What does fractality mean?
A fractal is a shape whose parts look like smaller copies of the whole. A fern is the usual example. Each frond looks like a small fern, and each leaflet on that frond looks like a smaller one again. A coastline seen from a plane and from the beach shows the same kind of jagged outline at both scales. The mathematician Benoit Mandelbrot coined the word in 1975.
Elliott Wave Theory makes a comparable claim about markets. In the 1930s Ralph Nelson Elliott described how prices rise and fall in a small set of recurring wave patterns, and how each of those waves is made of smaller waves of the same kinds. So a single wave can contain smaller waves and at the same time belong to a larger wave. Elliott himself never used the word fractal. Later writers, Robert Prechter among them, made that connection.
The basic unit is a five-wave move in the direction of the trend, followed by a three-wave move against it. Because every wave subdivides, the number of waves grows in a fixed way as you go down one level at a time.
An impulse subdivides 5-3-5-3-5, so 5+3+5+3+5 = 21 waves one degree lower. Counts as given by Frost and Prechter [1].
Similar, not identical
Market waves are not exact geometric fractals like the computer-drawn ones you may have seen. When Elliott analysts speak of self-similarity, they mean similarity of form. A five-wave advance at one level has the same sequence of up and down legs as a five-wave advance at another level. Lengths, durations, slopes and the type of correction differ from case to case, and no pattern repeats exactly.
Mandelbrot studied markets too, but his work describes how the size of price changes scales statistically across time spans [4][5]. That is a much looser kind of self-similarity than a wave count. His findings do not test or confirm Elliott Wave counts, and they should not be quoted as if they did.
How do wave degrees fit together?
A wave degree is the rank of a wave in this hierarchy. Each wave subdivides into waves of the next lower degree and is itself one part of a wave of the next higher degree. Frost and Prechter name nine degrees [1]. This guide uses four neighbouring ones.
Degrees, notation and typical time spans
Elliott Wave is a theory about price structure, not a calendar. A wave is complete when its pattern is complete, not on a schedule. Practitioners still link each degree to a rough, typical time span, which helps when you check which degree you are probably looking at.
DEGREES, NOTATION AND TYPICAL TIMEFRAMES (FROST & PRECHTER). HIGHLIGHTED ROWS ARE USED IN THIS GUIDE.
| Degree | 5s, with the trend | 3s, against the trend | Typical timeframe |
|---|---|---|---|
| Grand Supercycle | IIIIIIIVV | abc | Millennial, secular |
| Supercycle | (I) (II) (III) (IV) (V) | (a) (b) (c) | Secular, annual |
| Cycle | I II III IV V | a b c | Annual, quarterly, monthly |
| Primary in this guide | 12345 | ABC | Quarterly, monthly, weekly, daily |
| Intermediate in this guide | (1) (2) (3) (4) (5) | (A) (B) (C) | Monthly, weekly, daily |
| Minor in this guide | 1 2 3 4 5 | A B C | Monthly, weekly, daily, 240 min |
| Minute in this guide | iiiiiiivv | abc | Weekly, daily, 480–60 min |
| Minuette | (i) (ii) (iii) (iv) (v) | (a) (b) (c) | Daily, 480–60 min |
| Subminuette | i ii iii iv v | a b c | 480–60 min and less |
These are typical viewing timeframes, not requirements. A Minor-degree wave can run longer than usual, and a Cycle-degree wave can run shorter. The structure (5-3-5-3-5, or 5-3-5, 3-3-5 and 3-3-3-3-3) is what defines a wave, never the clock or the notation style.
Elliott Wave and Fibonacci give us price levels, such as targets, retracement zones and structure. They don't reliably give us time. Treat any duration in this table as a loose reference for orienting yourself on a chart, never as a forecast of when a wave will finish.
Motive and corrective waves
Elliott described two kinds of waves. A motive wave moves in the same direction as the trend of the next higher degree. A corrective wave moves against it. Whether a wave counts as motive or corrective is always judged one degree up. The table lists the standard patterns and how they subdivide.
