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Teaching You to Trade Stocks 65: More on Fractals, Strokes, and Line Segments

2007/7/16 22:14:16

If you truly understood the previous lessons, this one wouldn't need to be written. This ID repeatedly emphasizes that the key to this ID's theory is a set of geometrized thinking. Therefore, you need to start from the most basic definitions, and in practical identification during real operations, this point is even more important. All complex situations, in fact, present absolutely no difficulty when approached from the most basic definitions.

For example, with fractals, the biggest headache is the so-called inclusion relationship between preceding and following K-lines. Beyond that, with a little simple geometric thinking, anyone can immediately derive the following corollaries from the definitions:

  1. Using [di, gi] to denote the interval formed by the lowest and highest points of the i-th K-line: when moving upward, a group of n sequential K-lines with inclusion relationships is equivalent to a K-line with the interval [max(di), max(gi)]. That is, these n K-lines are the same thing as a K-line whose lowest-to-highest interval is [max(di), max(gi)]. When moving downward, a group of n sequential K-lines with inclusion relationships is equivalent to a K-line with the interval [min(di), min(gi)].

  2. The associative law is the most fundamental principle in this ID's theory. In the inclusion relationship of K-lines, it must of course also be obeyed. The inclusion relationship does not satisfy the transitive property—meaning if K-lines 1 and 2 have an inclusion relationship, and K-lines 2 and 3 also have an inclusion relationship, this does NOT mean that K-lines 1 and 3 necessarily have an inclusion relationship. Therefore, in analyzing K-line inclusion relationships, the sequential principle must also be followed: first use the inclusion relationship between K-lines 1 and 2 to determine a new combined K-line, then compare this new K-line with K-line 3. If there's an inclusion relationship, continue combining into a new K-line using the inclusion law. If not, treat it as a normal K-line and proceed.

  3. Some people might ask: what counts as "upward"? What counts as "downward"? Actually, there's really nothing to explain—anyone who has looked at a chart knows what up and down mean. Of course, this ID's theory is a rigorous geometric theory, so "upward" and "downward" can be rigorously defined geometrically. It's just that for those unaccustomed to mathematical notation, their heads would explode again.

Suppose the n-th K-line satisfies the inclusion relationship with the (n+1)-th K-line, and the n-th K-line does NOT have an inclusion relationship with the (n-1)-th K-line. Then: if gn >= gn-1, we say K-lines n-1, n, n+1 are moving upward; if dn <= dn-1, we say K-lines n-1, n, n+1 are moving downward.

Someone might ask: what if gn < gn-1 and dn > dn-1? That IS an inclusion relationship, which contradicts the assumption that K-lines n and n-1 don't have an inclusion relationship. By the same logic, gn >= gn-1 and dn <= dn-1 cannot hold simultaneously.

The above definition of the inclusion relationship is already perfectly clear—it's just some of the most precise geometric definitions. As long as you follow the definitions, there is no chart from which you cannot precisely and uniformly find all fractals without error. Note: this kind of definition is unique, with a unified answer. Even if this ID made an error, it would still be an error—there is no ambiguity whatsoever. The unique answer can be clearly and unambiguously given at any moment, at any time. This answer is independent of time, independent of people—it is objective, unalterable. The only requirement is that the K-lines being analyzed have already been formed.

From this, the real-time nature (当下性) of this ID's theory also gets a very objective description. Why must it be real-time? Because if the K-lines for that moment haven't formed yet, the specific fractals can't be found, and correspondingly the strokes, line segments, lowest-level hubs, higher-level trend types, etc., can't be delineated, making analysis impossible. But once the real-time K-lines have formed, you can immediately find the corresponding fractal structures according to objective, unified standards. Real-time analysis and after-the-fact analysis are the same—the results are the same, with absolutely no difference. Therefore, real-time applicability is actually this ID's objectivity.

