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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 productivity.

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 microbe’s 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 soil’s 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,