All posts by Gary Lammert

The Elegant Interpolated Fractal Self-Assembly Math: The ACWI 7 April 2025 to 24 April 2026 53/107/106 day :: x/2x/2x 3-Phase Final Peak Valuation Fractal Growth Series and the 7 April 2025 53/107/132-133 day :: y/2y/2.5y 3-Phase Initial Crash Fractal Decay Series Devaluation.

New 7 April 2025 Terminal 3-Phase Fractal Peak Growth Model :: 53/107/106 days :: x/2x/2x with ACWI terminal peak valuation on Friday 24 April 2026.

Valuation growth and decay of the asset-debt system’s tradable assets occur in a highly ordered time-based mathematical fractal pattern.
Since the 7 April 2025 nadir, maximal growth for ACWI has occurred in a 53 day/107 day/98 of 106 day :: x/2.5x/2x 3 phase fractal growth series with an expected final peak valuation on 24 April 2026. This terminal growth fractal growth series is elegantly interpolated in a 7 April 2025 53/107/132-133 day :: y/2y/2.5y incipient 3 phase fractal crash decay series.

The 53 day 1st fractal is composed of a 10/25/20 day : x/2.5x/2x sub-fractal series. Each sub-fractal is composed likewise of self-assembly fractal subunits as depicted above.



The 107 day 2nd Fractal is composed of 4 sub-fractal series as shown above (the 12 day 2nd sub-fractal of the 29 day 1st sub-fractal series is actually 13 days) and the 3rd 14 day sub-fractal of the 4th sub-series is 13 days vice 14 days making the total length of the 2nd Fractal 107 vice 108 days) or alternatively, as below: a 29/62 :: x/2-2.5x 1st and 2nd fractal growth series growth followed by a peak to nadir 3/7/6/5 day :: y/2-2.5y/2y/1.5y 4-phase fractal decay series.



The 106 day 3rd Fractal to terminal peak growth follows the fractal pattern of the above 107 day 2nd fractal 2-phase fractal growth series and peak to nadir fractal decay series model with two sequential fractal series : a 19/47 day :: x/2.5x 2-phase growth maximum growth series followed by a peak to nadir 5/13/8 day :: y/2.5y/1.6y decay 3-phase fractal decay series and a 6(-)/14 day :: x/2.5x maximum growth series to reach a peak valuation on Friday 24 April 2026.



A 3-phase peak to nadir 6/14/9-10 day :: y/2-5y/1.6y fractal decay series or a 3-phase peak to nadir 5/12-13/12 day :: y/2-2.5y/2-2.5y fractal decay series or a 4-phase peak to nadir 4-5/10/10/7 day :: y/2-2.5y/2-2.5y/1.5y fractal decay series would represent the initial 27-28 day crash fractal decay series resulting an April 2026 53/107/132-133 day :: y/2y/2.5y decay series with an initial crash fractal series low on 1 or 2 June 2026.

This 53/107/132-133 day series is the 290-291 day 3rd fractal of a 27 October 2023 120/243/290-291 day :: y/2y/2-2.5y series.

The 120/243/290-291 day series becomes the 651-652 day 2nd fractal of a 13 Oct 2022 262/651-652 day :: x/2.5x 1st and 2nd Fractal series.

The base 1st fractal for the 4-phase 2026 crash fractal decay series maybe the 17 Dec 2025 10/25 day 1st and 2nd fractal series or 34 days. A 17 Dec 2026 34/82-3/82-3/50 day :: y/2-2.5y/2-2.5y/1.5y crash fractal decay series would place the 1982 to 2026 13/33 year :: x/2.5x 1st and 2nd fractal nadir in Dec 2026.

25 April 2025 Postscript … Added 25 April 2025

While the ACWI global equity ETF did not make a final higher high on 24 April 2026, because of the effect of the higher Hormuz oil energy prices on the European Equity Markets, the US Wilshire 5000, composite of US equities, did reach a new high on 24 April 2026 as shown below.

The SPX final 30 Mar 2026 x/2.5x :: 6/14 day 1st and 2nd fractal series reaching its higher high on 24 April 2026 was a 36-37/93 hour :: x/2.5x 1st and 2nd fractal series reaching its higher high on the 93nd hour of the 93 hour 2nd fractal.

