You might be surprised how comes nonlinear dynamics with a straight ruler. For simple mathematical explanations I send you over to Ian Stewart, an English mathematician.
What pertains to fractals in our case the problem was that the scaling numbers/fractal multipliers are at the same time fixed geometrical points of the unit fractal in a 2D space, and they also have a second coordinate which is not F=4.669 or 9.1299 etc. but something different.
Until recently I wasn't able to find out how that second coordinate works in a chaotic system.
I tried to see the logistic map which is a 1D map in a 2D space. The results are really astounding for their precision and order.
Certainly this makes the chaotic picture more detailed. How much more? Well, I can say that due to the second dimension it is twice more detailed and more than twice more complex if we take into account various relationships.
Forex is easy  this slogan should be banned from the public space forever.
Walking is easy, when you have learned how to do it.
Speaking is easy when you have acquired the ability to speak.
Actually nobody teaches walking or speaking.
Who teaches Forex?
Do you really think that you can learn Forex in less time than required for learning walking or speaking? 95% of the Forex population becomes extinct in less number of years than required to learn speaking.
100% of the population living in social groups can speak though.
Why 95% of those who try Forex go extinct?
Traders and analysts wrongly take patterns for models. There is no equation between patterns and mathematical models. There are actually no rules for patterns. But there are universal rules for models.
Markets can create an infinite number of different patterns. The Mandelbrot set and its Julia sets say it all. In practice any "good" pattern will always have its "strange" exception.
My new chaos findings implemented in forex trading
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The curry taste of the ROOT
Dear Paul&Paul,
Thanks again for the quick reply.
I want to take a small note hoping to make a small contribution.
When I look at the youtube videos of the logistic map.
The evolution of the map, that picture, brings the trading crowd to my mind.
(Well, after this point I should be lucky to pick the right English words
It is difficult even in my native language to tell what I mean... let me try)
Since I am not a scientist but a mere observer I might not get many things correctly
But since I have no scientific prejudgments I can observe more freely:
i) From the very BASIC mathematical equation to magical chaos:
As far as I know the mathematical equation that creates Mandelbrot Set is a very basic formula and what creates the magic is the "feedback loop" Process. This tells me that the ROOT equation... (I mean the basic formula just before the feedback loop begins) is the key for the future states of the chaos. As the ROOT changes the magical chaotic creations change. But the chaotic ARCHITECTURE does not change. The fingerprints of the ARCHITECT can be detected via universal tools like Feigenbaum Constant. As an ordinary man I see this as something like: No matter what sort of cement the architecture uses the height of the floors are always 3 meters...etc... but after the building is finished you observe a totally different art piece since the ROOT/cement is different...
ii) The ROOT in human actions is the golden ratio:
There is no such thing as "consciousness"... it is nonsense. When you pick a perfectly grey piece of paper and ask a sample of people "if it is more black, or more white" then you observe that people always tend to split into the golden ratio. Either 62% white, or 62% black. When there is an uncertainty people always aim to make decisions so that the overall population is split by the golden ratio. I am not a good writer but you get the idea: When we observe the chaotic human actions we always witness the golden ratio because "the ROOT equation carries golden ratio"... so the normal distribution is like a perfect sphere... it is beautifully linear but the real world is not...
iii) Combining this two ideas:
When I look at the logistic map... thinking that every dot is a decision taken by an investor. Every new dot is a new investor that joins the herd by opening a position while some others takes profit and fades away... While some investors join the herd as buyers, some join it as sellers... some takes profit and goes away...etc... But ideally for every 62% new comers who think the market is black, there should be 32% who says it is white... when a split point is reached (Feigenbaum tells us when ) then the whole herd is leveled... then they begin to dance around golden ratio all over again...
To understand what I mean one should look at the classical "normal/Gaussian distribution". And then look at the logistic maps evolution... it is a movie of the distribution maps... mounting on each other... as the trend grows the new comers and the profit takers increase... but the ROOT has the golden ratio sauce... so the cooked meal should always taste like it... It is like curry, if it is in the pan there is no escape from it :  )
FINALLY: I know this was a handicapped and rather confusing narration.
But what I want to say is the Ellioticians captured one part of the reality:
"The markets should taste like golden ratio..."
But this only gives a blur vision and chaos needs more elaboration...
Now I see your work which captures the mathematics of the ARCHITECT
I believe that these two should be combined in some way..
ROOT + ARCHITECTURE = > nonlinear control...
==> I had the feeling that the Feigenbaum constant defines when the herd is in a split point. That is why I asked you questions about the time axis. Think of sand piles mounting on each other and then suddenly a TIME comes and the big pile collapses...etc... it feels like TIMErelated...
==> I had the feeling that the golden ratio and its "feedback looped derivatives" should define the price axis (targets, stops...etc...)
