In page 231 of James Gleick book "Chaos, making a new science" in the footnote describes how to emulate a Mandelbrot set
"A Mandelbrot set program needs just a few essential pieces. The main engine is a loop of instructions that takes its starting complex number and applies the arithmetical rule to it. For the Mandelbrot set, the rule is this: z-> z(square)+ c, where z begins at zero and c is the complex number corresponding to the point being tested. So take 0, multiply it by itself, and add the starting number; take the result-the starting number-multiply it by itself, and add the starting number; take the new result, multiply it by itself, and add the starting number."
Iterations at the heart of the Mandelbrot set that reveal stunning worlds and if the iterations continue unabated the points plotted can not escape the pull of the set, balanced between competing attractors.
What can this tell us about our lives? The worlds we create and we live in? The same principles apply, as well. The iterations, that give rise to the mathematical objects of the Mandelbrot sets, do happen in our every day lives as well. Certainly they can not be formulated mathematically, rigorously or not, but they 'live', they are inherent in the ways we spend our lives, the many tasks we repeat daily on and on, in and through the simple rules that govern our daily acts, the communities, the corporations we are part of, all the systems we have built up to now and continue to build.
We can not define them, they do not have a rigid form, escape our reasoned intuitions but nevertheless they are there.
In the same page continues,
"A complex number is written with two parts: for example, 2 + 3i (the address for the point at 2 east and 3 north on the complex plane)."
And if the notion of a complex number does not have a meaningful counterpart in our lives, the plotting of that number, the point represented with the 2 east and 3 north coordinates, do have. It represents the state we are in, the state we have acquired by virtue of the system which we are part of. And our coordinates, our complex number, is determined by the rules that define the system and confine it, at the same time. The rules be that norms, regulations, laws or whatever other prescriptions exist that define the boundaries and therefore the extents of our state in the system we belong to.
In page 232, the footnote continues,
"To break out of this loop, the program needs to watch the running total. If the total heads off to infinity, moving farther and farther from the center of the plane, the original point does not belong to the set, and if the running total becomes greater than 2 or smaller than -2 in either its real or imaginary part, it is surely heading off to infinity-the program can move on. But if the program repeats the calculation many times without becoming greater than 2, then the point is part of the set."
And there is the crunch, as continuously experiment and test the system we are part of, that defines the state we are in, testing its tolerance will determine whether a certain norm, or rule or any other prescribed guideline, is heading into infinity or not, whether it belongs into the set or not. If it belongs into the set it will allow the iterations to continue, it will continue to be balanced under the influence of the existing competing attractors. If it is not it will be lost for ever, away into infinity and into nothingness. It is not part of the set.
Chaos rules our lives, the systems we built and defines what norms, what regulations, what laws are applicable. That have a chance at all. Whatever falls under the influence of the attracting basins survives, whatever is not, perishes and is banished. And this applies to every human system built, at whatever level. The norms, the regulations, the laws are constantly tested and if they fall outside the influence of the attracting basins they do not stand a chance of surviving. They perish, languish into oblivion, vanish for ever. And what finally determines the attracting basins? To which each norm, each regulation, each law should be attracted to?
The human individual defines the attracting basins, as it is the entity that makes them up and spawn such systems. The single individual is more susceptible to ideas. Ideas that constantly test the norms, the regulations, the laws and is the one that can freely generate new ideas, unbiased, unhindered by the self-preservation angst organisations suffer. Organisations are rigid structures unable to adapt as quickly as the human single individual can. History bears witness as countless norms and laws have perished as they journeyed to infinity and oblivion as they were not part of the attracting basins and countless more keep perishing and will perish as the human kind draws closer to its goal.