Fractal groupings are determined by the underlying trendline from the first time unit to the last time unit of the grouping whereby all interim valuations are above that trendline.

From the 7 April 2025 low there are three identifiable fractal groupings consistent with this definition.

1: a 3-phase 10/25/20 day :: x/2.5x/2x growth fractal grouping

2: a 3-phase 6/12/13 day :: x/2x/2-2.5x growth fractal grouping and

3: a potential 4-phase 7/13 of 14/14/9- 10 day :: x/2x/2x/1.5x or 1.5xi growth and crash decay fractal grouping ending 29 or 30 September 2025.

A peak global equity composite valuation day on 5 Sept 2025 represents day105 from the 7 April low composed of two 53 day sequences 10/25/20 days and {6/12/13 and 7/14/6 of 14 days}

A Primer on Quantitative Time-based Self-Assembly Lammert Fractal Growth and Decay of Valuations of The Asset-Debt Macroeconomic System’s Composite Equities

Qualitatively …on the longest time-unit cycles (years) (e.g. 1807 36/90/90/54-57 years :: x/2.5x/2.5x/1.5-1.6x and 1982 13/32 of 33/32-33/20 years x/2.5x/2.5x/1.5-1.6x credit expands via governmental, corporate, and citizen debt; assets are produced and over-produced , overvalued and over-consumed; consumers reach maximum debt loads; the population of possible traders/invested are fully invested and composite equity asset valuations reach a singular fractal time-unit (minute, hour, day, week, month) peak valuation and thereafter undergo decay; recessions occur with weakening demand, interest rates fall; excess debt undergoes default and restructuring; individual and corporate bankruptcies occur; and composite equity (and commodity) asset valuations eventually reach a singular fractal time-unit nadir. The cycle thereafter repeats itself.

On smaller time-unit fractal cycles (quarters, months, weeks, days, hours, 15-minute/ 5 and 1-minute) : trader/investor population saturation of asset buying occurs ending in a transient peak valuation .. followed by trader/investor population saturation end selling resulting in a transient nadir valuation. These peaks and nadirs occur in one of the two quantitative fractal patterns as above.

Empirically composite equity asset valuation growth and decay cycles occur in 2 modes(laws) of mathematical self-organizing, self-assembly time-based fractal series:

a 4-phase fractal series: x/2-2.5x/2-2.5x/1.5-1.6x and
a 3-phase fractal series: x/2-2.5x/1.5-2.5x

In the 4-phase fractal series sequential elements are termed: the 1st, 2nd, 3rd, and 4th fractals and in the 3-phase fractal series: the 1st, 2nd, and 3rd fractals.

The 2nd fractal is characterized by terminal gapped nonlinear lower lows between the 2nd fractal’s terminal 2x and 2.5x time period. (These gapped nonlinear lower lows can be observed in weekly valuation units for the DJIA between 1929 and 1932, the terminal portion of the US 90 year 2nd fractal; within the last three day before the terminal 5 August 2024 139 day 2nd fractal low occurring in an interpolated ACWI/SPX 27 October 2023 55/139/135-136 day (SPX-ACWI respectively) :: x/2.5x/2.5x valuation maximum growth series ending 18/19 February 2025: and can be expected within the last months on a daily and weekly basis of the current 32 of 33 year 2nd fractal of the interpolated 1982 13/32 of 33 year 1st and 2nd fractal series. (The 27 October 2023 dominant fractal series appears to have a 119 first fractal base, whereas the 55/139/136 day 3 phase growth series was a secondary interpolated series).

With the exception of the 3rd fractal in the 4-phase series whose fractal grouping is determined by its terminal high or final lower high peak valuation, fractals (fractal groupings) are determined by the nadirs of the first and last time unit in the grouping with all intervening valuations above the connecting nadir trend-line.

The Macroeconomic System is composed of assets with changing daily valuations propelled higher or lower by an expanding or contracting GDP and ongoing debt obligations which represent both assets and liabilities. Money and debt creation are caused by the expansion of private, corporate, and government debt with central banks and private banks acting as the fortuitous intermediaries(and as a primary source with regard to the former element) accommodating ‘credit worthy’ loan applicants.

GDP grows as a result of money and debt creation. In recessions increased government borrowing (and central bank QE) acts as a counter-cyclical measure. Governments backed by nuclear-deliverable and capable military assets offer the greatest reassurance of loan repayment.

With an accommodating central bank and ongoing and future social contract promises to the 99% of private citizens, the US government will, per force, create more debt and money expansion than corporations(the billionaire class proxies) and the private sector combined.

