Are Elementary Cellular Automata structures considered to be fractals?
Cellular automata can generate fractal patterns (as in the case of Rule 90), but they don't always (e.g., Rule 0).

Willson was perhaps the first to demonstrate that CA can produce fractal patterns in the early 80's.

Shortly thereafter Wolfram characterized the fractal properties of a variety of 2-D CAs.

A few years later Culik and Dube went a bit further and proved that certain types of CA :


  ...will always produce a highly regular [fractal] behavior on an arbitrary finite configuration as the initial seed.


The take-home message is that some very simple CA rule sets generate complex behavior, but others don't do anything interesting at all.