After reading your findings I am not confident with those feelings anymore.
So I told you this story hoping to hit a correct note and contributing the music you play here :  )
Best wishes,
Sts
Thanks again for the quick reply.
I want to take a small note hoping to make a small contribution.
When I look at the youtube videos of the logistic map.
The evolution of the map, that picture, brings the trading crowd to my mind.
(Well, after this point I should be lucky to pick the right English words
It is difficult even in my native language to tell what I mean... let me try)
Since I am not a scientist but a mere observer I might not get many things correctly
But since I have no scientific prejudgments I can observe more freely:
i) From the very BASIC mathematical equation to magical chaos:
As far as I know the mathematical equation that creates Mandelbrot Set is a very basic formula and what creates the magic is the "feedback loop" Process. This tells me that the ROOT equation... (I mean the basic formula just before the feedback loop begins) is the key for the future states of the chaos. As the ROOT changes the magical chaotic creations change. But the chaotic ARCHITECTURE does not change. The fingerprints of the ARCHITECT can be detected via universal tools like Feigenbaum Constant. As an ordinary man I see this as something like: No matter what sort of cement the architecture uses the height of the floors are always 3 meters...etc... but after the building is finished you observe a totally different art piece since the ROOT/cement is different...
ii) The ROOT in human actions is the golden ratio:
There is no such thing as "consciousness"... it is nonsense. When you pick a perfectly grey piece of paper and ask a sample of people "if it is more black, or more white" then you observe that people always tend to split into the golden ratio. Either 62% white, or 62% black. When there is an uncertainty people always aim to make decisions so that the overall population is split by the golden ratio. I am not a good writer but you get the idea: When we observe the chaotic human actions we always witness the golden ratio because "the ROOT equation carries golden ratio"... so the normal distribution is like a perfect sphere... it is beautifully linear but the real world is not...
iii) Combining this two ideas:
When I look at the logistic map... thinking that every dot is a decision taken by an investor. Every new dot is a new investor that joins the herd by opening a position while some others takes profit and fades away... While some investors join the herd as buyers, some join it as sellers... some takes profit and goes away...etc... But ideally for every 62% new comers who think the market is black, there should be 32% who says it is white... when a split point is reached (Feigenbaum tells us when ) then the whole herd is leveled... then they begin to dance around golden ratio all over again...
To understand what I mean one should look at the classical "normal/Gaussian distribution". And then look at the logistic maps evolution... it is a movie of the distribution maps... mounting on each other... as the trend grows the new comers and the profit takers increase... but the ROOT has the golden ratio sauce... so the cooked meal should always taste like it... It is like curry, if it is in the pan there is no escape from it :  )
FINALLY: I know this was a handicapped and rather confusing narration.
But what I want to say is the Ellioticians captured one part of the reality:
"The markets should taste like golden ratio..."
But this only gives a blur vision and chaos needs more elaboration...
Now I see your work which captures the mathematics of the ARCHITECT
I believe that these two should be combined in some way..
ROOT + ARCHITECTURE = > nonlinear control...
==> I had the feeling that the Feigenbaum constant defines when the herd is in a split point. That is why I asked you questions about the time axis. Think of sand piles mounting on each other and then suddenly a TIME comes and the big pile collapses...etc... it feels like TIMErelated...
==> I had the feeling that the golden ratio and its "feedback looped derivatives" should define the price axis (targets, stops...etc...)
After reading your findings I am not confident with those feelings anymore.
So I told you this story hoping to hit a correct note and contributing the music you play here :  )
Best wishes,
Sts
Just a small addition/correction.. I have just said: "thinking of the sand piles... it feels like the Feigenbaum constant is TIME related"...
But I checked my notes and there I had written this note to myself: " the sand pile narrations resembles the volume data..." so the volume data (perhaps one should filter the effective volume here, or open interest...etc...) might be considered as the sand pile. And the time related analysis might be based on VOLUMEbased data...
I took this note because the number of participants does not matter in a market. What matters is the net buying and selling force (effective volume, delta open interest?) of each participant... So each dot on the logistic map can't be interpreted as an investor joined the herd... but "a new unit position taken" or "an old unit position that is closed"...
But I checked my notes and there I had written this note to myself: " the sand pile narrations resembles the volume data..." so the volume data (perhaps one should filter the effective volume here, or open interest...etc...) might be considered as the sand pile. And the time related analysis might be based on VOLUMEbased data...
I took this note because the number of participants does not matter in a market. What matters is the net buying and selling force (effective volume, delta open interest?) of each participant... So each dot on the logistic map can't be interpreted as an investor joined the herd... but "a new unit position taken" or "an old unit position that is closed"...
To sts
Thank you for your post, sts.
I will need some time to think over your observations. I haven't noticed ideas which I would instantly object to.
