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I'm not exactly sure what you mean.  There are many fractal programs that can generate non-fractal images (that is, images that don't obviously contain fractal details).  And, there are programs which can generate fractal images, but the programs were not designed for that.  So, while most fractal images were probably generated with fractal programs, one can't necessarily say what type of program generated a given type of image.

In general, I don't think I could tell. Is the world a big simulator of physics formulas? Are photographs of coast lines or mountain ranges or river deltas then images resulting from a fractal program?

I admit that with a bit of experience, people can probably accurately distinguish linear fractals from nonlinear fractals in most cases (i.e. strictly self-similar vs. statistically self-similar). And linear fractals have a somewhat "unnatural" feel. But nonlinear fractals are such a huge group ... the distinction between artificial and natural is almost lost in the noise.

Now, one could try to measure fractal dimensions of some resulting image. But a program for julia fractals can produce a perfect, non-fractal, circle. And a random number generator could, with extremely low probability, happen to fill pixels of an image with some fractal structure.

From a purely theoretical point of view, the resulting images do not, in a strictly rigorous sense, reveal the nature of the programs that generated them. But in practice there surely is a strong correlation.