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# Bill Williams Fractal Signals

The study calculates and displays the Bill Williams Fractal signals.

Let \(H_t\) and \(L_t\) denote the High and Low Prices at Index \(t\). Let \(N\) be the number of bars in the chart, and let \(k\) denote the **Arrow Offset Percentage** Input. The Buy and Sell Fractal Signals are generated for \(t \geq 2\) and \(t + 2 < N\) according to the following rules.

Buy Fractal Signals generated at Index \(t\) are indicated by green arrows drawn at the position \(H_t + \frac{k}{100}(H_t - L_t)\) if the following conditions are met.

- \(H_t > H_{t - 1}\)
- \(H_t > H_{t - 2}\)
- \(H_t > H_{t + 1}\)
- \(H_t > H_{t + 2}\)

Sell Fractal Signals generated at Index \(t\) are indicated by red arrows drawn at the position \(L_t - \frac{k}{100}(H_t - L_t)\) if the following conditions are met.

- \(L_t < L_{t - 1}\)
- \(L_t < L_{t - 2}\)
- \(L_t < L_{t + 1}\)
- \(L_t < L_{t + 2}\)

#### Alert Example

Since the Bill Williams Fractal does not provide a signal on the current bar, and instead references the previous 2 bars, for an Alert Formula you need to use the following formula to alert when a signal occurs: =OR(SG1[-1], SG2[-1], SG1[-2], SG2[-2])

#### Inputs

**Arrow Offset Percentage**: This is a percentage where 1 equals 1%. This specifies a percentage of the High to Low range of a bar which is used to offset the Up and Down triangles (default Subgraph**Draw Style**) from the High and Low of a bar, respectively.

#### Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through **File >> Open Spreadsheet**.

*Last modified Monday, 26th September, 2022.