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Williams Fractal (FRACTAL)

Summary

Williams Fractal: a causal swing-pivot detector. A bar is a swing high when its high strictly exceeds the highs of the optInLeftBars bars before it and the optInRightBars bars after it; a swing low is the mirror on the lows. Bill Williams' original is the symmetric five-candle case; independent left and right arms generalise it.

The right arm cannot be known until it has closed, so the verdict is reported on the confirmation bar, optInRightBars bars after the pivot itself. Each output value therefore describes the bar optInRightBars back, not the bar it is written at: a flag at output index k names input bar outBegIdx + k - optInRightBars, whose price is inHigh[...] / inLow[...] at that index.

The two outputs are independent flags rather than one signed value, because an outside bar can be a swing high and a swing low at once.

Formula

With L = optInLeftBars, R = optInRightBars and pivot c = i - R:

swingHigh(i) = 100 if High[c] > High[j] for every j in [c-L, c+R] other than c, else 0.

swingLow(i) = 100 if Low[c] < Low[j] for every j in [c-L, c+R] other than c, else 0.

Notes

  • Strict on both sides: a bar tied with any other bar of its window is not a pivot. TradingView's Pine runtime differs — its ta.pivothigh / ta.pivotlow let a tie with an older bar stand and let a tie with a newer bar cancel, i.e. non-strict left and strict right — so a plateau Pine reports as a pivot is not one here.
  • Each output is decided on its own side: a high tied with any other high in the window forces outSwingHigh to 0 while leaving outSwingLow free to fire 100, and the mirror holds. Only a window flat in both series emits 0 on both.

Inputs

  • inHigh — High price series
  • inLow — Low price series

Outputs

  • outSwingHigh — 100 when the bar optInRightBars back is a strict swing high, 0 otherwise
  • outSwingLow — 100 when the bar optInRightBars back is a strict swing low, 0 otherwise

Parameters

ParameterTypeDefaultAccepted valuesDescription
optInLeftBarsinteger21–100000Bars before the pivot that it must strictly dominate
optInRightBarsinteger21–100000Bars after the pivot that it must strictly dominate, and the delay before the verdict is reported

Properties

Numerical Stability: Start-Independent

☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1

Implementation

TA-Lib Definition: fractal.c · fractal.yaml

NativeFile
Cta_FRACTAL.c
Rustfractal.rs
JavaCore_FRACTAL.java

TA-Lib is also available for Python, R and more using a wrapper.

Aliases

Williams Fractal, Fractals, Swing High, Swing Low, Pivot High, Pivot Low

See Also

AROON · MAXINDEX · MININDEX · MINMAXINDEX

References

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