A Primer on Fractal series

The beginning and ending boundaries of time based fractal series are defined by uptrend and downtrend lines with positive and negative slopes, respectively, that are formed by connecting the two low points at the beginning and the end of the fractal series.

In a bar chart, unit bars can be minutes, hours, days, weeks, months, and years. It is the hypothesis of this website that the asset debt macroeconomic system is deterministic and the growth and decay of the ongoing unit time valuations of its asset classes automatically self assembly in the most efficient manner with self similar fractal patterns of the unit time based bars.

There are only two elegantly simple laws of self-assembly time-based fractal asset-debt valuation growth and decay macroeconomics:

While money and credit growth (and contraction)by central banks and government spending is periodically irregular, equity and commodity composite valuations grow and decay by only two distinct time-based fractal patterns(mathematical laws):

a three phase pattern: composed of three subfractals:1/2/ and 3 :: x/2-2.5x/1.5-2.5x – where x is the base first fractal time length in days, weeks, months, and years.

and a four phase pattern: composed of 4 subfractals: 1/2/3/ and 4 :: x/2-2.5x/2-2.5x/1.5-1.6x, where x is the base first fractal time length in days, weeks, months, and years. In a four phase fractal series the sum of the length of subfractal 1 and 2 may be exceeded by the sum of the length of subfractal 3 and 4 by 0.1x.

The time length of subfractal 2 (2-2.5x) of the 3 and 4 phase fractal series often determines the ideal time length of subfractal 1 : (x’) upon which the lengths of sub-fractals 3 and 4 are based: e.g., the 4 phase fractal pattern’s time lengths become x/(2-2.5x divided by 2.5 = x’)/2-2.5x’/1.5-1.6x’.

The US Hegemony macroeconomic system is following an 1807 4 phase fractal series of 36/90/90/54 years with a 90 year Subfractal 3 high on 8 November 2021 for for the Wilshire and Bitcoin/USD. Smaller unit time based fractal series make up the 36,90,90 and upcoming 54 years.

Previously, this post had defined a 13 March 18/45/36 day growth fractal series with an expected Subfractal 4 decline of 27 days. This model violated the uptrend line definition defining fractal units.

The current model is based on a 13 March 4 phase 38/93-95/76-95/54-58 day fractal series.

There are only two elegantly simple laws of time-based  fractal asset-debt macroeconomics: 

While money and credit growth (and contraction)by central banks and government spending is periodically irregular, equity and commodity composite valuations grow and decay by only two distinct  time-based fractal patterns(mathematical laws): a three phase pattern: composed of three subfractals:1/2/ and 3  ::  x/2-2.5x/1.5-2.5x – where x is the base first fractal time length in days, weeks, months, and years.

and a four phase pattern: composed of 4 subfractals: 1/2/3/ and 4  :: x/2-2.5x/2-2.5x/1.5-1.6x, where x is the base first fractal time length in days, weeks, months, and years.   

The time length of subfractal 2 (2-2.5x) of the 3 and 4 phase fractal series often determines the ideal time length of subfractal 1 : (x’) upon which the lengths of sub-fractals 3 and 4 are based: e.g., the 4 phase  fractal pattern’s time lengths become x/(2-2.5x divided by 2.5 = x’)/2-2.5x’/1.5-1.6x’.

Using the Wilshire 5000, 31 July 2020, the Wilshire’s secondary high to its 8 November 2021 high was day 36 of subfractal three of a 18/44/36 day blow-off growth fractal series starting 13 March 2023.

For an ideal 4 phase fractal series of x/2.5x/2x/1.5x, the length
of subfractal four would equal 27 days, 1.5 times subfractal one, 18 days.

Decay starts in finale of growth valuation saturation.
A decay fractal series starting 27 July 2023 , which includes the peak on day 36, 31 July 2023 of 5/13/13 days would complete a three phase fractal and complete a subfractal four 27 day peak to nadir valuation process.

Subfractal two of this decay series lasted 13 days and is composed of a 3/6/6 day fractal.

