Student: OK, I've seen lots of fractals now; what makes a fractal a fractal???
Mentor: Let's list the properties they all have in common:
- All were built by starting with an "initiator" and "iterating" using a "generator." So we used recursion.
- Some aspect of the limiting object was infinite (length, perimeter, surface area) -- Many of the objects got "crinklier."
- Some aspect of the limiting object stayed finite or 0 (area, volume, etc).
- At any iteration, a piece of the object is a scaled down, otherwise identical copy of the previous iteration ( self-similar).
Mentor: These are the characteristics that Benoit Mandelbrot (who invented the term) ascribed to Regular Fractals
Student: Why call 'em fractals??
Mentor: Mandelbrot used that word because in Latin, fractus means broken. Mandelbrot viewed these things as being highly irregular and crinkley. Another good reason to use the word fractal is that they have fractional dimension! Before I can explain that, we need to talk about Dimension and Scale.