On this page
Fractal Dimension — Volatility, in its own panel below the chart.
What Fractal Dimension measures
Higuchi's estimator rebuilds the curve length at several decimation steps k, keeping every k-th close, and relies on the fact that curve length scales with k raised to the power minus D. The dimension is the negative slope of log length against log k, fitted across k from 1 up to kmax. A trending move with few reversals yields short decimated lengths and a dimension near 1, while alternating bars inflate the length at k = 1 relative to coarser steps and push the value toward 2. The defaults of 30 closes and kmax 5 keep enough points for the coarser steps while staying local; kmax is clamped to half the window, and the series returns nothing during warm-up or when a computed length is zero.
The formula, as implemented
This is not how the indicator is usually defined elsewhere — it is what the shipped code computes, documented next to the implementation:
Dimension fractale de HIGUCHI des N derniers closes — méthode, choix de Higuchi (vs Katz / box-counting) et dégradations : cf. `higuchiFd`. Résumé : L(k) ∝ k^(−D) sur les longueurs de courbe décimées au pas k = 1…kmax, D = −pente du log-log. D ≈ 1 = courbe lisse (tendance propre), D → 2 = marche très hachée. Défauts N=30 (assez de points pour k jusqu'à 5, assez court pour rester local) et kmax=5 (le compromis usuel : au-delà, les échelles grossières deviennent trop bruitées) ; kmax est clampé à ⌊N/2⌋. Warm-up (< N barres) → null ; L(k) nul → null.
How to read it
- Falling values describe a path becoming cleaner — fewer reversals per bar — which is what a developing trend looks like to this measure.
- Rising values toward 2 describe chop: distance is covered without progress, and each bar undoes part of the previous one.
- A clean advance and a clean decline read the same low value: what is graded is the shape of the path, not its sign.
- It reads closes only, so a bar with a long wick contributes exactly as much as one without, provided the closes match.
- Compare values within the same chart and the same settings rather than against a universal threshold — the absolute level shifts with window size and bar type.
Parameters and defaults
Period defaults to 30 closes, short enough to stay local and long enough to support the coarser decimation steps, and accepts 4 to 500. Kmax defaults to 5, the usual compromise since larger steps leave too few points to estimate a length reliably, and accepts 2 to 50; the implementation clamps it at half the period so the estimate stays defined.
| Parameter | Type | Default | Range |
|---|---|---|---|
| Period | number | 30 | 4 – 500 |
| k max | number | 5 | 2 – 50 |
What it does not show
The estimator reads closes only: bar range, volume and delta play no part, so two very different footprints with identical closes produce the same dimension. It describes the recent path and forecasts nothing — a low reading says the last thirty bars were smooth, not that the next thirty will be. Values depend on the window and on kmax, so numbers produced with different settings cannot be compared. Missing bars change the sampling grid the method assumes and bias the result without any visible sign.
Related indicators
- True Range — Volatility
- Std Dev — Volatility
- Squeeze — Volatility
- Chaikin Volatility — Volatility
- Realized Vol — Volatility
- Skewness — Volatility
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Frequently asked questions
- What does a fractal dimension near 1.5 mean?
- It sits midway between a smooth line and a fully space-filling path, which is the value a random-walk-like series tends to produce. In practice it describes a path with no dominant structure — neither a clean trend nor persistent alternation. Read it against the recent history of the same line rather than as an absolute verdict.
- Is fractal dimension the same as the Hurst exponent?
- They describe related properties but are computed differently. The Hurst exponent in Senzoukria uses rescaled range analysis on returns, while this indicator uses Higuchi's curve-length method on closes. For fractional Brownian motion the two are theoretically linked as D = 2 − H, but the estimators differ enough that the relationship should not be assumed to hold on live data.
- Which settings does the fractal dimension indicator use?
- A 30-bar window of closes and a maximum decimation step of 5. The window is adjustable from 4 to 500 and kmax from 2 to 50, but kmax is automatically clamped to half the window so that each decimated series still has enough points. Changing either parameter changes the absolute level of the output, not only its smoothness.