OPEN-SOURCE SCRIPT
Fractal Dimension Index [JOAT]
FRACTAL DIMENSION INDEX [JOAT]
A proper Higuchi-method Fractal Dimension Index that tells you whether the market is currently trending (D approaches 1.0 — a smooth, linear path), chopping (D approaches 2.0 — a noisy, plane-filling random walk), or somewhere in between. Unlike volatility, FDI does not care about how much price moved — it cares about how convoluted the path was getting there. That makes it the single cleanest regime-classification number in technical analysis.
What FDI measures
The fractal dimension of a curve is a number between 1.0 (a perfect line) and 2.0 (a curve dense enough to fill a plane). For price series:
The Higuchi-paper canonical thresholds are 1.4 (trend) and 1.6 (chop); both are configurable.
Higuchi algorithm — done properly
The implementation is the standard Higuchi method:
A minimum-valid-pairs guard (default 3) prevents D from being computed when too few (k, L) pairs are finite, and a warmup-bars gate (default 50) prevents wild D values on sparse early data.
Regime classification with hysteresis
Raw D is mapped to one of three regimes — Trending / Random / Chop — using the two-threshold scheme. Two extra alert thresholds (Extreme Trend D < 1.30 and Extreme Chop D > 1.70) flag the high-conviction tail cases.
Visual system
A locked Pastel palette (mint trend / coral chop / cream random on a warm-white ground) gives the indicator a distinctive soft-institutional look.
Dashboard
Monospaced table positionable to any of nine corners. Surfaces:
Alerts
Four alert conditions, each independently controllable:
How to read it
Two reads, in order of conviction:
The single most useful workflow is to use FDI as a meta-filter — pair every signal-generating indicator with FDI regime. Trend signals from a momentum tool become high-conviction when D < 1.4; reversion signals from a Z-score oscillator become high-conviction when D > 1.6. The Suggested JOAT Indicator dashboard rows in Hurst Regime Sentinel and Entropy Oscillator follow exactly this principle.
Suggested settings
Defaults (window 30, k_max 8, EMA smoothing 5, warmup 50) are tuned for 15m–1H. For lower timeframes drop window to 20 and EMA to 3. For HTF (4H+) raise window to 50 and EMA to 8. The Higuchi-paper thresholds (1.4 / 1.6) are intentionally classical — tighten only if you find the regime classification too sensitive on your instrument.
Originality / what's reused
The Higuchi fractal-dimension algorithm is the textbook 1988 method — a public-domain piece of applied mathematics, implemented from the paper. The implementation here — the bounded-loop Higuchi pipeline with minimum-pairs guard and warmup gate, the two-threshold regime classifier with extreme-tail alerts, the pastel-palette regime tint, the pin-to-scale D-line companion logic, the right-side floating label, and the dashboard — is JOAT-original. No third-party code reused.
Open source
Published open-source under the default Mozilla Public License 2.0. The Higuchi loop, the regime classifier, the alert logic, and the dashboard are isolated modules — adapt any single piece without reading the whole file. Forks welcome with credit.
Limitations
Higuchi D is statistical — it tells you about recent path complexity, not future direction. A trending regime (D < 1.4) does not say which way; it says momentum tools should work. Combine with a directional indicator. The algorithm uses bounded Pine loops; very large window values increase compile cost. D is smoothed (EMA-filtered) by default, which trades some lag for substantially reduced flicker; turn smoothing off to see raw D.
—
-made with passion by jackofalltrades
A proper Higuchi-method Fractal Dimension Index that tells you whether the market is currently trending (D approaches 1.0 — a smooth, linear path), chopping (D approaches 2.0 — a noisy, plane-filling random walk), or somewhere in between. Unlike volatility, FDI does not care about how much price moved — it cares about how convoluted the path was getting there. That makes it the single cleanest regime-classification number in technical analysis.
What FDI measures
The fractal dimension of a curve is a number between 1.0 (a perfect line) and 2.0 (a curve dense enough to fill a plane). For price series:
- D ≈ 1.0–1.4 — the price path is close to a straight line. The market is trending; momentum tools work, reversion tools don't.
- D ≈ 1.4–1.6 — the path is in a transitional regime. Use neutral tools.
- D ≈ 1.6–2.0 — the path is chaotic and self-intersecting. The market is chopping; reversion tools work, momentum tools whipsaw.
The Higuchi-paper canonical thresholds are 1.4 (trend) and 1.6 (chop); both are configurable.
Higuchi algorithm — done properly
The implementation is the standard Higuchi method:
- For each k from 1 to k_max (configurable, default 8), compute the average curve length L(k) across k starting offsets, normalised by the window length N.
- Build the k_max pairs (log k, −log L(k)).
- Fit a least-squares line through those pairs; the slope is the fractal dimension D.
- Apply optional EMA smoothing (configurable, default 5 bars) to suppress per-bar jitter.
A minimum-valid-pairs guard (default 3) prevents D from being computed when too few (k, L) pairs are finite, and a warmup-bars gate (default 50) prevents wild D values on sparse early data.
Regime classification with hysteresis
Raw D is mapped to one of three regimes — Trending / Random / Chop — using the two-threshold scheme. Two extra alert thresholds (Extreme Trend D < 1.30 and Extreme Chop D > 1.70) flag the high-conviction tail cases.
