Arthur C. Clarke

Arthur C. Clarke's The Ghost of the Grand Banks includes a description of the exploring the Mandelbrot set (both woven into the story and as a technical appendix), a castle with a lake whose shape mirrors the main features of the Mandelbrot set.
A typical Clarkean twist involves a very peculiar psychological effect of extensive exploration of the Mandelrot set.
(Also, so far as we know, this novel contains the first widely-distributed mention of the Y2K "problem.")
Clarke expressed his interest in fractals further by narrating the videotape Fractals: The Colors of Infinity.