Student: So fractals like Sierpinski's Triangle and Sierpinski's Carpet have recursion, because they each have an initiator and a generator. Is this what it takes to be a fractal?

Mentor: That's part of it. Do you remember what else we've discussed?

Student: Well, there is self-similarity too.

Mentor: Good. Here's something else to think about:

Student: These all seem to be contradictory statements.

Mentor: This is why infinity was such a hard concept to understand for so long and there are still many debates about it.

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:

Mentor: These are the characteristics that Benoit Mandelbrot (who invented the term) ascribed to Regular Fractals in 1975.