Visual system
- Background tint by regime — pastel mint for trend, coral for chop, cream for random. Transparency configurable (default 88, institutional-subtle).
- Regime-change markers — tiny up/down/circle glyphs above price at every confirmed flip.
- Optional candle tinting by regime (off by default to preserve user's chart style).
- Optional D-line companion — when enabled, the smoothed D is plotted as a series. Because the script is overlay, pin the line to its own scale (right-click → Pin to scale → No Scale). For a true sub-pane, add the indicator a second time and drag that instance into a new pane.
- Right-side floating label — anchored N bars right of the live close showing current D and a regime glyph. Configurable size, offset, regime text.
- Optional reference horizontal lines at D = 1.4 / 1.5 / 1.6 when the D-line is shown.
A locked Pastel palette (mint trend / coral chop / cream random on a warm-white ground) gives the indicator a distinctive soft-institutional look.
Dashboard
Monospaced table positionable to any of nine corners. Surfaces:
- Current D value and smoothed D value.
- Regime classification with glyph.
- Bars in current regime.
- Distance to nearest threshold.
- Extreme-state badge when in tail regions.
Alerts
Four alert conditions, each independently controllable:
- Regime Flip (any classification change)
- Extreme Trend (D crosses below 1.30)
- Extreme Chop (D crosses above 1.70)
- D Series Crosses 1.5 (the random-walk centre)
How to read it
Two reads, in order of conviction:
- Regime classification + bars in regime — the more bars the current regime has persisted, the more reliable the read. Brand-new flips can flicker; multi-bar confirmed regimes do not.
- Extreme regime alerts — when D crosses below 1.30, the market is in an extremely directional regime — momentum trades are the highest-conviction setups. When D crosses above 1.70, the market is in pathological chop — fade extremes, do not chase breakouts.
The single most useful workflow is to use FDI as a meta-filter — pair every signal-generating indicator with FDI regime. Trend signals from a momentum tool become high-conviction when D < 1.4; reversion signals from a Z-score oscillator become high-conviction when D > 1.6. The Suggested JOAT Indicator dashboard rows in Hurst Regime Sentinel and Entropy Oscillator follow exactly this principle.
Suggested settings
Defaults (window 30, k_max 8, EMA smoothing 5, warmup 50) are tuned for 15m–1H. For lower timeframes drop window to 20 and EMA to 3. For HTF (4H+) raise window to 50 and EMA to 8. The Higuchi-paper thresholds (1.4 / 1.6) are intentionally classical — tighten only if you find the regime classification too sensitive on your instrument.
Originality / what's reused
The Higuchi fractal-dimension algorithm is the textbook 1988 method — a public-domain piece of applied mathematics, implemented from the paper. The implementation here — the bounded-loop Higuchi pipeline with minimum-pairs guard and warmup gate, the two-threshold regime classifier with extreme-tail alerts, the pastel-palette regime tint, the pin-to-scale D-line companion logic, the right-side floating label, and the dashboard — is JOAT-original. No third-party code reused.
Open source
Published open-source under the default Mozilla Public License 2.0. The Higuchi loop, the regime classifier, the alert logic, and the dashboard are isolated modules — adapt any single piece without reading the whole file. Forks welcome with credit.
Limitations
Higuchi D is statistical — it tells you about recent path complexity, not future direction. A trending regime (D < 1.4) does not say which way; it says momentum tools should work. Combine with a directional indicator. The algorithm uses bounded Pine loops; very large window values increase compile cost. D is smoothed (EMA-filtered) by default, which trades some lag for substantially reduced flicker; turn smoothing off to see raw D.
—
-made with passion by jackofalltrades
Script open-source
Nello spirito di TradingView, l'autore di questo script lo ha reso open source, in modo che i trader possano esaminarne e verificarne la funzionalità. Complimenti all'autore! Sebbene sia possibile utilizzarlo gratuitamente, ricordiamo che la ripubblicazione del codice è soggetta al nostro Regolamento.
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Le informazioni e le pubblicazioni non sono intese come, e non costituiscono, consulenza o raccomandazioni finanziarie, di investimento, di trading o di altro tipo fornite o approvate da TradingView. Per ulteriori informazioni, consultare i Termini di utilizzo.
Script open-source
Nello spirito di TradingView, l'autore di questo script lo ha reso open source, in modo che i trader possano esaminarne e verificarne la funzionalità. Complimenti all'autore! Sebbene sia possibile utilizzarlo gratuitamente, ricordiamo che la ripubblicazione del codice è soggetta al nostro Regolamento.
The AI Trading Ecosystem, Built to win trades 📈
Get Full Access 👇
jackofalltrades.vip 🌐
t.me/jackofalltradesvip 🃏
Get Full Access 👇
jackofalltrades.vip 🌐
t.me/jackofalltradesvip 🃏
Declinazione di responsabilità
Le informazioni e le pubblicazioni non sono intese come, e non costituiscono, consulenza o raccomandazioni finanziarie, di investimento, di trading o di altro tipo fornite o approvate da TradingView. Per ulteriori informazioni, consultare i Termini di utilizzo.