Fractals Part I

This is the first of three activities that explore the construction and visualisation of fractals.

Although arising from simple processes, fractals exhibit infinite complexity, and exist at the nexus of mathematics, nature, and art. No matter how closely you look at a fractal, however much you zoom in, they remain equally complex (i.e. bumpy). They are nowhere smooth!

Two key concepts are:

  • Recursion – i.e. repeating a transformation on its own output. This may remind you of Russian dolls, or the infinite reflections in parallel mirrors, or even the process of revising an essay.
  • Self similarity – the features of the whole object are repeated infinitely often in its parts, at finer and finer scales. At all magnifications, the object exhibits the same complex structure.

In this activity we repeatedly stamp a 2D pattern, getting smaller each time, to generate fractal patterns known as gaskets. Wacław Sierpiński in particular made these shapes famous through his work on them in the early 1900s.



Sierpiński Stamping
Recursive Fractal Art
Click on the cells in the small stamp mask at the bottom right, then use the buttons below to explore the patterns you can make. You can change the stamp pattern at any step.

  Choose a shape:   Choose a base colour:

     

You might like to imagine the kind of objects that a three dimensional version of this process might produce.