Since the Mandelbrot fractal has infinite complexity and we can zoom inside of it infinitely long one might ask if any combination of pixels eventually emerge and thus It contains all possible images (assuming an adecuate colormap that samples all necessary colours).

I guess the answer is that we don't know yet.

A similar question asks if you can find any possible sequence of digits inside the decimal expansion of Pi. We know that Pi has a non-periodic infinite decimal expansion but still we don't really known if some sequences might be forbidden. In other words, we don't know if Pi is a normal number. Even if unproven, many matematicians think Pi is probably normal and thus contain every sequence.

It has been show that the number Pi is naturally encoded in the Mandelbrot set. This might imply that the random non-repeating pattern of Pi might translate into random non-repeating shapes in the fractal. If we eventually prove that Pi is normal, would this mean that the Mandelbrot set is also normal, and thus that It really contains all possible images?

Another way to prove It, I guess, would be finding a known normal number shaping some patterns of the fractal somewhere somehow, instead of Pi.

By the way, I'm considering pictures of the fractal where each iteration is represented and not only the boundary between the set and the non-set, which has properties that might forbid some possible shapes (since that would only allow connected shapes with infinite lenght boundaries)