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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 \(t \geq 2\) according to the following rules.

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

- Case 1: \(t + 2 < N\) and the following are all true:
- \(H_t > H_{t - 1} > H_{t - 2}\)
- \(H_t > H_{t + 1} > H_{t + 2}\)
- \(L_t \geq L_{t - 1}\)
- \(L_t \geq L_{t - 1} > L_{t - 2}\)
- \(L_t \geq L_{t + 1}\)
- Case 2: \(t + 3 < N\) and the following are all true:
- \(H_t > H_{t - 1}\)
- \(H_t > H_{t - 2}\)
- \(H_t = H_{t + 1}\)
- \(H_t > H_{t + 2}\)
- \(H_t > H_{t + 3}\)
- Case 3: \(t + 4 < N\) and the following are all true:
- \(H_t > H_{t - 1}\)
- \(H_t > H_{t - 2}\)
- \(H_t = H_{t + 1} = H_{t + 2}\)
- \(H_t > H_{t + 3}\)
- \(H_t > H_{t + 4}\)

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

- Case 1: \(t + 2 < N\) and the following are all true:
- \(L_t < L_{t - 1}\)
- \(L_t < L_{t - 2}\)
- \(L_t < L_{t + 1} < L_{t + 2}\)
- Case 2: \(t + 3 < N\) and the following are all true:
- \(L_t < L_{t - 2}\)
- \(L_t < L_{t - 1}\)
- \(L_t = L_{t + 1}\)
- \(L_t < L_{t + 2}\)
- \(L_t < L_{t + 3}\)
- Case 3: \(t + 4 < N\) and the following are all true:
- \(L_t < L_{t - 2}\)
- \(L_t < L_{t - 1}\)
- \(L_t = L_{t + 1} = L_{t + 2}\)
- \(L_t < L_{t + 3}\)
- \(L_t < L_{t + 4}\)

#### 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 Tuesday, 23rd October, 2018.