The Order of Chaos

The image here is something a fellow math geek would be familiar with, but likely not many others.  It’s a fractal.  This one is specifically an image of a ‘Julia set’.  I find the Julia set to be beautiful in such a profound way that it’s difficult to describe, but I’ll try anyway.  I won’t get into too technical a description of fractals, but they fascinate me so bear with me for a moment.  While mathematically fractals are a type of equation, it’s the visual they create that’s most impressive.  They portray a concept known as self-similarity, meaning that the image can be broken down into smaller images with the same shape.  So basically the entire likeness is the same shape repeated in varied scales (Koch curve is a really good example).

The Julia set is a type of fractal based on a function.  When values are assigned, the function will behave in a way considered either ‘regular’ or ‘chaotic’.  If the behavior is chaotic it is considered the Julia set, and its image will be similar to the one at the beginning of this post.  Beautiful even if you know nothing about it, but mesmerizing when you see the details.

There is practical application for today’s math lesson.  The study of fractals and chaos theory is intensely interesting.  The fact that chaos – “a state of disorder” – can be studied at all is fascinating to me.  I see it as an example of God’s perfect order.  In everything there is system, organization.  It’s there even (maybe especially) when we can’t see it. 

I consider chaos theory to be applicable to so many more abstract things than topographical maps, shorelines, or whichever mathematical uses we’ve found so far.  In the chaos of my life, there is order even when I cannot fathom it.  To see order in the chaos of anything – weather systems, for instance – you have to change your perspective.  You can’t look only at the data in front of you but must analyze patterns that only a trained eye would be able to discern.  Similarly, the only way to find order in our lives at times is with an eternal perspective.  The problem is our minds are finite and not capable of a true eternal perspective.  So in the midst of chaos we’re told to trust that our God is faithful.  Jeremiah 29:11 says, “for I know the plans I have for you, declares the Lord, plans for welfare and not for evil, to give you a future and a hope.”  This is what I cling to, and I look forward to one day being able to see the beauty in my chaos.