The end of prominent of major economic cycles and recessions occur for the pleurality of private citizens when the valuation of assets are too high, the personal debt load is collectively too great, the liabilities of held and sought after assets, e.g., property taxes, new home and car loans, and the cost ongoing assets of daily living exceed the ability to pay or to further expand private debt. After lofty overvaluation of asset prices, these devaluations occur periodically and in a nonlinear fractal manner. The major self-ordering US fractal cycle is an 1807 36/90/90/54-57 year :: x/2.5x/2.5x/1.5-1.6x cycle with nadir commodity/equity prices in 1807, 1842-32, 1932, and expected in 2074-2077 with a 90 year 3rd fractal peak in November 2020 extended to higher highs by 7-15% annual US deficit to GDP spending in 2020 -2025.

After a 1932 10-11/21-22/21-22 :: x/2x/2x fractal growth cycle ending in 1982, the dominant interpolated fractal cycle from 1982 is 13/32 of 33/33/20 years ending in 2077.

A March 2020 9/23/14 month :: x/2.5x/1.5x fractal cycle was followed by a 27 Oct 2023 119/ 243 day cycle ending 7 April 2025. Nonlinearity in the 2nd 243 day 2nd fractal is seen between days 240 and 241 and days 241 and 242 with a final low on day 243 7 April 2025.

From the 7 April 2025 nadir an ACWI 105 day 53/53 day peak is expected to occur on 5 September 2025 composed of two sequential fractal growth series of 10/25/20 days and 10/20/25 days. A 5 Spet 2025 15-22 day crash series of 5/11/7 days will take the ACWI to a 11 day 2nd fractal low on 25 September 2020 with a lower low or higher low on day 7/8 of the 3rd fractal on 3-6 October 2025.

With the market (and the fed following) creating lower interest rates, a 119 day rebound is expected with a final crash of 15-21/22 days with a low in March/April of 2026.

In the asset-debt macroeconomic system there is an underlying self-ordering mathematical fractal pattern in composite asset valuation growth to composite asset peak valuation and thereafter decay to composite asset nadir valuation.

Governments and central banks can expand credit and the money supply but are constrained by inflation of assets affecting the pyramid base population of the system. Overvaluation of assets represents a limiting barrier to further consumption in the face of constrained base population job availability and the nonlinear limiting factor of ongoing financial stress of debt servicing and further debt expansion. The mathematical self-assembly deterministic fractal process in the tradeable markets represents the optimal growth and decay investment pathway in the global asset debt macroeconomic system – just as does the steady state of the self-assembly process of the growth and decay of galaxies and black holes occur in the infinite universe.

In the current system, 40 years of billionaire-led. corporation-led, both US political party led globalization, lowest-wage highest corporate profit led, and resulting international production, transport supply chains, and assembly … are being suddenly rent apart by US tariffs politically intended to bolster American internal product line manufacturing.

This populist political anomaly is coincident with the timing of the 1982 credit cycle began by Volcker’s 13-15.5% 3 month interest rates which has been fueled by gradually declining interest rates and extraordinary US peacetime percentage GDP-deficit spending.

A 1982- 2026 13/33 year x/2.5x fractal credit cycle is an interpolated part of a greater US 1807 36/90/90/54-57 year x/2.5x/2.5x/1.5-1.6x.

The 2020 15% US deficit to GDP COVID money expansion economy began with a nadir in the global composite ACWI equity index in March 2020. It is hard to imagine how a president whose name was at the bottom of the treasury checks sent to unemployed individuals resting at home and now making more than their usual salary, lost the Nov 2020 election.

The current fractal projection from the 27 Oct 2023 low is: 118-119 //243//119-120 and 124 = 243//147 days :: x/2x+/2x+/1.5x’.

An ACWI peak is predicted on 22 Aug 2025 followed by a 5/10-11/10-11 day 3 phase crash decay fractal series ending near 25-26 September 2025. From the April 2025 low a 10/25/20 day :: x/2.5x/2x growth fractal series is followed by a x/2x/2x’ growth series of 10/20/16 days with x’ = 8 days of the observable 20 day 2nd fractal and the 3rd fractal 2x’ or 16 days, reaching a peak on 22 Aug 2025.

A growth fractal of 119-122 days is expected with falling US fed funds rates and lowered US interest rates with the US 3 month rate reaching near zero. The following ACWI 119-122 high will not exceed the 22 Aug 2025 high. A nonlinear collapse will the result in a sequential 124 day or total 2x+ 243 day nadir. The 147 day 1.5 x’ 4th fractal double low nadir will occur near the 2026 midterms. Tariffs will be perceived as the post hoc ergo propter hoc etiology of an otherwise natural nadir valuation fractal progression.