fractal

Since everyone has a computer, the fractal is a popular curve to play with.
But what is a fractal? The name fractal is derived from the idea that the dimension of such a curve is a fraction of an integer. Since some interesting fractal-like curves do have an integer dimension, there is no ground left for this relationship. However, the name fractal persisted.
You could say that a fractal is a complex curve, for which a certain amount of similarity can be seen, when magnifying parts of the curve.
The curves were discovered in the late 17th century, and they shocked the mathematicians of that era.

A special case of the fractals are the space-filling curves, curves which completely fill an area:

• Cantor square fractal
• Peano curve

A so-called base motif fractal can be generated by an iteration of implementations of a motif on a base:

• box fractal
• Cantor
  • - dust
  • - set
• Koch
  • - curve
  • - snowflake
• Peano curve
• Sierpinski
  • - curve
  • - gasket

Other fractals are the following:

• ant of Langton
• bifurcation
• blancmange curve
• Mandelbrot set

In 3d we have the following fractal:

• Menger sponge