This is an image of one of the more bizarre ice phenomena that I have come across in nature. Perhaps this is something rather common, but it is the one and only time that I have come across it.
While out hiking one frozen, frosted morning I decided to see if the seasonal stream that runs near my house had frozen. It had, but in a way that I had never imagined.
During the night, as the barely moving stream sat in the deepening cold, it began to freeze, and it froze into raised crystalline, geometric shapes with angled sides. I don’t know the how or the why of it, but I captured it with my camera all the same.
The lighting is natural, as is the color. The sun was beginning to rise, and while it was not hitting the ice directly, it colored the sky, which was reflected by the ice.
I used a 200mm lens, and crouched down nearby to get the closeness and angle that you see.
The second picture was taken at the same time, but at 116mm. Aperture was wide open for both at f/4.0. Shutter speed was rather slow 1/30. I used a tripod in this case to eliminate shake.
If you’d like to see another example of math in nature, check out these photographs of natural cauliflower fractals
Galen Leeds Photography 
Compare the photograph of ice patterns at:
http://purpleshoephotography.wordpress.com/2011/07/28/fractured-river/
I guess the phenomenon isn’t an anomaly, but it’s still fascinating.
Steve Schwartzman
http://portraitsofwildflowers.wordpress.com
Ice (and prickly pears) are amazing things. I actually don’t believe there are true anomalies in nature, only thing that we don’t see often enough to fit into our own patterns (even when they are patterned themselves), that we call them mysteries, anomalies, or even magic. Nature seems to have many patterns, many of them mathematical, we just don’t always know the math well enough to see it. Sometimes zooming in or out a little can help
This long-time math teacher will gladly second what you said about mathematical patterns in nature. One well-researched pattern is the one corresponding to the Fibonacci numbers. Just do a search for “Fibonacci nature” and you’ll see. Another pattern, only recently discovered and investigated, is that of fractals. As for zooming in and out, I’m with you. And though we get hardly any ice in central Texas, we never have a shortage of prickly pears, which I never get tired of photographing.
Steve Schwartzman
http://portraitsofwildflowers.wordpress.com
Ha! I just barely kept myself from mentioning Fibonacci numbers in my last reply to you. I have also seen may cases where fractals occur in nature, the easiest to find in any grocery store is a common cauliflower. I first saw them in “Romanesco” cauliflowers which appear especially fractal like, but then I noticed that all cauliflowers have a “fractal” patterning.