Friday, January 29, 2010

Fractals: Who Knew?

The word fractal was coined in ca. 1980 by the mathematician who was the first to demonstrate how an obscure branch of geometry could be used to generate remarkable models that show properties that are stunningly similar to complex configurations in nature: the branching of trees, coastlines, broccoli florets, galaxies and clusters of galaxies, and many more.

I had heard the word, but didn't know much about them until I read a post in Christine Quigley's blog (my favorite blog!). I especially recommend the 50 minute video she showcased, it is entitled Fractals: The Colors of Infinity.

Despite my engineering education, advanced mathematics (Calculus and beyond), has always been a weak area for me. Even after the excellent explanations and examples in the video, I could not actually generate an image using a fractal. Nonetheless, one property of fractals really popped out at me.

A fractal is a short mathematical expression (example: Z = z times z plus c) which can be iterated to produce artifacts of enormous complexity, endlessly unique shapes with recognizable similarities.

Thus fractals can be used to create geometries more characteristic of nature than of a machine shop's product. One example would be the shapes of trees. Although every oak tree branches in a unique pattern, the patterns of oak tree branches is readily distinguishable from the patterns of pine tree branches. The coastline of Ireland is quite different from the coastline of Puerto Rico, and yet island coastlines are easily recognizable as such on a map. The scale is not important, a bonsai cypress bears a striking resemblance to a huge old growth cypress. Australia's island coastline is clearly in a class with Jamaica's .

What struck me was that a process composed of a few simple steps can create infinitely complex shapes with easily recognizable similarities. I see a parallel with Christian lives. Following Jesus
requires us to invite him to help us iterate on relatively straight forward set of teachings: love one another, forgive one another, give generously, serve humbly, and so on. As each of us repeats those steps over and over, a pattern emerges that is unique to our own life and yet recognizably similar to the lives of other faithful followers of Christ. In a similar way, the pursuit of worldly goals consists of iterations of pride, greed, lust, hate, and so on. Again, each worldly life will differ from all others and yet there are easily recognizable patterns that emerge.

Scale is not important here, just as with fractals. A small kindness resembles a large kindness; a small theft resembles a large one.

Simple steps are not necessarily easy steps. Even small simple steps may be very difficult. Forgiving a small injury may prove more difficult than forgiving a larger one. Giving a billion dollars may be easier for Bill Gates than giving a thousand is for a single mom of limited means.

Fortunately, each of us is simply responsible to follow God's leading, one step at a time. And because God knows that we will fail apart from his help, he has provided the grace we need.
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