Is it a fractal?

I often see this question in forums or galleries, or as a rule for a contest or challenge. This is mostly because forums, galleries and contests usually have some categories, and some are thematic and others are for specific software, so there isn't a neat fit. So how do we answer?

As an artist or a program developer, it doesn't matter to me; fractals are merely tools. But since you asked...

One reaction to the question is that it is a false dichotomy to assume that a picture is a fractal or not. By analogy, it's like saying that a picture is or is not a spiral, and by extension, spiral art is a category that contains all spiral pictures, created by spiral enthusiasts... which would obviously be a strawman argument in the absence of extreme examples. Sometimes collages are acknowledged as a crossover category, allowing for elements that either are or are not fractals, but this has not addressed the underlying assumption. To escape from the dichotomy, we might encourage people to treat fractal as an adjective instead, that applies to structure or process. A picture or object may have fractal structure in shape, coloring, texture. Or tools may use fractal processes to create shapes or coloring, whether evident in the end result or not.
Having divided the picture into various aspects, each of them can have multiple parts, and each might be categorized, for example, as 1. arbitrary or 2. algorithmic but not fractal or 3. having genuinely fractal aspects. Some of them might be further subdivided until the analysis itself seems both recursive and chaotic.
But it may be "too much information."

Some fractal structures have already been assimilated into mainstream computer art/illustration without question - fractal terrains, and many procedural textures use fractal noises - and nobody says the resulting art 'is a fractal'. So if you consider making an arbitrary shape and using a fractal texture in Maya or Photoshop, or doing the same in UltraFractal or XenoDream, what is the difference? Practically, the steps in each program may be different, but the viewer's (and often the artist's) perception is likely to be shaped by expectations of what the programs are for.

We could simply choose one of Yes/No/Partly/Sort of. we could sometimes say that it is a fractal in principle but all the coefficients that would make it look like a fractal are zero. But all this assumes an informed artist. Many would have to admit "I have no idea but I made it with program X". I haven't yet received any requests to automatically generate an answer along with the picture.

Changing the subject slightly, here is the Blogofractal.