|Photograph taken at Seapoint Beach, Kittery Maine: December 2010|
Sunday, January 23, 2011
This photograph and a version of this essay was published in the Concord Monitor 1/16/11
I took this photograph at Seapoint Beach in Kittery Maine recently. It is of a natural etching cut into the sand by ocean water flowing back down the beach after high tide. To me, it looks like a row of plants, some with long, luxurious roots.
Self-similar things can really be fascinating as I discovered many years ago when I first learned to create unbelievable images on my first Apple computer, using fractal-generating software, based on the work of Benoit Mandelbrot.
“Fractal” is a term used by mathematicians to describe the unique “self-similar” property of certain structures; specifically, a fractal is a geometric shape that retains the same shape regardless of the level of magnification used to view it. 
Natural fractal objects include clouds, mountain ranges, lightning bolts, snowflakes, and coastlines. The Maine coastline would be a good example of the self-similar nature of fractals. Whether you view the Maine coast far above from an airplane or up close walking down the beach, the shape remains the same.
It defies the imagination, doesn't it?
Mandelbrot’s theory became popular after he published a paper in 1967 entitled How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. This paper investigated yet another amazing fractal property: that the measured length of a stretch of coastline (because it is a fractal) depends on the scale of measurement.
Empirical evidence suggests that the smaller the increment of measurement, the longer the measured length becomes. If one were to measure a stretch of coastline with a 12” ruler one would get a longer result than if the same stretch were measured with a yardstick. This is because one would be laying the ruler along a more curvilinear route than that followed by the yardstick. The smaller the unit of measurement the longer it becomes until, carried to it's extreme, the length of the Maine coastline becomes infinite! 
This is exciting stuff, not just about fractals but scientific discoveries in general.
Contrary to conventional thinking, science doesn't necessarily lead to a loss of freedom through expanded abilities to predict and control. Neither does science necessarily lead to a secular life style that is amoral and non-spiritual.
Instead, as I have tried to show in this small essay, science has the ability to make us grow by shaking us up: reminding us that we live in a mind-blowing place of unfathomable mystery. The only constant in this brave new world is that we all are connected. The human embryo as it develops repeats the history of the evolution of life on earth–ontogeny recapitulates phylogeny–part of Mother Nature’s master plan: whether an image in the sand, a plant with fractal roots, a puppy dog or a human being, we are all the same.