Although strictly meanwhile more than 99 years old, a well-known example here 
are the [Julia- and Fatou sets][1]. -- 
These sets were first investigated by Gaston Julia and Pierre Fatou in 1917/18,
but this work was more-or-less ignored until the invention of computers made it
possible to explore the beauties of these sets, and -- following the works of
[Benoit Mandelbrot][2] -- they became widely popularized in the 1980's. 

  [1]: https://en.wikipedia.org/wiki/Julia_set
  [2]: https://en.wikipedia.org/wiki/Benoit_Mandelbrot