We could see Fibonacci at work in the stock markets. Elliott Wave also demonstrated Fibonacci sequence in the wave counts. Below is an example of how Fibonacci and fractal works in the nature. Each water drop captured using high speed camera shows that the drop was bounced back while a bigger portion of itself joined the water surface. We could see that this happens so often in stock markets. Each market rally was interrupted with trend correction while each stock market fall was pause by bounce-back rally before continuing its trend directions.
It would be wonderful to observe if the bounce-back strength of the water drop coincide with the Fibonacci retracement ratio. Hopefully someday, some scientists take the effort to measure that.