|Photograph taken at Kittery Sea Point Beach, 12/29/10|
I took this photograph at Seapoint Beach in Kittery Maine a few days ago. 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 in nature are fascinating. That’s what sparked my interest, years ago, with Benoit Mandelbrot’s work with fractals. Because fractals appear similar at all levels of magnification, fractals are often considered to be infinitely complex. Natural fractal objects include clouds, mountain ranges, lightning bolts, snowflakes, and coastlines. 
The Maine coastline is 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 newfound abilities to predict and control. Neither does science necessarily lead to a secular life style that is amoral and non-spiritual.