I saw this video a few years ago on television.  I found the first 35 minutes to be very interesting.  The last 20 minutes not so much...
I learned about Fractals and the Mandelbrot set in the 1980's.   Back then I had friends who were experimenting with drawing the Mandelbrot set on computers.  In those days it would take a really long time to draw a single picture on a computer.
  
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