1999issue C021-12
Log-spiral wave construction from seed pivots
Three dated turning points form a seed triangle and lock one growth-ratio. Later log-spiral, rectangular-spiral, time-price-square, fibonacci-retracement, and elliott-wave legs are kept only when they reuse that same ratio on both price and calendar.
- A log-spiral keeps a constant shape as it grows or shrinks, and a related rectangular-spiral inherits the same growth-ratio.
- Turning points from 1974, 1976, and 1978 are treated as a seed triangle, with seed-segments of 497, 362, and 859 days used as generators.
- Axis-segments and spiral sides can be swapped without changing shape, and one worked interchange produces a triangle whose perimeter sums to 3,256 in the source diagram units.
- A later date is treated as stronger only when other pattern algorithms confirm the projection and spirals from different time frames intersect at that candidate.
Constant shape under growth
A log-spiral is a growth curve that keeps the same shape while it grows or shrinks. Radius and length scale by one constant growth-ratio, so the essential shape does not change.
A rectangular-spiral is the right-angle counterpart of that curve. Its side lengths are fixed by the same growth-ratio, so it inherits the same constant parameters.
The seed triangle and its measured intervals
Three turning points from 1974, 1976, and 1978 are treated as a seed triangle. Later major and minor swings are measured against that triangle.
The construction uses numbered calendar dates from October 1974 through October 1998. When two indexes reverse on different days, the turn is marked as a compound-pivot and both dates are kept.
Charted seed-segments include 497 days, 362 days, and 859 days. Those early measured intervals, in calendar days, are the generators for later spiral and square constructions.
One growth-ratio for later price and time legs
Successive growth increments are united by one common growth-ratio. Radius and length increase proportionately while the essential shape stays unchanged.
A later fibonacci-retracement is a swing measured as a constant-ratio fraction of a prior seed move, not an independent guess. An elliott-wave sequence of major and minor swings is likewise constrained by the same seed triangle and growth-ratio.
A time-price-square treats a measured time span and a measured price span as interchangeable legs of one square or right triangle. Those legs are admissible only when they reuse the growth-ratio already locked by the seed triangle.
Right triangles, matched perimeters, and interchangeable sides
A later construction can be placed on a seed-segment. Adjacent sides are then calculated with the square root of the same growth-ratio. The result is a right triangle whose perimeter can be matched to opposing triangles in the same figure.
Because every segment shares the same growth-ratio, an axis-segment and a spiral segment can be interchanged without changing the spiral's shape. A worked interchange of those segments produces a triangle whose perimeter sums to 3,256 in the source diagram units.
What must confirm a later candidate
The method requires other pattern algorithms to confirm a growth projection. It also requires spirals from different time frames to intersect at a candidate future pivot before that date is treated as stronger.
All readings on this track · 12 readings
- 1988Four sugar-futures turns as a ranked wave-ratio audit
- 1989Cluster-first construction of change-in-trend days from two ratio families
- 1992Wheat bull leg from a squared counterswing and Gann angles
- 1999Log-spiral wave construction from seed pivots
- 1999Compound pivots and market symmetry
- 1999Squaring charts for Gann angles
- 2007Constructing Gann time-price squares, angles, and 144 grids
- 2010Constructing Gann angles to square price and time
- 2011How a Lucas time series is built onto an Elliott wave map
- 2013Time-price boxes for wave-four construction
- 2016Gann circle eighths, Fibonacci neighbors, and time-price squares
- 2016Constructing wave cycles, Fibonacci spans, and time-price squares