Fractal Dimension Pass Node

Fractal Dimension — Series Input

StatisticalFractalPass

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

FD ≈ 2 − H (Hurst exponent)
FD near 1.0 = strongly trending (smooth path)
FD near 1.5 = random walk
FD near 2.0 = highly choppy / mean-reverting (space-filling path)

Parameters

ParameterDefaultDescription
period20Rolling window in bars. Larger values give more stable estimates.

Inputs & Outputs

SlotDirectionTypeDescription
inputInput{ values, timestamps }Any upstream numeric series
valuesOutput(number | null)[]Fractal dimension per bar; nulls during warm-up
timestampsOutputnumber[]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.

Related Indicators