The SPX final 30 Mar 2026 x/2.5x :: 6/14 day 1st and 2nd fractal series reaching its higher high on 24 April 2026 was a 36-37/93 hour :: x/2.5x 1st and 2nd fractal series reaching its higher high on the 93nd hour of the 93 hour 2nd fractal.

Expect The Expected: The Great 20 February 2026 to 24-28 April 2026 8/20/18-20 day :: y/2.5y/2-2.5y ACWI Incipient Global Equity Crash

Gold, Crypto, and global Equities are all undergoing a 1982 global equity 13/33 year :: x/2.5x 1st and 2nd fractal series’ terminal 33 year 2nd fractal incipient nonlinear crash which will transpire over the next 10 trading days starting 10 April 2026 and is following a 20 Feb 2026 to 24-28 April 2026 ACWI 8/20/8 of 18 to 20 day :: y/2.5y/2-2.5y 3 phase Lammert Fractal Crash Decay Series self similar to the incipient 11/26/27 day 1929 DJIA 3 phase Lammert Fractal Crash Decay Series.


The cause of the crash is a summation result of terminal 33 year 2nd fractal cycle enormous accumulation of global bad corporate and private debt that cannot be repaid – by the underlying ongoing dynamics of global wages and total job numbers of its citizens. This private debt expansion and accumulation has leveraged extreme over ownership and overvaluation of – equity, crypto, gold, silver, residential and commercial real estate, et. al. – pricing.

The Israeli-Trump war is a coincidental red herring accelerant to a predetermined 33 year terminal 2nd fractal private-debt-dependent nonlinear asset valuation crash.

A 17 Feb 2026 11/28/28 day :: y/2.5y/2.5Y 3-Phase Lammert Crash Fractal Decay Series?

The ACWI 3 March 2026 28 day 2nd Fractal of the 17 Feb 2026 11/28/28 day 3-phase crash fractal decay series appears conforming to a 5/10/9/7 day :: 28/70/56-57/42-43 hour :: y/2.5y/2-2.5y’/1.5y’ 4-phase fractal series where the 3rd 56-57 hour 2-2.5y’ subfractal of the series ends on a lower high. This 56-57 hour subfractal is composed of a 12/25/21-22 hour :: x/2.5x/2x 3-phase deteriorating growth fractal series.

The Two Lammert Time-Based Fractal Laws of Self-Assembly:

  1. A 4-Phase Series: x/2-2.5x/2-2.5x/1.5-1.6x , where the 3rd fractal ends on a peak or lower high valuation and the other 3 Fractals end on nadir valuations.
  2. A 3-Phase Series: x/2-2.5x/1.5-2.5x, where all 3 fractals end on nadir valuations. This can be written as y/2-2.5y/2-2.5y for crash devaluations where ‘y’ denotes declining valuations.

Added 31 March 2026 … A 23-30 % Devaluation in the French CAC by 13 April?

1929 initial DJIA fractal decay series: 10-11/26-27/27 days :: y/2.5y/2.5y

2026 initial ACWI fractal decay series : 17 Feb 2026 11/28/28 days :: y/2.5y/2.5y

1 April 2026 will be day 22 or 2y, a final lower high or lower lower high of the ACWI 28 day 2nd decay fractal following a 3 Mar 2026 5/10/9/7 day :: y/2y/2-2.5y’/1.5y’ 4-phase deteriorating growth and decay (sub)fractal series. (Day 9 of the 3rd fractal of this 5/10/9/7 series is day 22 of the 22 of 28 day 2nd fractal.) The expected 28 day ACWI nadir is 10 April 2028. The complementary hourly ACWI 2nd (sub)Fractal 4-phase deteriorating growth and decay series is 28/70/56/42 hours :: y/2.5y2y/1.5y.

For the French CAC with trading holidays on 3 Apr and 6 Apr, the expected 28 day 2nd Decay Fractal nadir is 13 April 2026. Looking at the first 5 day (5/10/9/7 days) 2nd fractal trendline, the CAC should lose greater than 22% of its 1 April 2026 lower high value by 13 April 2026.

See Lammert Saturation Macroeconomics for French CAC illustrations.