| Pattern | Mode | Subdivides | Where it appears |
|---|---|---|---|
| Impulse | Motive | 5-3-5-3-5 | The most common motive wave. Wave 3 of an impulse is always an impulse itself. |
| Leading diagonal | Motive | 5-3-5-3-5 or 3-3-3-3-3 | Wave 1 of an impulse or wave A of a zigzag. Wedge shape, wave 4 overlaps wave 1. |
| Ending diagonal | Motive | 3-3-3-3-3 | Wave 5 of an impulse or wave C of a correction. Wedge shape, wave 4 overlaps wave 1. |
| Zigzag | Corrective | 5-3-5 (A-B-C) | A sharp correction. Waves A and C each unfold in five waves. |
| Flat | Corrective | 3-3-5 (A-B-C) | A sideways correction. Wave B retraces nearly all of wave A. |
| Triangle | Corrective | 3-3-3-3-3 (A-B-C-D-E) | Sideways, usually narrowing. Appears just before the final wave of the larger pattern, for example as wave 4 or wave B. |
| Combination | Corrective | W-X-Y (-X-Z) | Two or three simple corrections joined by connecting waves labelled X. |
A five-wave move can sit inside a correction
Look at the zigzag row again. Its waves A and C each unfold in five waves, which makes them motive in structure. On its own, wave A of a zigzag can look exactly like wave 1 of a new trend. What makes it part of a correction is its role one degree up. It belongs to a three-wave A-B-C move that runs against the larger trend.
The diagram shows the same five-wave rise in two settings. The bold part is identical in both panels. Only the grey context differs.
Setting A · wave (1) of an impulseAfter a three-wave decline, the five-wave rise starts a new advance. A pullback (2) follows and then a longer rise (3) to new highs.
Setting B · wave (A) of a zigzagAfter a five-wave decline, the same rise is only wave (A) of a counter-trend zigzag. After (B) and (C), the larger decline resumes and breaks below the start.
At the moment the five-wave rise ends, both panels look the same. The difference shows only later, in how the following waves unfold, and in the structure that came before. In Setting B the decline before the rise was itself five waves, which points to a downtrend that may not be over. That is a clue, not proof.
Wave degree and chart timeframe are different things
A chart timeframe is the time interval of each bar or candle, such as weekly, daily or hourly. It sets the magnification of your chart. A wave degree is a position in the wave hierarchy. Degree is relative. It follows from where a wave sits compared with the waves it contains and the wave it belongs to. The table above lists the rough durations Frost and Prechter attach to each degree [1]. Treat them as orientation rather than as a definition.
| Chart timeframe | Wave degree | |
|---|---|---|
| What it is | The bar interval you choose to display | The rank of a wave in the structure |
| Who sets it | You, in your charting software | The price structure itself, as interpreted by the analyst |
| Changes when you switch charts? | Yes | No. The same wave keeps its degree on every timeframe |
| Example on this page | Timeframe, example only · daily | Degree · Intermediate (1)–(5) |
The two are related in practice. A lower timeframe shows the subwaves of a wave more clearly, so analysts often use lower timeframes to study lower degrees. But one timeframe can show several degrees at once, and the same degree can last days in one market and months in another. On this page, degree labels always appear as solid dark tags and timeframe labels as dashed grey tags.
One consistent chart example
The following four charts show one hypothetical rising market at four levels of magnification. View 1 shows the Primary-degree count. View 2 enlarges one wave from View 1. View 3 enlarges one wave from View 2. View 4 enlarges one subwave from View 3. All prices are invented, so you can check every rule against actual numbers, and every pivot price is identical across the four views.
How the labels work
Each degree gets its own label style and keeps it in every view. Higher-degree labels are printed larger. Where a pivot ends waves of two degrees at once, the higher-degree label sits further from the line and is printed in grey, for example “end of (2)”. The thin grey path carries its own small labels. Its last wave ends at the same pivot as a bold label, so that one is not repeated. Colour shows the role of a wave relative to its parent, and line style shows what kind of information you are looking at.
In the widely used Frost and Prechter table, circled numbers mark Primary, (1) marks Intermediate and 1 marks Minor degree. The next degree down, Minute, is normally printed as circled lowercase numerals. This guide uses plain i–v instead because they are easier to read on screen. Notation varies between book editions and charting tools, so always check the legend of the chart in front of you. What matters is one label style per degree, used consistently.
View 1 · The Primary count
- Bold line and circled labels: the Primary count in focus.
- Thin grey line and small grey labels: the Intermediate waves inside each Primary wave, (1)–(5) in waves with the trend and (A)–(C) in corrections.
- Dashed blue box: Primary wave 3, shown enlarged in View 2.
- Dashed grey line right of NOW: one possible start of Primary wave 4. Not observed.
Chart scrolls horizontally
View 2 · Close-up of Primary wave 3
- Bold line and large labels (1)–(5): the count in focus.
