frac · tal:
  any of various extremely irregular curves or shapes for
  which any suitably chosen part is similar in shape to a given
  larger or smaller part when magnified or reduced to the same size
  -- Merriam-Webster online dictionary



There are many different types of Fractals such as the Mandelbrot set (right), the Sierpiński triangle (below, left) and the Pythagoras tree (below, right). Other variations include the Koch snowflake, Cantor set, Julia set, Terdragon curve,
Apollonian gasket, Pascal triangle, and the Lorenz attractor.


          


Fractals can happen in nature as well. some examples of natural fractals include cauliflower, coastlines, and the surfaces of the human brain or lungs.