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
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).
iteration, a piece of the object is a scaled down, otherwise identical copy of the previous
Mentor: These are the characteristics that Benoit Mandelbrot (who invented the term) ascribed to
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.