Fractals, like so many sights in nature, can seem both static and dynamic at the same time. A cloud can change its shape right before your eyes, and so can a slice of the Mandelbrot set, with a slight nudge of the bailout values. Try to find the same spot later on, without the same exact values, and you may never see it again. This fractal, in shades of tangerine, is a typical Mandelbrot set, colored with an “alternative” fBm algorithm using 4n linear arrays. (The algorithm was written by David Makin, whose spectacular fractals can be seen here.) The combined effects of the chaotic, repeatitive curves of the Mandelbrot set, combined with the random, misty noise of the fBm algorithm create endless foggy terraces:
But a computer-generated form cannot quite compare to the dynamic beauty of nature, in Yellowstone National Park:
A photograph of Mammoth Hot Springs, taken on a rainy day, by Martin Richard
I visited Mammoth Hot Springs as a child, during a family gathering at Yellowstone. Decades later, the great mounds of smooth, steaming travertine, undoubtedly one of the most beautiful sights on earth, still stand out in my memory. Yet, when I first looked at the photograph above, the view seemed strangely unfamiliar. It isn’t just different weather, or another location or viewpoint. The springs themselves are constantly changing, following disturbances in the flow of hot water.
Mammoth Hot Springs are located just off the edge of the Yellowstone Caldera, close enough to the massive hot spot to constantly steam, but far enough to keep from building too much pressure. Calcium carbonate-rich water slowly steeps through limestone bedrock before flowing across the hillside, resulting in mounds and terraces of travertine. (The mounds are similar in form to those in Pagosa Springs, which I wrote about this summer, but differ in chemical composition.) In these shallow, acidic waters, bacteria and other microorganisms alter the appearance of the terraces, both in form and color.
For more information about Mammoth Hot Springs, or other geothermal features at Yellowstone, be sure to check out the National Park Service virtual tour of the springs.