Fractals Part II
This is the second 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 use repeated transformations of lines to generate fractal curves. The first of these, the Koch snowflake, was first described by Helge von Koch in 1904, and is a fractal curve with dimension ≈ 1.26. (See the discussion on dimension below.)