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 selfsimilarity 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.
