Recently, I’ve given a lot of thought to the natural structure of trees (see On Wood on Wood) and how this pattern is repeated throughout nature. After capturing these images last week of century old Japanese maples at the Biltmore Estate in Asheville, NC, curiously I began to look online for an explanation on this natural phenomenon. What I found is utterly fascinating! I hope you will read on, and be inspired as you learn a little more about the elegant, intelligent design blueprint found in nature.
After a moderate amount of digging, two primary explainations emerged – Fractal Geometry and the Fibonacci Sequence or Golden Mean. The later will have to be discussed in a later post.
Fractal geometry emerged 100 years ago as mathematicians struggled with formulas which described and visualized a curve. A the time Georg Cantor and Helge von Koch offered formulas which visualized how self-simulation (extending a basic structure by repeating itself, each time on a smaller scale) is used to create infinitely complex branching structures. During WW1, Gaston Julia would apply a feedback loop to a simple formula to create an even more complex set of numbers, the Julia Set. Unfortunately, the huge amount of numbers was too complex to visualize. Enter Benoit Mandelbrot in the 1980s.
While working at IBM, Mandelbrot made further mathematical refinements to the Julia Set and applied the emerging power of computers to iterate his equations millions of times. The results were then applied to a visual graph. Thus the Mandelbrot Set and fractal geometry was widely introduced to the world. Suddenly, we had a new tool to see previously hidden structures reoccurring over and over again, throughout the natural world and the heavens above.
We can see fractals in the systems which distribute life sustaining resources – circulatory, respiratory, neural and renal systems; and, in clouds, steams, rivers and lightening As life grows, Nature uses a simple fractal code to instruct biological networks how and when to branch. There’s beauty not only in the visual aspects of the branching tree images in this post, but also in knowing there is a natural order (albeit mathematically) underlying our perceived chaos. Spiritually, there seems to be something going on here. Perhaps this supports the case for God’s hand in the world – an elegant, intelligent design.
Thanks for taking time to read this post. For a deeper dive, see PBS Nova’s Fractals The Hidden Dimension.