1. Self-Similarity Behaviour of Financial Fractals 

Self similarity is a concept use to describe prevailing rhythms from one cycle to another – this is the same thing as saying that smaller cycles exhibit the same or exact characteristics, or internal structure or behaviour as their parent cycles, or vice-visa.  

The concept is very popular among Geographers and Geologists in studying drainage networks and other treelike patterns from maps using a method called “stream ordering’ or the ‘law of stream numbers’ which allows objective description of a drainage basin based on the knowledge of the characteristics of smaller order streams in a network.

Figure 1 : Self-Similarity Behaviour in Drainage Network

In Figure 1 above, the concept holds that the functioning of the main drainage depends on the smaller networks and by understanding the processes taking place in the smaller drainage networks one can determine the nature and processes of the larger networks. In other words, the processes that lead to the formation of the smaller networks, e.g, stream order 1, tends to repeat themselves in stream order 2, 3 and 4 in that sequential order. Of cause, in a sense streams of order 1 are fractals and have smaller drainage cycle before they are discharged into stream of order 2, and so.

 Because of its almost universal applicability, this process is also found to exist in virtually all chaotic systems or natural branching systems including trees, blood veins, human brains, road transport networks, electricity and telecommunication systems, electromagnetic waves, etc, and in just about any system in the universe that is built upon smaller cycles or waves.

What this concept is saying is that, the internal structure of chaos exhibit the same process irrespective of the level or time frame that one is viewing the chaos system and each time frame depends on the processes taking place in the smaller time frames. In the case of river systems, we can use the volume of discharge expressed as (bifurcation ratio or some sort of Fractal Dimension Index) of smaller order streams to predict the volume of discharge of higher order streams, and be able to use this information to plan for development projects such as building of dams, agriculture, urban development at  down streams or locations of higher order streams.

However, such application of fractal self similarity is not of any great practical significance and indeed its theoretical justification does not seems very revealing or appealing to live financial trading. This is more so, since most natural systems are one directional. The concept is meaningless unless it is interpreted as future process. In other words, if a process e.g. bullish or bearish sentiment occurred in lower cycle or time frame what degree of confidence do we have to say or know that the same process will also repeat itself all through the other time frames to the highest time frame.  The problem is more compounded because processes taking place in any fractal phase space or cycle are two directional having buy or sell sentiments as depicted in Figure 2 below.

Figure 2 : Schematic Representation of Self-Similarity of Financial Fractals

Nevertheless, when correctly applied, what the concept is saying is that, if in a bullish trend, the opposing sell fractal in step 1 (see Figure 2 above) is conquered; the same behaviour will repeat itself by conquering the opposing fractal in step 2, and on to step 3 and to the end of step 4 or the end of day or the end of the general chaos pattern or market cycle, assuming each step above represent fractal phase space or market cycle. 

Such self similarity behaviour then provide us with clues on what

1.    Time frame to fixed stop loss or locked profit once one is in a favourable trend;

2.    Time frame or market cycle one should expect to take profit in order to avoid market turbulence or profit ruins arising from market corrections or end of chaos or market cycle.

3.    Time frame to implement hedging of trades.

4.    Time frame to scalp trades 

An understanding of the application of fractal self-similarity in financial markets gives traders significant edges over their brokers as they will be able to avoid stop loss hunting by brokers, and be able to know when to lock in profit, take profit, hedge and scalp trades all at the same time with one instrument of trade. To read more on how to corrrectly apply the concept of fractal self-similarity in financial markets click here.

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Related links:

Fallacies of Wave Theories and Fibonacci Numbers

How God Brought Order out of Financial Chaos

Self-Similarity Behaviour of Financial Fractals 

Fractal Sensitive Dependence to Initial Conditions and Butterfly Effects