Lammert Nonstochastic Saturation Macroeconomics: Lammert Second Fractals: Current Model: Significant SPX Nadir on 14 Oct and Lower Nadir on 20-21 Nov 2025

Everything in the known universe self-assembles ... on the Planck level and macro level, including time- based quark interactions and the more complex molecules of the fused zygote and developing embryo. Combined entities also under decay and dissolution with occasional nonlinear collapse such as the gravitational collapse of a star. This is a natural deterministic process that can be observed and studied. Valuations of assets both debt and nondebt, likewise grow and decay in a time based fractal manner, based on buyer and seller saturation and the work-debt-credit-wage conditions of the underlying economy. The Nonlinear Second Fractal (cycle): From the main web page in the 2005 Economic Fractalist: The ideal growth fractal time sequence is X, 2.5X, 2X and 1.5-1.6X. The first two cycles include a saturation transitional point and decay process in the terminal portion of the cycles. A sudden nonlinear drop in the last 0.5x time period of the 2.5X is the hallmark of a second cycle and characterizes this most recognizable cycle. After the nonlinear gap drop, the third cycle begins. This means that the second cycle can last anywhere in length from 2x to 2.5x. Since 2005, the 1807 36/90/90/54-57 year :: x/2.5/2.5x/1.5-1.6x pattern recognized 4-phase Fractal Series has added 0.5x to the original 2x time length 3rd cycle(fractal). After a 1932 10-11/20-21/-21 year :: x/2x/2x 3 phase series concluded in 1982, an interpolated 13/32 of 33/33/18-20 year 4-phase cycle :: x/2.5x/2.5x/1.5-1.6x can be identified and inferred to complete the larger 1807 4-phase fractal cycle ending in 2074-2076. Composite equity valuation growth of the 1982 to 2026 13/33 year 1st and 2nd fractal series has been propelled in the 2nd fractal terminal 2x-2.5x portion, i.e. years 26-33, by unprecedented % deficit to GDP US spending and mass migration that has created growth the work-debt-credit-wage conditions of the underlying economy. After the Covid March 2020 low, US Equity composites followed a 8/17/11 month fractal : x/2-2.5x/1.5x' 3-phase fractal series. Since the December 2022 8/17/11 month low ending fractal series, equity growth has self assembled in a series of 1st and 2nd fractal groupings: 15/30 weeks :: x/2x ending on 27 October 2023 and 26/52 weeks :: x/2x ending 7 April 2024 . The 2nd fractal nadir low ending valuation has come shortly after a 2x time length and within 2-4% of the 1st fractal base time length x. For example, the 27 Oct 2023 1st and 2nd fractal series were 120/243 days in length. Nonlinearity occurred after 2x or day 240 with nonlinear lower low gaps between day 240 and 241 and day 241 and 242.

The 1st and 2nd fractal series starting 7 April appears to be a 53/107-108 day :: x/2x fractal series ending 20-21 Nov 2024 with an interim low on 14 October. 4 identifiable subfractal series make up the 107-108 day second fractal. The lengths of the 4 subfractal series are shown in diagram. A final 27-28/55-57 day:: x/2x 1st and 2nd fractal series could place a final SPX low on 24-25 March 2026.

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 on 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 now appears to have a 120 day first fractal base with a 243 day 2nd fractal ending 7 April 2025, whereas the 55/139/136 day 3 phase growth series was a secondary interpolated fractal 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. SPX from 1982 Quarterly: