ALPINE Through fractal education, Sul Ross University Math 1310 students found definitive patterns to mathematics.

Fractals are rough or fragmented geometrical shapes that can be split into parts, each part reduced but continuing to have the same pattern after reduction. The term "fractal" was coined by French mathematician Benoít Mandelbrot in 1975.

Approximate fractals can be found in nature such as lightning and mountain ranges. Some coastlines and river networks can loosely be considered fractals as well. Other examples of fractals are broccoli, parsley, trees and photographs of sunspots exploding off the sun's rim.

Taught by Robbie Ray, the spring semester honors class included Clare Ritzi, Alpine; Jim Tims, Fort Davis; Lacy Shackelford, Wink; Marisela Baca, Presidio; Jess Dean, Dell City; and Paul Escamilla, Rio Hondo.

Ritzi produced a fractal using a group picture of the class, reducing and repeating the image, then arranging them by what is called an "iterative" process.

"A fractal has to have the same pattern," she said. "I grouped the pictures in a backwards ‘C' in a counter clockwise rotation."

Ritzi then reduced the image and rotated it slightly in the pattern. Reducing and rotating the image four times to make the pattern, she created her new image. Next she used the new image and repeated the process until the image was too small to see on paper.

Ritzi's project ended in a similar pattern to fractals in the famous Gaston Julia set.
Julia was a French mathematician who developed haunting images during his study of imaginary numbers. The same technique of step-by-step change can be seen in savings accounts, population growth and games.

Class members used a computer program to create a variety of fractals such as the Koch snowflake, a fern, a crystal and a triangle. With the program, students were able to see how the formula of a fractal works by seeing it drawn out.

Another interesting fractal the class found is the brain cell pattern, which is similar to the pattern of the universe.