First up – this isn’t anything daunting in terms of the math – in market technical analysis the term fractal is used only to indicate a recurring pattern. There’s no difficult stuff like chaos theory or the theory of groups involved…

Fractals are a suggestion of reversal among larger market movements.

A bearish turning point fractal = 5 consecutive bars, the highest high preceded and followed by two lower highs.
A bullish turning point fractal = 5 consecutive bars where the lowest low preceded and followed by two higher lows.

It’s possible to calculate fractals using groups of 7, 9, etc. time periods – using 3 isn’t going to tell you a whole lot… And notice that fractals may share bars, so that a buy and a sell fractal can merge into each other.

And there ain’t a whole load more to fractals than this. A fractal signal remains in force until replaced by an opposite signal. They have their place, ie. don’t place a trade when the fractal sign is contrary – but, as should be fairly obvious, these signals on their own are nowhere near solid enough to initiate a trade and so fractals have to be used in combination with eg the Alligator or other indicators.