It may be that a rock is very complex, but it is random complexity. It has no context - it is just noise - so does not indicate design. In the same way, a random page of text, while complex in many ways, would be less indicative of design than a short sentence in an understandable language.
On the other hand, the full works of Shakespeare are very complex, but also are in context, so the people of the 17th century would infer design. While they are equally complex in binary, they could not infer design from those patterns without knowledge of binary systems.
So, it would be reasonable to conclude that neither simplicity nor complexity alone imply design, but something else comes into play - the context. There is a difference between syntactic information and semantic information.