You already know about 2-dimensional shapes like squares and circles, and 3-dimensional figures such as cubes and pyramids. But a fractal has a dimension that is not a whole number!

A fractal is a geometrical figure that that includes the same pattern, scaled down and rotated, and repeated over and over. We say a fractal is self-similar, and we see the same image again when we "zoom" in and examine a portion of the original.

You can design a fractal by choosing a simple pattern and applying a rule over and over. Repeating the rule is called recursion. Each time the rule is applied is called an iteration.

For example, take a large plus sign. Attach a half-size plus sign to the ends of the four original arms. Attach a quarter-size plus sign to the ends of the second iteration. Keep adding smaller plus signs to make the design more complicated. Here are the first three iterations of the plus fractal.

"The universe is a labyrinth made of labyrinths. Each leads to another. And wherever we cannot go ourselves, we reach with mathematics." Stanislaw Lem, Fiasco