Someone might ask: what if on a 30-minute chart, K-lines are constantly zigzagging and you can't find any fractals? What's so strange about that? On a yearly chart, the chances of finding fractals are even smaller—it would be perfectly normal not to find one for over a decade. This is still the microscope magnification analogy. Once the microscope magnification is determined, strictly follow the definitions based on what you see. If nothing matches the definition, then there's nothing—it's that simple. If you want more precise analysis, use a smaller-level chart. For example, don't use the 30-minute chart; use the 1-minute chart, and naturally you can distinguish things more clearly. Let me emphasize again: what chart you use has absolutely no necessary relationship with what level you operate at. Using a 1-minute chart, you can still find yearly-level divergence and then conduct operations at the corresponding level. Looking at 1-minute charts does NOT mean you must do ultra-short-term trading. Confusing the microscope with what's under it means you've got way too much water in your brain.

From fractals to strokes: it must be one top followed by one bottom. So can two tops or two bottoms constitute a stroke? Here, there are two situations. First: between the two tops or bottoms, there are other tops and bottoms. In this case, it's just that several strokes have been mistakenly counted as one. Simply by continuing to apply the one-top-one-bottom principle, the problem naturally resolves. Second: between the two tops or bottoms, there are no other tops and bottoms. This means the reversal after the first top or bottom is too small in scale to constitute a worthy object of examination. In this case, the first top or bottom can be ignored—simply disregarded.

So, based on the above analysis, by applying appropriate handling for the second situation (similar to the handling of inclusion relationships in fractals), we can rigorously state: top first then bottom constitutes a downward stroke; bottom first then top constitutes an upward stroke. And all charts can be uniquely decomposed into a connected sequence of alternating upward and downward strokes. Obviously, except for fractals resembling the first top or bottom in the second situation described above, all other types of fractals uniquely belong to two adjacent up and down strokes and serve as the connection between these two strokes. Using the simplest analogy: the knee is the fractal, while the thigh and calf are the two connected strokes.

With strokes established, line segments become very simple. A line segment has at least three strokes. Line segments come in only two types: those starting with an upward stroke, and those starting with a downward stroke.

For line segments starting with an upward stroke, the fractals within form this sequence: d1g1d2g2d3g3…dngn (where di represents the i-th bottom, gi represents the i-th top). If we find i and j, with j >= i+2, such that dj <= gi, then the upward line segment is said to be destroyed by a stroke.

For line segments starting with a downward stroke, the fractals within form this sequence: g1d1g2d2…gndn (where di represents the i-th bottom, gi represents the i-th top). If we find i and j, with j >= i+2, such that gj >= di, then the downward line segment is said to be destroyed by a stroke.

Line segments have one most fundamental premise: the first three strokes of a line segment must have overlapping portions. This premise may not have been particularly emphasized before, so it must be specially emphasized here. A line segment has at least three strokes, but not every set of three consecutive strokes necessarily forms a line segment—these three strokes must have overlapping portions. From the above definition of line segment destruction by strokes, we can prove:

Chan's Line Segment Decomposition Theorem: A line segment is destroyed if and only if it is destroyed by at least one stroke among consecutive three strokes that have overlapping portions. And as long as the first three strokes with overlapping portions are formed, a line segment will necessarily be created. In other words, the necessary and sufficient condition for a line segment's destruction is that it is destroyed by another line segment.

All of the above are the most rigorous geometric definitions. If you truly want to get things clear, please draw many diagrams on your own based on the definitions, or compare them against real price charts and analyze thoroughly using the definitions. Note: all analytical answers depend only on the traded instrument and the chart level you're looking at. Given these objective observation targets and microscope magnification, any analysis is unique, objective, and independent of anyone's will.

If you haven't even figured out these most fundamental things—fractals, strokes, and line segments—and can't achieve rapid and correct real-time decomposition of any complex chart at any moment, then claiming to have mastered this ID's theory is pure bullshit.

Replies​

缠中说禅 2007/7/16 22:15:29
Not traveling tomorrow for now. Signing off first. See you tomorrow.