Fibonacci Arcs

Semicircular retracement levels centred on the swing end. Time is normalised by the leg's bar-width, so the construction is chart-scale-free: each arc starts on its retracement level and curves back to the swing-end price one leg-width later.

Quick reference

Item	Value
Family	Fibonacci
Input type	Candle (uses high, low)
Output type	FibArcsOutput (arc_382, arc_500, arc_618)
Output range	between the retracement level and the swing-end price
Default parameters	none (swing threshold 5%, baked)
Warmup period	2 (two confirmed pivots)
Interpretation	Decaying time-and-price support/resistance

Formula

last two pivots define a leg start -> end at bars (start_bar, end_bar):
  u      = (cur - end_bar) / (end_bar - start_bar)
  arc(r) = end + (start - end) * r * sqrt(max(0, 1 - u^2))
for r in {0.382, 0.5, 0.618}, cur = current bar index

At the end bar (u = 0) each arc sits exactly on its retracement level; as time elapses it curves back toward end, reaching it at u = 1 (one leg-width later) and staying there (u > 1 clamps the curve to 0). Normalising by the leg's bar-width removes any dependence on chart scale. See crates/wickra-core/src/indicators/fib_arcs.rs.

Parameters

None. The swing threshold 0.05 is a baked-in family constant; the three arc ratios are fixed. FibArcs::new is infallible.

Inputs / Outputs

const _: fn(&mut wickra::FibArcs, wickra::Candle) -> Option<wickra::FibArcsOutput> =
    <wickra::FibArcs as wickra::Indicator>::update;

• Python. update((o,h,l,c,v,ts)) → (arc_382, arc_500, arc_618) or None; batch(high, low) → (n, 3) ndarray (NaN warmup).
• Node. update(high, low) → { arc382, arc500, arc618 } or null; batch(high, low) → flat number[] length n*3.
• WASM. update(high, low) → object (same camelCase keys) or null.

Warmup

warmup_period() == 2. Two confirmed pivots define the leg; before that update returns None. Pinned by tests accessors_and_metadata and no_output_before_two_pivots.

Edge cases

• Arcs curve back toward the swing end as time passes (test arcs_curve_back_toward_the_swing_end).
• Beyond one leg-width the arcs collapse onto the swing-end price as the curve clamps to zero (test arc_clamps_to_zero_beyond_one_leg_width).
• reset clears all state (test reset_clears_state).
• Streaming equals batch (test batch_equals_streaming).

Examples

Rust

use wickra::{Candle, FibArcs, Indicator};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // Leg 200 (bar 0) -> 100 (bar 2), confirmed at bar 3 → u = 0.5.
    let bars = [
        (199.0, 200.0, 199.0, 199.0),
        (160.0, 190.0, 160.0, 160.0),
        (100.0, 150.0, 100.0, 100.0),
        (105.0, 110.0, 105.0, 105.0),
    ];
    let mut arcs = FibArcs::new();
    let mut last = None;
    for (ts, (o, h, l, c)) in bars.iter().enumerate() {
        last = arcs.update(Candle::new(*o, *h, *l, *c, 1.0, ts as i64)?);
    }
    let v = last.unwrap();
    // curve = sqrt(0.75) ≈ 0.866; arc(r) = 100 + 100*r*curve.
    println!("{:.3} {:.3} {:.3}", v.arc_382, v.arc_500, v.arc_618);
    // 133.082 143.301 153.520
    Ok(())
}

Python

import wickra as ta

bars = [
    (199.0, 200.0, 199.0, 199.0, 1.0, 0),
    (160.0, 190.0, 160.0, 160.0, 1.0, 1),
    (100.0, 150.0, 100.0, 100.0, 1.0, 2),
    (105.0, 110.0, 105.0, 105.0, 1.0, 3),
]
arcs = ta.FibArcs()
print([arcs.update(b) for b in bars][-1])
# (133.0821805, 143.3012702, 153.5203699)

Node

const wickra = require('wickra');
const arcs = new wickra.FibArcs();
const bars = [[200.0, 199.0], [190.0, 160.0], [150.0, 100.0], [110.0, 105.0]];
let last = null;
for (const [h, l] of bars) last = arcs.update(h, l);
console.log(last.arc382.toFixed(3)); // 133.082

Streaming

arcs = ta.FibArcs()
for o, h, l, c, v, ts in candle_feed:
    a = arcs.update((o, h, l, c, v, ts))
    if a is not None and abs(c - a[2]) < 0.5:
        pass  # price near the 61.8% arc — time-and-price confluence

Interpretation

1. Time + price. Arcs combine retracement depth with elapsed time; a level matters less the longer price takes to reach it.
2. Decaying relevance. The inward curve encodes the idea that a retracement zone loses force as the swing ages.

Common pitfalls

• Scale convention. The arc is normalised to the leg's bar-width, not to a pixel aspect ratio; values differ from a charting package that uses screen geometry. The formula above is exact and reproducible.
• Collapses after one leg-width. Past u = 1 all arcs read the swing-end price — by design, not a bug.

References

• Fischer, R. Fibonacci Applications and Strategies for Traders (1993).

See also

• FibFan, FibChannel, FibRetracement.
• Indicators-Overview — full taxonomy.