# Technical Studies Reference

### 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.