Channel regimes and Gann angle hinges

Channels as the current linear regime

Stocks and commodities are described as repeatedly traveling in upward and downward price channels and oscillating from one channel boundary to the other while remaining inside that structure. Nested rallies and declines are described as forming straight inner channels that zigzag between the boundaries of a larger outer channel.

In this usage, a price channel is a pair of boundaries that contain those repeated swings and are treated as the current linear regime of price versus time. A linear regime is a stretch in which the response of price to the passage of time stays proportional and can be sketched with straight channel lines.

Price can also change at an increasing rate and trace a curve rather than a straight line. That stretch is nonlinear acceleration. A linear scale is said to display the channel mode more clearly, while a logarithmic scale is said to display the curved mode more clearly.

Geometric order and more than one rest state

Market order of the geometric kind associated with Gann angles is presented as real but imperfect, because price is said to follow the physical behavior of a chaotic system rather than one unbroken linear rule. A linear system is described as having a single rest state, while a nonlinear system can have more than one rest state and, when it does, is treated as chaotic.

Inside one domain of behavior the next motion can be projected from the current relationship, but at the boundary between domains that same relationship no longer decides the outcome. A domain boundary is the meeting of two incompatible price relationships. A simple rule may apply inside one domain but does not cover both sides of the boundary.

The hinge at a domain boundary

At the meeting of two behavioral domains, prices are described as either coiling in a triangle, often of five waves, or shifting rapidly into a new region, often with a gap that means prior channel boundaries need not still apply. A gap is an abrupt price jump read as evidence that a new relationship now governs and that prior channel lines need not still bind.

The unstable balance between two domains of behavior is a strange attractor, where a small push can send price back into the old regime or into a new one. Gann angles are geometric rays taken from chart scale to mark candidate hinges where an existing channel regime may hold, fail, or give way to a new set of boundaries.

Index cases from the late 1980s

After the 1987 break, a major U.S. industrial average is described as staying inside marked channel lines through 1988, then breaking the top of that channel at a precomputed hinge in early 1989. Newly drawn channel boundaries are then said to have held until a sharp break in October 1989.

After the October 1989 break, two nearly overlapping nonlinear boundary regions were computed on a broad U.S. equity index, with a high in late December or early January. Price is described as reaching that hinge and then falling sharply in a January selloff.

A rising growth-boundary curve on a major Japanese equity average is described as ending in December 1989, with a labeled high of 37233 on December 27, 1989, after which price turned down from a linear channel top on December 29.