All the chart patterns can be analyzed as attractors. That is a modern explanation of the chart patterns that make sense. I will give a definition of an attractor using the Wikipedia. The problem is that the traders do not understand the science of chaos, and the scientists do not understand the trading. As for me I do not understand them both but I will try my best.
An attractor is a set towards which dynamical evolves over time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.
Please read this short article in the Wikipedia
What is important is that "A dynamical system is generally described by one or more differential or difference equations. The equations of a given dynamic system specify its behavior over any given short period of time. To determine the system's behavior for a longer period, it is necessary to integrate the equations, either through analytical means or through iteration, often with the aid of computers."
And The Fibonacci numbers are defined using the linear recurrence relation. And they can be helfull in the analysis.
According to my analysis the chart patterns can be analyzed as chaotic attractors.
Fixed points: In a trend environment, Higher highs, or lower lows, does it look familiar
Limit cycle: Oscillating price patterns: In fact all the technical analysis chart patterns are in this category: Triangles, Wedges, Harmonic patterns etc.
Limit tori: Complex patterns. It is arguable if they are a part of the technical analysis.
maybe the Elliott Wave Sequence may be close, but I am not sure.
Strange attractors: are not part of the technical analysis. Of course the Elliott wave theoreticians claim that they can predict a lot but their instruments are not adapted to the this task. Moreover those attractors are not necessary for trading, it is better to use lower order attractors for trading.
What is important that the price in the Forex markets are not in the void. They are in a phase space.
The phase space is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables.
For example the daily volatility can be analyzed in practice as a phase space of the price time series for the day. Of course as according to the hypothesis that the distribution is not normal but stable paretian with infinite variance this does not holds true, but is an useful practical approach (in fact we can detect in real time with the peaks of Hurst difference how and when the a powerful shift occurs).
Sensitivity to initial conditions
Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by other points with significantly different future trajectories. Thus, an arbitrarily small perturbation of the current trajectory may lead to significantly different future behavior.
In practice a powerful spike even it is corrected will influence the future price action and will set a new set of solutions. If a spike modifies the current phase space (current volatility) it is a signal that the system will be perturbed.
In practice we can analyze the beginning and the end of the market periods.
Let look what happened in the Euro.
For example when we had a powerful trend in September that state was set be the initial conditions. Unless they were not perturbed they set particular attractors that were working. In this case the trend was so simple that it was unbelievable how simple trading can be. But some people did not make money because they cannot believe that and countered the trend for a reversal.
After that Happened in October a break - out in the European session that was directed downwards. What did that mean? That means that the structure of the market has been perturbed. The market started to make another type of patterns: oscillating patterns.
In November this week a powerful shift and spike has occurred. This spike perturbed the structure of the chaotic attractors (cyclic type of patters with nice swings ). The subsequent break - out upwards was a part of the new structure and will participate in the new chaotic attractor that will emerge.
So we can analyze the price action as chaotic attractors in a particular phase space. What is important to know when a powerful shift in the structure occurs. We cannot know how, when, and why and that cannot be predicted. You can analyze that by your experience or you can use an algorithm (like this which is posted on this blog).
The most common errors that is made by the technicians is when a powerful shift in the structure occurs they try to use a pattern that was in force before.
That is a point when the complex neural net models fail, because they are used for a structure that is not anymore valid and a new structure is about to emerge.
This is just a theory guys and gals. But the calculation of the Hurst exponent showed a clear long term process in the markets. The lyapunov exponents calculations showed that even sometimes the processes are really not dissipative.
All the chart patterns can be analyzed as attractors. 
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