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WilliamsFractals

Incremental, causal technical analysis documentation

Summary

WilliamsFractals is RTTA's streaming 5-bar Bill Williams fractal detector. An up fractal is confirmed at the middle bar of a five-high pattern; a down fractal at the middle of a five-low pattern. Confirmation always lags by two bars.

Update API

result = rtta.WilliamsFractals(fillna=True).update(high, low)
# result.up, result.down

Until five bars are available, fillna=True returns up=0, down=0; fillna=False returns NaN for both fields.

Theory Of Operation

Williams fractals mark local turning points: a high fractal is a bar whose high is strictly greater than the highs of the two bars on either side; a low fractal is strictly less than the lows of the two bars on either side. Because the pattern needs two subsequent bars to confirm, the fractal is only known two bars after the middle bar forms. RTTA emits the fractal price level on the confirmation bar (when the newest bar completes the five-bar window), or 0.0 when no fractal is confirmed.

Recurrence

Maintain a shift register of the last five highs and lows, indices \(0\) oldest through \(4\) newest. After each update with at least five bars:

\[\begin{aligned} \operatorname{up}_t &= \begin{cases} H^{(2)}, & H^{(2)} > H^{(0)},\; H^{(2)} > H^{(1)},\; H^{(2)} > H^{(3)},\; H^{(2)} > H^{(4)} \\ 0, & \text{otherwise} \end{cases} \\[6pt] \operatorname{down}_t &= \begin{cases} L^{(2)}, & L^{(2)} < L^{(0)},\; L^{(2)} < L^{(1)},\; L^{(2)} < L^{(3)},\; L^{(2)} < L^{(4)} \\ 0, & \text{otherwise} \end{cases} \end{aligned}\]

where \(H^{(i)}, L^{(i)}\) are the register entries. Both can be non-zero on the same bar only if both patterns hold (uncommon).

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class WilliamsFractals. Result fields are up and down.

Reference