The word “fractal” was coined less than twenty years ago by one of history’s most creative mathematicians, Benoit Mandelbrot.  He derived the term “fractal” from the Latin verb frangere, meaning to break or fragment.  Basically, a fractal is any pattern that reveals greater complexity as it is enlarged.  Thus, fractals graphically portray the fascinating notion of “worlds within worlds”.  Even we are fractals, with DNA maps nestled in each cell.

Traditional Euclidean patterns (squares, octogons) appear simpler when they are magnified; as you zone in on one area, the shape looks more and more like a straight line.  In the language of calculus such curves are differentiable.  But fractals, like dendritic branches of lightning or bumps of broccoli, are not differentiable: the closer you come, the more detail you see.  Infinity is implicit and invisible in the computations of calculus but explicit and graphically manifest in fractals.

Whether generated by equations, computers or natural processes, all fractals are spun from what scientists call a “positive feedback loop.”  Something -data or matter- goes in one “end,” undergoes a given, often very slight, modification and comes out the other.  Fractals are produced when the output is fed back into the system as input again and again.  The video below explores the famous Mandelbrot set.  When this equation is computed and graphed on the complex plane, it’s shows  an elaborate boundary, which does not simplify at any given magnification, unfurling in every direction to infinity.

Fractal artists do not create but explore, do not manufacture but discover.  They know well, the synthesis of man and machine.  For the fractal image is the face of chaos -determined at every point but wholly unpredictable, first-born of reason yet utterly irrational.

***

“What is a Fractal? by A. Beck

Posted by: Annie Lalla

 Print This Post