fractals

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"Nature Guide Journal"

15 November 2001

We were fortunate to fly out of the North Bend airport under sunny, mid-day skies last week.  As we gained altitude, the red-and-yellow vine maples became small flecks of brilliant color in the deep velvet green of the conifer forests.

Flying inland, another feature commanded my attention:  The shapes of the valleys etched into the hills by eons of rain.

Slightly curved, each watershed fit between it's neighbors like pieces in a child's puzzle.  Each watershed divided into sub-drainages, with steep, narrow valleys drawing down to the stream tracing the bottom.  High ridges separated the watersheds; lower ridges separated each drainage within the watersheds.  The overall visual effect was one of nested paisleys.

It seems to me that the size and shape of each drainage and sub-drainage, as well as the steepness of land drained, are functions of the amount and timing of precipitation, the kind of soil and the formations of bedrock, the plants living on the surface, and the length of time the land area was exposed to such erosion.

Whatever the effect of the various elements and processes, the resulting pattern is a "fractal."  Fractals are patterns that repeat on a descending scale.  The classic example is the branching on a head of cauliflower.  As you break apart a cauliflower head, you can clearly see how large branches divide into smaller ones; smaller branches break down into branches that are still smaller.  The characteristic that makes it a fractal is that the angle and relative arrangement of the branches is similar at each level.

The nested, recurring patterns of fractals are very common in nature.  Examples include:  the tight spiral of a coiled fern head, cracks in dried mud, lacy frost on a window pane, the rhythm of dunes and the ripples on their surfaces, spiral arrangement of galaxies.

Material from those watersheds followed the path of another fractal.  Looking like sinuous twigs and branches on a tree, tiny rivulets collected into creeks that gathered into streams.  The streams formed narrow winding valleys, joining with others to widen the river.  Sediment eroded from the steep hillsides settled in the more level areas where watersheds met, creating narrow ribbons of flat-bottomed floodplains.  The sediment-built floodplain broadened where the river's path was slowed by obstructions and as it neared sea level.

It was clear that different species of trees lined the edges of the rivers than grew on the hillsides—plant communities dictated by the water and the sediment it relocated.

I had flown over these hills many times before, but not when the sun was so low in the southern sky.  The low angle of the November sunlight cast deep shadows that starkly accentuated the shape of the forested hills, dramatically detailing the complex patterns of drainage that are lost in the high sun of summer's midday.

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Since self-organizing systems (which produce fractals) play an important role in robotics and advanced computing as well as in the natural sciences, there are many websites on the topic.  You can find more information on self-organizing systems on CALResCo's FAQ site managed by Chris Lucas.  J.C. Sprott maintains an extensive suite of sites featuring fractals, including a variety of photographs of natural fractal examples.  The Research Group for Computational Neuroscience and Artificial Intelligence in Vision also maintains a large library of fractal images.  

For related information on this site, see plant communities and change of color.

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