Constructing polarized fractal efficiency as a path filter

Path measurement comes first

A folded path is assigned a non-integer fractal dimension between 1 for a straight line and 2 for a plane, and that score is used to judge how trendy or congested a price path has been.

Measured coastline length depends on ruler size: a shorter ruler fits more inlets and reports a longer distance, and ruler length versus measured length has a constant slope on a log-log chart.

Editorial: those two facts are a reason to build a path measure before reading any oscillator as a trade cue.

Two hypotenuses over one span

Polarized fractal efficiency is the straight-line net move divided by the squiggly close-to-close path, then signed plus when the span is down and minus when the span is up.

Each close-to-close step is a short ruler: a hypotenuse equal to the square root of the squared sides. Those lengths sum to path A. Path B is the long ruler, the single first-to-last-close hypotenuse over the same span. A worked case with B at 9 and A at 25 is 36% efficiency.

Span and sign smoothing

Using the oscillator requires choosing a bar span and applying a five-period exponential moving average to damp sign-flip noise. A ten-bar span is offered as a balance because delay is half the span.

Ceilings, lock-in, and the zero line

On the illustrated stock-index chart the reading tended to cap near 43% in either direction, a ceiling also reported for other stock indices, while other stocks and commodities showed different but still present maxima.

Direction changes in the reading are often smooth, but the value may bounce or oscillate around zero. That mid-zone is treated as zero-line congestion, a region of balanced supply and demand.

After the illustrated index reading passed 66% it often jumped toward 80% and stayed efficient. That stretch is an efficiency lock-in. Just before such a stretch ended, a late maximizing candlestick hook often printed as tall opposite-color candles, so the reading can filter candlestick patterns.

Keep the construction as a filter

The historical pairing is to follow price with trailing-stop follow-through, park a stop beyond the hook extreme, hold through a clean zero cross until opposite-side maximum efficiency, and exit if price congests near zero.

Editorial: keep polarized fractal efficiency in a filter role. Its extremes become a testable setup only when a trailing stop bounds follow-through and a late opposite-color candle marks the hook.