Fractal Dimension Pass Node
Fractal Dimension — Series Input
Overview
The Fractal Dimension Pass Node estimates the fractal dimension (FD) of any upstream series over a rolling window. The fractal dimension describes how jagged or complex the price path is relative to a straight line.
FD is related to the Hurst exponent H by the approximate relationship FD ≈ 2 − H. A smooth trending series has FD near 1; a highly erratic, choppy series approaches FD 2.
Formula
Parameters
| Parameter | Default | Description |
|---|---|---|
| period | 20 | Rolling window in bars. Larger values give more stable estimates. |
Inputs & Outputs
| Slot | Direction | Type | Description |
|---|---|---|---|
| input | Input | { values, timestamps } | Any upstream numeric series |
| values | Output | (number | null)[] | Fractal dimension per bar; nulls during warm-up |
| timestamps | Output | number[] | Unix timestamps aligned to input |
Use Cases
Regime Filter
Use FD < 1.4 to filter trend-following entries; FD > 1.6 to enable mean-reversion strategies.
Market Complexity Measure
Monitor how complex (choppy) a market is becoming over time — useful for volatility regime detection.
Hurst Complement
FD provides a direct geometric interpretation (how space-filling the path is) that complements the H exponent.
Tips & Best Practices
Intuitive Interpretation
Think of FD as "how much the path wiggles". A straight line has FD = 1; a fully random walk approaches FD = 1.5; extreme choppiness → FD → 2.
Apply to Smoothed Series
For cleaner signals, apply to a smoothed price or indicator series rather than raw tick noise.
Combine with DFA
Use both FD and DFA exponent for a more robust fractal market assessment, as they capture different aspects of self-similarity.