Walking On A Fractal

I was recently hiking on the Blue Ridge Trail, which is a great study in design on so many levels. I am not sure what a studied definition of “design” would be, but one that works for me is “the intentional creation of patterns.”

Though at times design seems to betray obvious patterns, they are there. An obvious example of this is the work of Jackson Pollock, that silly man splattering paint on canvases in the 40’s and 50’s and calling it art. Many people ridiculed Pollock. They were sure that any child could do what he did. In a sense they thought that his paintings lacked pattern and were simply random splattering of paint on canvas.

As it turns out they were wrong. Pollock’s paintings have the repeating patterns of rather high level two dimensional fractals. Something that is not accomplished by others randomly splattering paint on canvas. Though, a cleaver physicist did figure out how to create paintings that also reflect fractals in this range. He calls his devise a “Pollackizer.” It captures the random movements of nature such as tides and wind and uses them to distribute paint drips on canvas. Fractals are made up of patterns that repeat in approximation at any scale. Pollack was a force of nature able to project these patterns.

Back to the Blue Ridge Trail. In the forests of North Carolina I walked in amazement of the huge, towering trees and everywhere fractal designs. The trees themselves, the distribution of any one species of tree, the distribution of all of the trees, the distributions of places that the trees thinned to let just a bit more light pour in projecting the patterns of the branches. And the trail that I walked on undulating in fractal patterns along the mountain’s edge. The plane of the trail sliced into the mountain was a fractal reflecting the pattern of erosion on the mountain. It was a graph of erosion at a single point in time. But you could also imagine a fractal plane in a perpendicular direction as the mountain eroded over time. This added dimension of time and how it affected the physical geometry made me wonder about the ratio of those two equations and other fractal equations. Is the one slice similar to the other? In other words, does their ratio come close to 1?

As far as I know the physicist Richard Taylor has only looked at the pattern of Pollock’s splatters as they fell on the canvas. What other patterns could be revealed? What is the pattern in the shades of color on Pollock’s paintings or in the woods of North Carolina?