Subfractal three of the 5/13/13 day series started on 18 August and completed day 3 of 13 days. Day 3 may have completed subfractal three’s maximal saturation growth. Using 30 minute fractals, two fractal series are observed: an 18 August 4 phase fractal series of 3/6/7/5 units followed by a 5/11/7 of 8 unit x/2-2.5 / 1.5-1.6x (final peak growth.) Like subfractal two, a 3/6/6 day three phase decay series for subfractal three seems likely.

Notice the tangent slope lines touching the lowest valuations of day 1 and day 5 of the 5 day subfractal one vice day 1 and day 13 of the 13 day subfractal two. The rate of deterioration is increasing.

If this model is correct, the slope of the 13 day subfractal 3 will be significantly and nonlinearly down.

The 27 July 2023 three phase 5/13/13 day decay fractal series is proportionally similar to the August-November 1929 11/26/28 day :: 3/7/7 week three phase incipient decay fractal series.

There are only two elegantly simple laws of time-based  fractal asset-debt macroeconomics: 

While money and credit growth (and contraction)by central banks and government spending is periodically irregular, equity and commodity composite valuations grow and decay by only two distinct  time-based fractal patterns(mathematical laws): a three phase pattern: composed of three subfractals:1/2/ and 3  ::  x/2-2.5x/1.5-2.5x – where x is the base first fractal time length in days, weeks, months, and years.

and a four phase pattern: composed of 4 subfractals: 1/2/3/ and 4  :: x/2-2.5x/2-2.5x/1.5-1.6x, where x is the base first fractal time length in days, weeks, months, and years.  

The time length of subfractal 2 (2-2.5x) of the 3 and 4 phase fractal series often determines the ideal time length of subfractal 1 : (x’) upon which the lengths of sub-fractals 3 and 4 are based: e.g., the 4 phase  fractal pattern’s time lengths become x/(2-2.5x divided by 2.5 = x’)/2-2.5x’/1.5-1.6x’.

China’s fastest growing economy has been based on the world’s largest % GDP corporate debt and money expansion. The Chinese population has placed its saving in domestic real estate whose valuation had steadily and reliably grown for twenty years but crested about 2-3 years ago and is now diminishing in valuation. Building corporations such as Country Garden and Evergrande have lost 90-99 % of their valuations over the last two and a half years. Chinese wages are now decidedly less competitive than other capable emerging countries with shorter and politically less complex supply chain issues. Wages in the Chinese financial sector have been cut by 25-33% resulting in real estate mortgage defaults.

The Bank of Shanghai is the canary in the Chinese asset debt macroeconomic coal mine and is following a 12/2017 three phase 9/20/18 – 23 month x/2-2.5x/2-2.5x fractal series and a sequential three phase fractal series : (5)/13/11 of12 months :: x/2.5x/2.5x and (2)/5/4-5/(3) months with an anticipated nadir low in 10 to 11 months

A daily three phase fractal pattern for the Bank of Shanghai started on 6/27/2023 and follows a 9/22/4 of 21-22 day pattern :: x/2.5x/2.5x ending with an expected nonlinear low in 17-18 trading days.

Starting 13 March 2023 the US Wilshire had a 4 phase blow-off fractal series of 18/45/36/10 of 27 days with a peak valuation on 31 July the 36 day 2x of subfractal 3. A nonlinear low is expected in 17 trading days. The decay fractal series starts on 7/ 27/2023 following a 3 phase 5/8 0f 13/13 day :: x/2.5x/2.5x fractal pattern or from the 31 July 2023 peak valuation: 5/6 of 12/12 days :: x/2.5x/2.5x.

US equity valuation decay from its peak in September 1929 to its nadir in June 1932 occurred over 32 months and started in August 1929. Two sequential three phase x/2x/2x fractal decay series of 15/33/30 weeks followed by 16/34/32 weeks are observable and completed the mathematical decay in June 1932 as debt was liquidated and restructured and assets sold at lower and lower prices.

By the law of a four phase fractal, Japan’s March 2020 Nikkei is expected to reach a low in 10 -11 months.