Fractal Dimension (Katz, Quant Lab)

This indicator estimates the Katz Fractal Dimension of the price series over a rolling window.

It computes:
• L = sum of absolute price changes within the window
• d = maximum distance between any point and the first point in the window
• n = window length

Then applies Katz’s formula:

FDI = ln(n) / (ln(n) + ln(d / L))

The resulting Fractal Dimension typically lies between 1.0 and 2.0:
• FDI ≈ 1.0–1.3 → Strong, directional trend (low randomness)
• FDI ≈ 1.3–1.5 → Mixed / transitional behavior
• FDI ≈ 1.5–2.0 → Noisy, choppy, mean-reverting / range market