Before any longer considerations I undertake, one basic thought that comes to my mind is that it is more important what mathematicians/analysts/observers can say or write about things arising from formulas than how those formulas are formally written.
Very few mathematicians can describe in ordinary words what they have worked out. They are not used to it and most of them would treat such an exercise with disdain. They leave their formulas like ingredients in the kitchen together with some mysterious scientific recipe. But they would not cook. Oh no, not them.
Cooking is for lower strata. Since cooking is not their habit, they would not taste your food either. They make abstracts for breakfast, lunch and dinner but in order not to die they allow to be fed on real food  what a horrible nuisance it must be, what a discomfort to the strict mind.
On my own experiences I can say that some of them are simply extraordinarily lazy. But smart. Yes, smart and lazy.
Experimentalists work at the back room of mathematical kitchen and do the really hard job.
A mathematician would have never made a bicycle. No way. In revenge they are not considered for Nobel prize.
I will return after some time...
I will need some time to think over your observations. I haven't noticed ideas which I would instantly object to.
Before any longer considerations I undertake, one basic thought that comes to my mind is that it is more important what mathematicians/analysts/observers can say or write about things arising from formulas than how those formulas are formally written.
Very few mathematicians can describe in ordinary words what they have worked out. They are not used to it and most of them would treat such an exercise with disdain. They leave their formulas like ingredients in the kitchen together with some mysterious scientific recipe. But they would not cook. Oh no, not them.
Cooking is for lower strata. Since cooking is not their habit, they would not taste your food either. They make abstracts for breakfast, lunch and dinner but in order not to die they allow to be fed on real food  what a horrible nuisance it must be, what a discomfort to the strict mind.
On my own experiences I can say that some of them are simply extraordinarily lazy. But smart. Yes, smart and lazy.
Experimentalists work at the back room of mathematical kitchen and do the really hard job.
A mathematician would have never made a bicycle. No way. In revenge they are not considered for Nobel prize.
I will return after some time...
To sts
One problem is to understand the mechanism behind the market changes.
Another problem is to determine the rules.
A model is to show that some rules work. But a model may not explain the machanism 9of the whole).
There is a difference between rules and mechanisms. You may have rules and formulas and even a model and not being able to understand the mechanism.
It is perhaps too early, I/you need more time and experience or luck.
We are trying to understand the logic behind nonlinear behavior of a system forgetting that nonlinear dynamics is counterintuitive.
You will find this last part of the sentence almost in every book on chaos.
You mention the golden ratio. I wrote months ago that all major Fibonacci ratios are linked with the Feigenbaum constant. All of them. The proof is right in front of me. Simple and elegant.
You mention Time.
I do not want to create any more confusion about Time but I want to say that Time can create nonlinearity from very simple linear incremental changes of the market (monitored for prices, naturally). And it will look VERY nonlinear to the eye also.
You mentioned Time.
Time helped construct properly a model. Then years later I had to remove Time from it. In chaos time can be replaced with something which just sounds absurd. Replacable time... Polarized time. Multidimensional time.
Energy is mass. Mass is energy. There is no time here.
There is no time in fractal expansions.
I will be back some time later.
Another problem is to determine the rules.
A model is to show that some rules work. But a model may not explain the machanism 9of the whole).
There is a difference between rules and mechanisms. You may have rules and formulas and even a model and not being able to understand the mechanism.
It is perhaps too early, I/you need more time and experience or luck.
We are trying to understand the logic behind nonlinear behavior of a system forgetting that nonlinear dynamics is counterintuitive.
You will find this last part of the sentence almost in every book on chaos.
You mention the golden ratio. I wrote months ago that all major Fibonacci ratios are linked with the Feigenbaum constant. All of them. The proof is right in front of me. Simple and elegant.
You mention Time.
I do not want to create any more confusion about Time but I want to say that Time can create nonlinearity from very simple linear incremental changes of the market (monitored for prices, naturally). And it will look VERY nonlinear to the eye also.
You mentioned Time.
Time helped construct properly a model. Then years later I had to remove Time from it. In chaos time can be replaced with something which just sounds absurd. Replacable time... Polarized time. Multidimensional time.
Energy is mass. Mass is energy. There is no time here.
There is no time in fractal expansions.
I will be back some time later.
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Thank you for your support.
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I shall begin with something you already know
before I turn to something you do not know.
EURUSD comes first because it is popular and I agreed to open this chart. The story goes back to January 13.
What is the EURUSD doing above 1.3200? Is it not barely legal?
What was the mantra of the mass media until recently?
Do you consider this justice what the EURUSD has done?
Is it EURUSD and nothing else?
What or who changed the climate?
EURUSD closed at 1.3218 with the vector orientation up.
You have seen sentences many of this kind throughout this thread.
Yet behind it hides something new which is more a mechanism than a rule.
