(this article relates to the Exhibition of original works by Philippa Stewart-Hall at this link.

Z – > Z ^2+ C…
Who would have thought that with the discovery of the computer came this simple equation, which threw conventional science off its perch…
No longer could a universe be described by a detailed set of laws.

The belief in the inevitable end of time in complete entropy and the second law of thermodynamics where everything tends to break down are now being questioned. The cosmic clock image of establishment science first began to crumble at the turn of 20th century when discoveries were bringing to light that causal laws didn’t ring true and that the behaviour of the atom and the individual electron could not be predicted.

Einstein one of the worlds most brilliant scientists did not believe that God played dice with the universe… that we are not living in the midst of a game.
However by the 1980’s, a young, brilliant, and eclectic mathematician, Benoit Mandlebrot purported that chaos lurked behind all order. Thus the chaos theory was born.
The world is NOT a giant clock where everything is predictable. Most of the world works in jumps in a non-linear fashion that cannot be exactly predicted and out of chaos a higher order appears. This order comes out of spontaneity and unpredictability…. not just a one time event at the beginning but an on going process.
Over time all systems…from molecules, to life, to galactic clusters are continually creating new organizations and patterns out of the featureless and chaotic. To further evolution unpredictable relationships can occur.
As I said before the world is not a clock. It is a game …a game of chance and choice demonstrating unpredictability and giving infinite room for creativity within general perameters.
To Quote Mandlebrot in his book…”The Fractal Geometry of Nature” 1983…
“Clouds are not spheres, mountains are not cones, coastlines are not circles, bark is not smooth and lightening does not travel in a straight line.”We live in the 4th dimension… Time.

This fourth dimension includes an infinite set of fractional dimensions which lie between the zero and the first dimension, The first and the second dimension and the second and third dimension. The fourth dimension includes the fractional dimensions, which lie between the first three.

Fractal is a word based on the Latin word fractus, and as Mandlebrot proved nature uses the fractal dimensions to create the complex and irregular forms of the real world of the 4th dimension.

It has been stated that our natural consciousness is inherently fractal.
“Z -> Z ^ 2 + C”…
It is this formula which has embarrassed mathematicians by virtue of its ridiculous simplicity. No longer did Euclidean geometry reign supreme…. because a bright young mathematician thought out side the square.
The arrow symbol-> means Itineration. Itineration is the feedback process where the end result of the last calculation becomes the beginning constant of the next.
In other words the result of z +c becomes the z in the next repetition
So if say Z=2 and C=3, the result of the first iteration would be 7(2 +3). Then the next time Z=7, and C remains the same,3. So the result is 52(7 +3…
And so the process continues.
Like life it is a dynamic equation
And as Mandlebrot points out this idea of “recursive similarity” was originally developed by the philosopher Leibniz, and popularized by the writer Jonathan Swift in 1733 with the following verse:
“So, Nat’ralists observe, a flea
Hath smaller Fleas that on him prey,
And these have smaller fleas to bit ‘em,
And so proceed ad infinitum.”This same verse was followed in 1922 by Lewis Richardson, a mathematician studying weather predictions, who coined the quote concerning “turbulence”, the chaotic condition of liquids and gases.
“Big whorls have little whorls,
Which feed on their velocity;
And little whorls have lesser whorls,
And so on to viscosity”
The ideas of self-similarity and scaling embodied in these verses are critical to understanding the Laws of Chaos. Wherever we look in nature we find fractals with self-similarity over scales. It is in every snowflake, every bolt of lightening, every tree, and every branch. It is in our blood with its veins, in our Galaxies with their clusters; it’s even in broccoli.”

Researched and written by
Philippa Stewart-Hall
With quotes from Benoit B. Manlebrot’s book
“The Fractal Geometry of Nature”
New York: W.H. Freeman and Co., 1982
ISBN 0-387-96608-0