Impulse and correction as a recursive fractal recipe

The impulse and correction seed

The construction seed is the impulse and correction pair (3, -1): an impulse of +3 and a correction of -1, written as the recursive fractal (3, -1)F.

A recursive fractal is a self-similar wave generated by repeating and inverting that seed pair at each generation, so a completed sequence becomes one leg of the next larger sequence.

How each generation expands

The first generation is (3, -1), which can also be written as (1, 2, 3, -1). The second generation is three copies of (3, -1) plus the inverse pair (1, -3).

The inverse pair is the sign-and-order flip of (3, -1) into (1, -3). That inversion is required for the pattern to keep generating itself at the next degree.

The same recipe as a five-and-three count

The same two-number recursion is drawn as an idealized Elliott count. Under the five-and-three count used here, an impulse is counted as five waves and a correction as three waves, nested inside the next higher degree.

Price over time, not a time window

Construction uses only price displacement and retracement. Calendar time is omitted from the wave recipe. That price-over-time choice measures how far price moves and how far it retraces, not how long the move lasts.

Changing the seed to (4, -1) makes constructed retracements too shallow. Changing it to (2, -1) makes them too deep. The pair is therefore fixed by the geometry rather than by a time-window setting.

Three construction assumptions

The archive states three construction assumptions: market data may contain fractals, no movement is pre-labeled noise, and price outranks time.

The no-noise assumption is the rule that every price movement belongs in the model. Nothing is discarded as a statistical outlier before the wave is built.

Fractal retracements and the margin of error

A fractal retracement is the ratio of a corrective leg to the preceding impulse, read off the recursive (3, -1) geometry rather than from a separate overlay. Idealized fractal retracement ratios on the constructed series include values such as 0.496, 0.244, 0.195, 0.330, 0.162, and 0.498.

Because time is stripped out, the model can sequence retracements but cannot say when they occur. The archive lists that limit as a construction weakness.

The archive treats a finished description of past structure as having some forward use. It also states a residual error band, the margin of error, between idealized fractal retracements and observed index retracements. That band is treated as the band around any later target.