It required an investigation and some good luck as well. You never know what
you are going to find out.
There is always a thought what if...
EURUSD comes first because it is popular and I agreed to open this chart. The story goes back to January 13.
What is the EURUSD doing above 1.3200? Is it not barely legal?
What was the mantra of the mass media until recently?
Do you consider this justice what the EURUSD has done?
Is it EURUSD and nothing else?
What or who changed the climate?
EURUSD closed at 1.3218 with the vector orientation up.
You have seen sentences many of this kind throughout this thread.
Yet behind it hides something new which is more a mechanism than a rule.
It required an investigation and some good luck as well. You never know what
you are going to find out.
There is always a thought what if...
 Attachments

 eurusd28.01.gif (37.44 KiB) Viewed 263 times
Fractal burst
Take a zigzag.
After Wikipedia
http://en.wikipedia.org/wiki/Zigzag
A zigzag is a pattern made up of small corners at variable angles, though constant within the zigzag, tracing a path between two parallel lines; it can be described as both jagged and fairly regular. Traditionally a "zig" points in the left direction (/) and a "zag" points right (\). From the point of view of symmetry, a regular zigzag can be generated from a simple motif like a line segment by repeated application of a glide reflection.
Consider the lines of a zigzag are not parallel but skew.
Consider that these lines either converge or diverge from one another.
Consider that these zigs and zags can be obtained mathematically.
After Wikipedia
http://en.wikipedia.org/wiki/Zigzag
A zigzag is a pattern made up of small corners at variable angles, though constant within the zigzag, tracing a path between two parallel lines; it can be described as both jagged and fairly regular. Traditionally a "zig" points in the left direction (/) and a "zag" points right (\). From the point of view of symmetry, a regular zigzag can be generated from a simple motif like a line segment by repeated application of a glide reflection.
Consider the lines of a zigzag are not parallel but skew.
Consider that these lines either converge or diverge from one another.
Consider that these zigs and zags can be obtained mathematically.
Fractal burst
If a generator can be found for a zigzag then we would have a new type of
fractal behavior.
If a real zigzag is found which fits exactly the model, then we should expect something rare and extraordinary.
I have found it.
I called it the fractal burst.
fractal behavior.
If a real zigzag is found which fits exactly the model, then we should expect something rare and extraordinary.
I have found it.
I called it the fractal burst.
Fractal burst
In order to detect it one needs triggers' observations for a longer period of time. There will be a trigger which interests us most for the reason that only this trigger and not some others generates a zigzag very precisely like the model.
Time between the points of the zigzag is unimportant and it will never be of the same length. This condition implies that the zigzag will look nonlinear to the eye on the chart, whereas in the model it is strictly linear.
Then noticing that too many crucial things begin at some points of one chart and that the same or very similar behavior is found on other markets exactly at the same points of time, we can claim to have found a mysterious mechanism
in the functioning of chaotic systems.
Time between the points of the zigzag is unimportant and it will never be of the same length. This condition implies that the zigzag will look nonlinear to the eye on the chart, whereas in the model it is strictly linear.
Then noticing that too many crucial things begin at some points of one chart and that the same or very similar behavior is found on other markets exactly at the same points of time, we can claim to have found a mysterious mechanism
in the functioning of chaotic systems.
Fractal burst
The fractal burst requires additional information about the system and this information is already encoded in the model.
Why the market may need it?
Triggers and their fractal expansions do not contain, it seems, any information about their hierarchy. Semafors3 can help discern some sort of hierarchy only to some an extent. We know that semafors overpaint.
A trigger responsible for the fractal burst will act like a signalman to major market players. Over a couple of days you receive confirmation point after point (of the zigzag) that should alert every conscious and active trader.
Yes, you are right, we are heading this way. Divergent lines of the zigzag not only ambush many traders but the diverging tops and bottoms can really
leave many in disarray.
A divergent zigzag weakens the public so much so that eventually both directions become questionable to it. The public hesitates the most when the final stage of the whole plan unveils right in front of their eyes.
The market drives away and takes the prices into a new territory.
Why the market may need it?
Triggers and their fractal expansions do not contain, it seems, any information about their hierarchy. Semafors3 can help discern some sort of hierarchy only to some an extent. We know that semafors overpaint.
A trigger responsible for the fractal burst will act like a signalman to major market players. Over a couple of days you receive confirmation point after point (of the zigzag) that should alert every conscious and active trader.
Yes, you are right, we are heading this way. Divergent lines of the zigzag not only ambush many traders but the diverging tops and bottoms can really
leave many in disarray.
A divergent zigzag weakens the public so much so that eventually both directions become questionable to it. The public hesitates the most when the final stage of the whole plan unveils right in front of their eyes.
The market drives away and takes the prices into a new territory.
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Thank you for your support.
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