Discussion of article "Combinatorics and probability theory for trading (Part II): Universal fractal"

 

New article Combinatorics and probability theory for trading (Part II): Universal fractal has been published:

In this article, we will continue to study fractals and will pay special attention to summarizing all the material. To do this, I will try to bring all earlier developments into a compact form which would be convenient and understandable for practical application in trading.

Let's use the construction rules that we derived in the previous article, and supplement them to understand how a fractal is constructed. In addition, I have found a small mistake in my formulas, due to which downward or upward asymmetrization of borders was impossible. The derived formulas turned out to be correct, and thus they work for absolutely any fractal. Actually, this is a function for implementing absolutely any fractal. All possible fractals are a special case of a general fractal. If we take the three fractal types defined above, the conditions of the general fractal for the implementation of these three special cases will be as follows:

  1. m = n & [ m > s & n > s ]
  2. ( m > n || n > m )  & [ m > s & n > s ]
  3. ( m > S && n <= S ) || ( n > S && m <= S )

Schematically, these three types of fractals look like this:

3 fractals

Ideally, "S" should tend to infinity. The following variables were not described in my previous article. I will provide the relevant descriptions here to get a complete picture of how to use the general formula to get the special cases. A fractal is a function that works on the principle of a chain reaction, as in an atomic bomb. If the set chain reaction is too deep, the computer may fail to cope with such massive calculations. If the case is not particularly critical, it will simply count for a very long time — minutes, hours or even days.

Author: Evgeniy Ilin

 
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