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From Chaos to Beauty : Fractal Geometry and Freewill
Younger Geeks may not remember the work of Benoit B. Mandelbrot or the computer craze in the geek community of the 1980's when every one was generating fractals on their old 8 bits. It was in 1975 that Mandelbrot introduced his Fractal Geometry and began to show us how beauty could come out of chaos. The work of Mandelbrot led a research team at the Georgia Institute of Technology to develop techniques of generating images reminiscent of objects in the natural world by random selection of Affine Transformations.These transformations cause a collection of points to be changed into a new shape. They are of the form:
This transformation can also be written in the form of an iterated function system (IFS) as follows:
This system results in two equations for the transformation of x and y coordinates. They are as follows:
The transformation i is to be selected randomly. For sake of demonstration a javascript application is available here. To use this demonstration simply click your mouse randomly about the window to simulate randomness. As you do so you will soon see the emergence of a fractal fern.Included here is the javascript code for observation
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What is fascinating about fractals is that they demonstrate how truly random behavior can bring about a predetermined outcome through the application of random variables to inflexable law. This is important in the Christian faith because of the age old problem of freewill. The problem is simply the apparant paradox of the coexistance of freewill and an Omnipotent Omnipresent Omniscient God. The apparent paradox results from the thought that if God knows what a person is about to decide then He has somehow determined that choice. Likewise it is difficult to reconcile that every knee will bow and every tongue will confess that Jesus Christ is Lord (Phillipians 2:10-11) with freewill. As it is difficult to reconcile the apparent contradiction between Phillipians 2:13 and freewill. Yet if there is no freewill then how will God judge every person according to their deeds (Romans 2:5-11).
Fractals are one possible explanation of how these apparent paradoxes could be resolved. The choice of a person is like the choice of where to click on the screen. It has very little effect on the ultimate outcome other than that stubborn choices may result in slower results. Ultimately the self simularity and ordered design of a fractal fern will emmerge from the chaotic clicking. Likewise noone is able to break the law of God but only to break themselves against his law (Romans 6:1).
When I observe all of the chaos around me, I am sometimes afraid. I am sometimes distraught and unhappy. Sometimes I am angry at God. When these times come I remember the fractal and my mind is set at ease. To me the fractal is a symbol of the unfailing goodness of God that will triumph on that faithful day when every knee shall bow and every tongue shall confess that Jesus Christ is Lord.
If you would like to learn more about the transformation that can come through the Salvation of Jesus Christ then read the article What in the World is Salvation?
This Work and the Works contained in all Attached Media Files
are Copyright © Michael J. Ranck (March 2005-September 2010)
and Subject to Terms and Conditions
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