Polarized Fractal Efficiency (PFE)

Overview

The Polarized Fractal Efficiency represents a groundbreaking application of chaos theory to financial markets, emerging from Hans Hannula's insight that price movements exhibit fractal characteristics similar to natural phenomena. Published in the January 1994 issue of Technical Analysis of Stocks & Commodities, PFE measures how directly price moves from point A to point B compared to the actual path traveled. Just as a river meandering through a valley is less efficient than a straight canal, price movements that zigzag are less efficient than those moving in straight lines, and PFE quantifies this efficiency on a scale from -100 to +100.

The calculation compares the net distance price has traveled (straight line from start to finish) with the sum of all individual price movements over that period. This ratio, expressed as a percentage and given polarity based on direction, creates an oscillator that reveals not just trend direction but trend quality. Values near +100 or -100 indicate highly efficient, strong trends where price moves persistently in one direction. Values near zero suggest choppy, inefficient movement where price oscillates without clear direction. This unique perspective helps traders distinguish between trends worth following and noisy, directionless markets that are best avoided.

Interpretation & Trading Signals

Example Usage

Code examples will be available once the Rust implementation is complete.