A fractal is a geometric pattern that is repeated at ever-smaller scales. Fractals have the property of self-similarity, meaning that any part of a fractal can be repeatedly magnified, and each magnification will resemble all or part of the original fractal. This phenomenon can be seen in objects like snowflakes, ferns, and tree bark. Fractal simulations have been used to generate lifelike images of complicated, irregular natural objects, including rugged terrains and foliage used in movies and video games. The term fractal, from the Latin word fractus (“fragmented”), was first used by mathematician Benoit B. Mandelbrot in 1975. http://www.britannica.com/EBchecked/topic/215500/fractal
Here are two animations of a famous fractal, the Sierpinski Carpet. The first builds the fractal from stage zero, and the second zooms into a multi-stage fractal.
Make your own fractal!
Choose a template and some colored pencils. When you’re done, write a rule for the sequence generated by the unshaded regions at each stage of the fractal.