Mount Sierpinski Mountain Fractal Snow
March 27, 2010
I’m always on the lookout for photographic opportunities that illustrate the fractal geometry of scenes in nature. While returning to my home in Helena, Montana from a jaunt in nearby Marysville, I noticed the fascinating snow melt pattern shown above in the northeast extension of Helena Valley, which trends northeast to southwest. The exposure of this mountain flank is to the southwest. Snow first melts from the slopes facing the Sun. Of course, the snow remains longer in natural collection areas and on those slopes facing away from the Sun. The pattern seems to be one of ever-smaller triangles, and it was this “breakup” into the smaller triangles that drew my attention. I was reminded of Sierpinski triangles (also known as Sierpinski gasket), which are mathematically generated patterns that can be reproducible at any magnification or reduction. The redundancy of the title "Mount Sierpinski Mountain" is intentional; a reference to the recursion -- the underpinning of fractal patterns.
Photo details: Nikon D300S camera; Sigma 75-300 mm telephoto lens at 300 mm; shutter speed 1/320; aperture f/9. The image has been tweaked with Photoshop to lose the detail in the highlights while preserving the texture of the grays to bring out the pattern.