It's hard to understand how the Fibonacci sequence presents itself in price action. I remember I used to think it was nothing more than lines drawn in a chart in a fancy manner. However, as I began to learn about probability distributions, I began to understand where the sequence reared its head into price action. Although I don't fully comprehend the theory behind the Fibonacci retracement, I did find a mathematical demonstration that proves price action and this sequence are related. You can find the demonstration in the link below. I'm unsure, but I believe this is peer-reviewed.
However, you will notice that this approach is extremely different to the Fibonacci retracement. They look nothing alike. However, it's an interesting concept which could Shead light into understanding the fractal that governs price action. One of which is the Sierpinski triangle
So does the Fibonacci retracement actually work? Well I don't know, but there is only one way to find out, so lets try it
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