To me, there are many reasons why this logic will never ever work. But the most direct and noteworthy reason is that the product of price change that we can see as graphs is a result of human behavior. Now what is the similarity of human behavior and the phenomenon of fractals in nature? Nothing. Human behavior is irrational while fractals are. Fractals can be mathematically justified and mapped out. Human behavior cannot be mathematically mapped out. It would take an infinitely complex system with infinity of variables. Trading algorithms are simple mathematical equations with constants.

In fact, the very mistake of undertaking this whole project of "prediction" of price movement - a "Holy Grail" is irrational human behavior.

That said,the only area that is worthy of research in trading is exactly the opposite. It is to study what shouldn't be there - the inefficiency of the markets and develop trading approaches accordingly. So instead of looking at fractals and asking what's next, we should be asking what is out of place? What should not be in this fractal?
...this just gave me an idea...