This image contains four visualisations of the Mandelbrot set. The Mandelbrot set is a set complex numbers for which f_c(z) = z^2 + c does not diverge. The image is self similar and contains properties linked with chaos theory. The set was first defined and printing in 1978.
The dragon curve is made by taking a long strip of paper, and folding it in half many times. Unfolding the paper gives the patterns below. The pattern was first described in 1967 by Martin Gardner.
Fractal trees come a variety of different forms. The four trees below represent; a Christmas tree, a typical tree, broccoli and a fern. Leonardo da Vinci noticed these patterns in the 15th century.
The snowflake fracture is a shape with infinite perimeter but finite area. It is made by adding smaller and smaller triangles to the existing shape. It was first defined in 1904 by the Swedish mathematical Helge von Koch.