Fractals for Farming
By Sean Adams
August 1, 1997
Anyone bored by drawing ordinary circles, triangles and cones in geometry
class would be pleasantly surprised by what Agricultural Research Service scientists
are doing with fractal geometry. They are using this math of the rugged shapes
of nature to evaluate how organic farming and other practices affect soil
Yakov Pachepsky and Larry Sikora use fractals, endlessly repeating shapes,
to map the irregularities of the pores that riddle soil. These spaces between
soil particles are critical to crop yields. They allow air and water to pass
through. They also provide a home for beneficial microbes.
Fractals give scientists a microbes eye-view of the minute twists and
turns of soil pore edges. These edges are as rugged and diverse--in their own
microscopic way--as the U.S. east coast. If you measure that coastline on a
map, it grows longer every time you increase the scale, revealing
ever more coastal nooks and crannies. The same is true for soil pores.
Fractal dimensions are independent of scale, yet allow accurate
extrapolations from one scale to another. A fractal length has a value of 1 to
2. A straight line is 1.0, a typical river 1.1 to 1.5. A tangled mass of
branching filaments of soil fungi could be a 2.
The scientists use special software to measure fractal length of pores on
computer- scanned images. In one study they scanned thin slices of soil from an
organic farm. Pores from a field where red clover was grown and mixed into the
soil as green manure had a value of 1.6. Pores from a field planted
to grass or treated with manure or fertilizer scored about 1.4. The findings
indicate the clover would most promote the soils ability to store water
and harbor beneficial microbes. Based on this study, the scientists believe 1.6
is an ideal level of pore ruggedness.
Scientific contact: Yakov Pachepsky, ARS
Remote Sensing and Modeling
Laboratory, Beltsville, Md., phone (301) 746-5353, fax 504-5823,
Lawrence J. Sikora, ARS Soil Microbial Systems
Laboratory, Beltsville, Md, phone (301) 504-9384, fax 504-8370, firstname.lastname@example.org