I became familiar with fractals relatively early in my life (I used to study math, and was able to understand something beyond the very basics); or, to be more precise, those early years of my life happened to occur around the time when Mandelbrot and his beautiful concept became known more known to the general public. I was lucky to have a friend (then MA and later PhD in Chemistry) who introduced me to this idea before it was even published (in the Soviet Union, that is). I do remember a meeting when he was presenting his findings to the peers (docs and post-docs) who didn’t yet know the very F. word.
Then the fractal very rapidly became a mass-culture phenomenon, mostly because of the sheer beauty of the visualizations (I am not sure that the general public understands the concepts beneath the pictures). Mandelbrot became as canonical as someone like Plato or Aristotle, and of the same age; I was pleasantly surprised to see him alive and talking at TED; I enjoy his speech very much and event drafted a small posting on the impact of fractal theory on the future studies (never published it, though).
I was very sadden when learned today about the death of the Fractal Man. RIP.