I have a Ph.D. in computational and theoretical chemistry with advanced but field-oriented knowledge of mathematics.
I am fascinated by fractals, but I am unable to understand them from the formal point of view. To my level of understanding, they look like a graphical rendering of an ill-conditioned iterative problem, where small variations of the initial condition lead to huge changes in the final result, but that's just what I got out of it with my current knowledge.
How would you explain fractals (such as the Mandelbrot set) to a layperson with basic mathematics knowledge from high school, and how would you instead explain it to someone which has more math training, but not formal.
This question is collateral to a post on the Mandelbrot set I did on my blog some time ago. If you have any comments on what I was doing with my tinkering of the parameters (to get some keywords for further exploration), it's greatly appreciated. I would like to explain it better to my readers, but I am unable to do it. Thanks