A fractal is a drawing based on the geometric model of a set of mathematical calculations. Self-similarity is the main characteristic of the figures that create a fractal. They are both regular and erratic and, like all art, may be simple or complex. Formulas used to create fractals are most readily generated by a computer. Various software systems on the market promote ease in creating fractal art, but you don't necessarily need help to design a beautiful fractal picture.
Draw the Koch snowflake, one of the more common fractals. Draw an equilateral triangle by marking a base line of nine inches (or nine graph squares) in width, and having the apex point be at 4 1/2 inches (or 4 1/2 graph squares) from either side of the base.
Mark each side of the equilateral triangle at three inches from the angle of each side, dividing each side into three equal sections. (One method of creating fractals is by drawing other shapes, similar to the original, of different size and rotation, yet of ordered placement.)
Draw another equilateral triangle with three-inch sides from the center section of each side. One triangle will shoot off to the left on the left side, another to the right on the right side, and the other downward from the baseline. The outer perimeter of your triangle will now be the shape of a dodecagon.
Consider the size of the new triangles that protrude from the dodecagon. Divide each of the sides of one of them by three inches (making one-inch sections), and draw one-inch equilateral triangles out from each of the three-inch sides, creating new equilateral triangles that are one third the previous triangle’s size (thus reducing the formula of the geometric equation by one third, too.)
Repeat the process of creating and placing the equilateral triangles that will protrude out of one third of each side of all sides of the perimeter of the new shape until you achieve the desired intricacy of design.