**INTRODUCTION**

** A Fractal Model for the Elliott Wave Theory** is theorized by reducing the Elliott wave pattern into distinct sine waves of constant proportion. This essay is a step by step derivation of this theory and it’s practical use in forecasting the next downwave.

**WHAT IS A FRACTAL WAVE?**

What is a fractal? In mathematics and physics it is a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale such that certain mathematical or physical properties of the structure.

A fractal wave is a wave that is in constant proportion to other waves. Fractal Elliott Waves are a series of waves in constant proportion to one another. In the case of this derivation, we will create fractal sine waves of constant proportion to one another.

**THE ELLIOTT WAVE FRACTAL PATTERN**

Ralph Nelson Elliott discovered a basic pattern in market charts. The idea is very simple, a move forward is followed by a move backward. The up move is called an impulse wave, the downwave is the correction to the upmove. What has been observed in market charts is that if the move is measured as the unit 1.0 the countermove is 0.618, or 1-phi, the golden ratio.

This means the markets are being governed at least partially by a natural function found throughout nature.

The market is a seesaw of buying and selling being pushed by human emotions of greed and fear. Apparently, this oscillating pattern is governed by golden ratio fractions.

This is very important in understanding how the markets are bigger than governments and central banks especially when we get to the present position – on the cusp of the greatest panic in stock history.

This essay is being released at this exact point in time so that you know that not only that market movements are easily predictable, they are following a distinct pattern, and this pattern is the Elliott Wave Fractal pattern which can be modeled as sine waves.

What is going on in the market is a battle between an army of buyers versus and army of sellers and this process which seems chaotic has a pattern. The market does not move in straight lines nor simple curves, it is a jagged mountain surface. How can the market be predictable if millions of speculators are using every theory and math algorithm to time the market?

The stock price pattern is a chaos pattern – it is not predictable by any normal linear method. Normal math and science can’t be used otherwise one man with a computer would end up with it all. The market is not linear – it is seemingly crazy chaotic movement being dictated by human emotions, and since we are part of nature, governed by natural law functions.

If we take the basic pattern as shown in the first chart and then subdivide the pattern to the next lower scale, so the basic impulse and corrective move is made into another 8 wave pattern, then add up the number of waves we will get Fibonacci numbers.

Since Fibonnaci sequence converges on the golden ratio, phi, we then can conclude that the Elliott Wave pattern is governed by the golden ratio.

We have now established that the Elliott Wave Pattern is related to Fibonacci and phi, this is a clue as to how we will size the sine waves in relation to one another.

**SUPERPOSITION PRINCIPLE OF WAVES**

Superposition Principle of Waves is a principle in nature. All waves follow the superposition principle, they can be added together, if two waves are interfered with each other they will form a deeper trough and taller peak. This works for water waves, sound waves, light waves, and stock market waves.

If we take two identical waves or two different size waves and interfere them, we get superposition patterns, but not the Elliott Wave Pattern.

If we plot 3 waves in an attempt to model the Elliott Wave using Fibonacci numbers we start getting closer to what we are after. Using the online program Graph Sketch makes quick work of narrowing down the sine waves we need to plot to mimic the Elliott pattern.

Our first plot of 3 waves is created by staring off with a simple sin wave, we write this mathematically as 1sin(x/1) then we make an educated guess of the next two, 3sin(x/3) and 5 sin (x/5) because we already know that Elliott is a fractal and the waves must be of dissimilar size but Fibonacci related.

If we try to using the golden ratio in the equations this is what we still are not getting what we want because the waves are to close in size to one another.

**DERIVING THE FRACTAL PATTERN IN ELLIOTT WAVES**

After a few tries it becomes readily apparent that in order to the Elliott pattern we need to size the waves in a 4:1 ratio. The next graphic shows two waves in a 4:1 ratio, this is very close but not exactly right.

Since phi cubed is 4.236 that becomes the initial guess since it is close to the integer 4. We are going to size each wave 4.236 times bigger. Make sense? We are simply using phi fractions to fit the waves fractally, meaning it always take exactly 4.236… waves to make the next larger wave.

(BTW: To do this we use a sine equation written like this sin(x/4.236^i)

Fractals are infinite series, they are infinite in both directions, bigger and smaller. So for our purposes we have to start somewhere in the series, so we will choose the most logical starting point of 1sin(1x).

If we take 3 sine waves that are fractals of one another, we get the basic Elliott pattern as shown in the chart below. The waves are related to one another, the all have the same amplitude and wavelength *ratio*.

For the Elliott Wave Pattern we need at least 3 waves, and they must be in fractal relation to one another to have the Elliott look, and this fractal must be governed by the Golden Ratio, phi which is derived by many different means and is always the irrational number 1.6180339…. but rounded off to 1.618.

The 3 fractal waves must have an amplitude and wavelength using the phi ratio in order to produce the Elliott Wave pattern as shown in this next diagram. The 3 waves are in constant proportion to one another, the formula is

**fractal wave i = amplitude ratio sine (wavelength ratio)**

**= phi squared sine (1/phi cubed) or phi**2sin(1/phi**3)**

**= 2.618 i sin(1/4.236 i)**

**where phi = 1.6180… , derived from formula:**

**wave i = phi^2 sin ((1/phi^3)x)**

Now if you want the sharp edged Elliott Pattern you must use 5 waves as shown in the next diagram. First we write the equations of 5 sequential waves then we add them together.

**USING THE FRACTAL MODEL TO FORECAST**

Applying this fractal form to real chart data lines can be drawn through the wave structure to determine where the movement will terminate.

Once a wave pattern starts to form the remainder of the wave can be projected because the Elliott Pattern is being governed by the superposition principle of the underlying waves, the second half of the wave will be similar to the first half.

Applying this to the current Global Dow Index chart we see wave c unfolding just like wave a. The two waves will be very similar, but we know that c waves can extend in length especially during a deflationary collapse. The floor is the limit.

So is this going to happen? The big bank stocks were slaughtered again on Thursday 11 Feb 2016 so it seems very likely in my estimation looking at the charts. Just like in 2008 when Lehman Brothers went under, the entire system cratered – this time the decline is being led by Deutsche Bank. Most banks never recovered from the 2008-9 collapse and now they are collapsing again – and probably going to the floor (zero value).

In the next chart I’ve chosen the Philadelphia Stock Exchange Bank index, since the banking stocks are leading the decline.

DEFINITION of ‘KBW Bank Index’(Nasdaq symbol BKX)

“An economic index consisting of the stocks of 24 banking companies. This index serves as a benchmark of the banking sector. This index trades on the Philadelphia Stock Exchange, where it was created.”

Now if you are wondering how I went from sine waves to fractal boxes, we are also dealing with a central bank that fuels the fractal expansion and collapse with huge amount of quantitative easing that will only lead to a deflation implosion. The inflated skewed market works itself out fractally somehow – but it is still following a pattern of fractal sine waves.

What this essay is demonstrating is that the next downwave is part of a larger fractal pattern. ** The ‘c’ wave will be very similar to the ‘a’ wave.** Bet on it. You can bet your last wooden nickel that we are headed into a deflationary collapse and that many of the world’s biggest banks will not exist by this time next year.

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