Go on, export us a mesh of the 3D Cantor set Let's see how well suited triangular meshes are to rendering fractals...

Prediction: the mesh will be absolutely massive, very little surface detail, take up a ton of disk space and render at least 100x more slowly than a direct intersection algorithm.

Of course a triangular mesh of a fractal dust would be huge at any useful resolution. In practice meshes are always a compromise, especially for fractals with uniformly rough surfaces because there's not much scope for mesh simplification. Point cloud export would be more efficient for the 3D Cantor set, and the size is not constrained by memory. However, 100 million points (the current limit in XD point cloud export) is still only 464^3. You can do really cool animations with such point clouds in 3DS Max with Krakatoa or Realflow. However, for high resolution, export is a long way from competing with direct rendering (except for 3D printing, where it's currently ahead.)