The alternative is to accept an incongruity: we say that both sides of the equation are equal while also saying that one side is more complex.
You were saying that you found proof that a simple system can produce a complex system. This means less complexity is producing more complexity without any donations of complexity from outside systems. Not only does the Mandelbrot not help you, I don't see any other example that does.
You mentioned a "window" that allows a fraction of the whole to be viewed. I think you were possibly referring to imaginary perspective and not mathematics. In math, you either work with all the data or a fraction of it. If you work with fractions of it and unless you fudge the numbers, you cannot produce the same exact result as a formula that works with the whole.
Therefore, we reach another incongruity. Either your window is equal in complexity to the system it is viewing and your claim that a simple system produced a complex system still wants for proof or you are saying the window only represents a fraction of the entire system and therefore the window is not equal to the whole complex system. For one system that is not equal to another system to somehow then become equal to that system, it must gain the information it is missing either from the other system or from somewhere else. Either way, the simple system must borrow from other systems and therefore can't be said to solely, "produce" the complex system. Next, we have a shell game or a simple admission of spontaneous creation of information.