is balanced
  
• Infinite- no beginning, no end. It always comes from somewhere and goes somewhere
• Scalable- endless levels of depth
• Self-perpetuating- energy keeps moving
• Complete self expression- their totality exists to express an equation, every part of it manifests that initial imperative

What can fractals teach us (specifically for staff movement but adaptable to anything, really):

• Integration- all aspects of what we do contribute to what we create
• Consistency- every part is equal to every other part, all speeds are the same, all movements of equal energetic emphasis
• Our body is a part of the system and is integral to the movement of the staff
• Energy coalesces around certain patterns. Just as a fractal image reveals itself from the chaos, the energy pathways reveals themselves. This pathway creates space for effortless, efficient movement.
• There is no beginning and no end- energy comes from somewhere and goes somewhere. Nothing exists in isolation, our movements included.