Alligator

Bill Williams' Alligator — three SMMA lines (Jaw / Teeth / Lips) of the median price (high + low) / 2 with different smoothing periods.

Quick reference

Field	Value
Family	Moving Averages
Input type	Candle (uses high and low)
Output type	AlligatorOutput { jaw, teeth, lips }
Output range	unbounded; tracks the input price scale
Default parameters	jaw = 13, teeth = 8, lips = 5
Warmup period	max(jaw, teeth, lips) (13 for classic)
Interpretation	Three SMMA lines whose interleaving signals the Alligator state (sleeping / awakening / eating).

Formula

median_t = (high_t + low_t) / 2

Jaw_t   = SMMA(median, jaw_period)_t
Teeth_t = SMMA(median, teeth_period)_t
Lips_t  = SMMA(median, lips_period)_t

Smma is Wilder's smoothed moving average (RMA), SMA-seeded with a 1 / period smoothing factor. Williams' chart presentation also shifts each line forward (Jaw +8, Teeth +5, Lips +3); Wickra publishes the unshifted SMMA values — the visual shift is a chart convention left to the consumer.

Parameters

Name	Type	Default	Constraint	Source
jaw_period	usize	13	>= 1	Alligator::new (alligator.rs:59)
teeth_period	usize	8	>= 1	alligator.rs:59
lips_period	usize	5	>= 1	alligator.rs:59

Any zero period returns [Error::PeriodZero]. Alligator::classic() returns (13, 8, 5). Python defaults come from #[pyo3(signature = (jaw=13, teeth=8, lips=5))]; the Node constructor takes all three explicitly. The public class is Alligator in both bindings.

Inputs / Outputs

use wickra::{Indicator, Alligator, Candle, AlligatorOutput};
// Alligator: Input = Candle, Output = AlligatorOutput
const _: fn(&mut Alligator, Candle) -> Option<AlligatorOutput> = <Alligator as Indicator>::update;

Uses high and low (the median price).

• Python. update(candle) returns (jaw, teeth, lips) or None; batch(high, low) returns an (n, 3) np.ndarray with columns [jaw, teeth, lips]; warmup rows are NaN.
• Node. update(high, low) returns a { jaw, teeth, lips } object or null; batch(high, low) returns a flat Array<number> of length 3n, interleaved [jaw0, teeth0, lips0, …].

Warmup

All three SMMAs see every bar (fed unconditionally so they warm in parallel), so readiness is gated by the longest period — the Jaw. warmup_period() returns max(jaw, teeth, lips) (13 for classic). Pinned by warmup_emits_first_value_at_longest_period.

Edge cases

• Constant median. A constant (high + low) / 2 makes all three SMMAs seed to that constant and hold (test constant_series_yields_the_constant).
• Pure uptrend ordering. On a clean uptrend the fastest line leads: lips > teeth > jaw at the latest bar (test pure_uptrend_ordering).
• Reset. reset() resets all three SMMAs.

Examples

Rust

use wickra::{Alligator, BatchExt, Candle, Indicator};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let candles: Vec<Candle> = (0..80)
        .map(|i| {
            let base = 100.0 + f64::from(i);
            Candle::new(base, base + 1.0, base - 1.0, base, 1.0, i64::from(i)).unwrap()
        })
        .collect();
    let mut a = Alligator::classic(); // (13, 8, 5)
    if let Some(o) = a.batch(&candles).into_iter().flatten().last() {
        println!("jaw={:.2} teeth={:.2} lips={:.2}", o.jaw, o.teeth, o.lips);
    }
    Ok(())
}

Python

import wickra as ta
a = ta.Alligator(13, 8, 5)
out = a.batch(high, low)  # shape (n, 3): [jaw, teeth, lips]

Node

const ta = require('wickra');
const a = new ta.Alligator(13, 8, 5);
const o = a.update(101, 99); // high, low → { jaw, teeth, lips } or null

Interpretation

Williams read the three lines as a sleeping/feeding alligator:

1. Sleeping (ranging). The three SMMAs are intertwined and flat — no trend; stay out.
2. Awakening / eating (trending). The lines fan out in order (lips/teeth/jaw for an uptrend, reversed for a downtrend) and widen — ride the trend while the mouth stays open.
3. Sated. The lines converge again — the move is ending.

Williams paired the Alligator with fractals (FractalChaosBands): a fractal breakout outside the mouth is a trade; one inside is ignored.

Common pitfalls

• Forgetting the chart shift. Wickra's lines are unshifted; if you compare against a charting package that displays the shifted Alligator (Jaw +8 etc.), apply the forward shift yourself before lining them up.
• Trading the intertwined state. Overlapping lines mean "sleeping" — the Alligator is explicitly a don't-trade signal there.

References

• Bill Williams, Trading Chaos, Wiley, 1995.

See also

• Smma — the smoothed moving average each line uses.
• FractalChaosBands — Williams' fractals, the Alligator's usual partner.
• AwesomeOscillator — Williams' momentum gauge.