A Way Of Seeing Infinity │ Benoît Mandelbrot

 

 » Why is geometry often described as 'cold' and 'dry'? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line [...] Nature exhibits not simply a higher degree but an altogether different level of complexity [...] Bottomless wonders spring from simple rules, which are repeated without end. «

 

Benoît Mandelbrot,  Fractals: Form, Chance and Dimension, 1977.

 

Infinite Self-Similarity-Zoom.

The Gann 707 Fractal | Allen Reminick

W.D. Gann understood the nature of how markets expand, how they contract, the differences between time frames and the similarities between them. Nowadays we call this fractal geometry. Fractal geometry is extremely important to understand how markets develop and has been used by various market technicians. 

 

How do we use the 707 fractal to forecast the next few months in the S&P 500? In our most recent forecasts we've talked about a continued rally into the 20th or 25th of September 2023, and probably another high around October 3rd. After that we're looking for a decline that may be somewhat severe:

 

The number 707 shows up here on several different time frames. In the chart below the blue line is the 240 minute bar chart of the S&P 500 Futures shifted forwards by 707 units, and the red bars above are the actual current market: 

 

What is really interesting is that 707 weeks (707 weeks ≈ 12.9 years) and 707 months (≈ 58.916 years) are also repeating. This is where the concept of fractals comes in. Different time frames are having the same form or pattern. Look at this chart of the weekly S&P 500:

 

The major low of 2009 and the major low of October 2022 are 707 weeks apart.

 

The low in 2009 lines up to the week with the low in October 2022 - the major low that kicked off the whole bull market since 2009. This is lining up exactly with the low in October 2022, and the pattern in the decline between 2008 matches the decline in 2022. Even though the price action was much more severe back then, the form was the same. And we are talking about the form and now the rally that was taking place since October is also repeating very nicely 2009 into 2010 and 2011. 

 

 

So we saw two examples of 707, the first on the 240 minute bar chart and the second on the weekly chart. From this we take it one step further and look at 707 months (58.916 years). 707 months turns out to be two times the exact length of the cycle of Saturn. 25.457 years is the exact number of years of Saturn's revolution times two which equals 707 months to the day = 10,759 days.

Quoted from:
Allen Reminick (Sep 04, 2023) - Revealing the Gann 707 Fractal: Unlocking Market Secrets. (video)

 

See also:

Allen Reminick (2023) - Trade Forecast Mastery.

3 Bar Patterns - The Smallest Fractals of Market Structure | Larry Williams

»  Any time there is a daily low with higher lows on both sides of it, that low will be a short-term low. We know this because a study of market action will show that prices descended in the low day, then failed to make a new low, and thus turned up, marking that ultimate low as a short-term point. A short-term market high is just the opposite. Here we will see a high with lower highs on both sides of it. What this says is that prices rallied up to the zenith of that middle day, then began to move back down, and in the process formed a short-term high. For our purposes in identifying short-term swing points, we will simply ignore inside days and the possible short-term points they produce.  «

 

This is how Larry Williams defined market structure. This concept is universal and applies to all bars of all time frames.

 

• A Short-Term High (STH) is a bar with a high greater than or equal to the high of the bar to the left and greater than the bar high to the right. Neighboring bars should not be inside. If they are inside bars, the bars that follow them should be analyzed.
• A Medium-Term High (MTH) has Short-Term Highs to the left and and to the right that are below the high of this bar.
• A Long-Term High (LTH) has Medium-Term Highs to the left and and to the right that are below the high of this bar.
  

And for the lows it’s all vice versa: 

• Short-Term Low (STL) = bar with higher lows on both sides
• Intermediate-Term Low (ITL) = higher STL on both sides
• Long-Term Low (LTL) = higher ITL on both sides

In other words: 3 bar patterns are the smallest fractals and building blocks of market structure. Since price is always either in consolidation, in an uptrend or in a downtrend 3 successive price bars must form either a directional pattern (higher highs, higher lows or vice versa), a continuation pattern (inside bar) or a reversal pattern (outside bar, pin bar, head & shoulder, M&W patterns) (see also HERE):

 

  

Reference:

 Larry Williams (1990) - Long-Term Secrets to Short-Term Trading

Arthur A. Merrill (1980) - M & W Wave Patterns.