Do fractals necessarily have to be self-similar? What is the definition of a fractal? Is this figure a fractal?

Question

I am doing a dissertation in Materials Engineering. I obtained the following images regarding crystal growth:

In the literature they usually call these structures "fractals" and calculate their fractal dimension using the box-counting method. From what I read on the internet, a fractal has to have self-similarity.

However, these structures appear to be so irregular that they do not appear to have any kind of repetition. The fractals according to the DLA (diffusion limited aggregation) have a fractal dimension of approximately 1.70, which is close to that of these structures. Why do the authors consider these structures fractal if there is no self-similarity? What are the characteristics necessary for a figure to be considered a fractal?

Answer 1

This is more a comment than an answer, but I don't have the reputation.

Just a guess: A way that fractals arise is by iteration of a map. Perhaps what the authors have in mind is that the growth of these structures comes about by iteration of some simple rules, after translation or some simple function perhaps? The reason I'm saying this is that as far as I know, this sense of fractal (really just an approximate fractal) is what I would expect to see in nature, more than bona fide fractals.