- Thin grey line and small grey labels: the Minor waves inside each Intermediate wave, numbered 1–5 in motive waves and A–C in corrections.
Chart scrolls horizontally
View 3 · Close-up of wave (3)
- Bold line and labels 1–5: the five Minor waves that make up wave (3).
- Thin grey line and small grey labels: the Minute waves inside each of them, i–v in motive waves and a–c in corrections.
- Grey “end of (2)” and “end of (3)”: where the Intermediate waves (2) and (3) end. Wave (3) starts at the first and finishes at the second.
Chart scrolls horizontally
View 4 · Close-up of Minor wave 3 inside (3)
- Bold line and labels i–v: the five Minute waves that make up Minor wave 3.
- Grey “end of 2” and “end of 3”: where Minor waves 2 and 3 end. Minor wave 3 starts at the first and finishes at the second.
- Thin grey line: the next degree down, drawn but not labelled. Swings this small are close to noise.
Chart scrolls horizontally
All pivot prices used in the three views
| Degree | Wave | Pivots (start, then end of each subwave) |
|---|---|---|
| Primary | 1 to 3 | 60 → 1 135 → 2 100 → 3 192 |
| Intermediate | inside 1 | 60 → (1) 84 → (2) 72 → (3) 124 → (4) 110 → (5) 135 |
| Intermediate | inside 2 | 135 → (A) 108 → (B) 120 → (C) 100 |
| Intermediate | (1) to (5) inside 3 | 100 → (1) 130 → (2) 112 → (3) 178 → (4) 160 → (5) 192 |
| Minor | inside (3) | 112 → 1 124 → 2 116 → 3 162 → 4 154 → 5 178 |
| Minor | inside (5) | 160 → 1 168 → 2 164 → 3 182 → 4 177 → 5 192 |
| Minute | inside 3 of (3) | 116 → i 126 → ii 120 → iii 148 → iv 141 → v 162 |
| Observed after (5) | first decline | 192 → 185 → 188 → 183 (NOW) |
| Scenario only | (A) (B) (C) | (A) 172 → (B) 184 → (C) 163, not observed |
What should readers check on a chart?
Work from the larger context down to the smaller structures. Starting with the small swings is the most common way to end up with a count that looks tidy and means nothing.
-
Identify the larger pattern and its context
Open a chart that shows enough history to see the dominant structure. Ask whether price is trending or moving sideways, and whether the most recent large move looks like five waves or three.
In the example, View 1 shows the widest context, a five-wave rise and a pullback before the advance. View 2 then shows the five-wave advance that may have just completed.
-
Establish a plausible degree and the relevant swing points
Choose a degree for the structure you are labelling and stick to one label style for it. Mark only the highs and lows that are clear turning points at that size. A small dip inside a big rise is a pivot of a lower degree, not of the wave you are counting.
The pivots at 130, 112, 178, 160 and 192 are the obvious turns in View 2. The dip to 154 inside (3) is also visible there, but it belongs to Minor degree.
-
Examine the subdivisions and their role in the parent wave
Zoom into each labelled wave. Waves 1, 3 and 5, and waves A and C of a zigzag, should subdivide in a motive way (five waves or a diagonal). Waves 2, 4 and B should subdivide in a corrective way. If a wave you called (3) turns out to contain three waves, the label is in doubt.
Views 3 and 4 show five-wave subdivisions where the count needs them.
-
Check the count against the rules for that pattern
Rules are mandatory. Breaking one means the count is wrong as labelled. Guidelines describe what usually happens and only make a count more or less likely. Apply each rule to waves of the same degree and only to the pattern it belongs to.
-
Identify alternative counts and what would invalidate each
Write down at least one alternative and the price level that would rule each count out. This turns a story into something you can test against the market.
Rules (mandatory)
These rules follow Frost and Prechter [1]. Each one applies only to the patterns named in the second column.
| Rule | Applies to | Exceptions and special structures |
|---|---|---|
| Rule Wave 2 never retraces more than 100% of wave 1. | All motive waves (impulses and diagonals) | None. |
| Rule Wave 3 is never the shortest of waves 1, 3 and 5, measured in price. | All motive waves | None. Wave 3 does not have to be the longest, only not the shortest. |
| Rule Wave 4 never enters the price territory of wave 1. | Impulses | Does not apply to diagonals, where wave 4 almost always overlaps wave 1. Frost and Prechter also note that in highly leveraged futures markets, brief overlaps at daily or intraday extremes can occur, though rarely. |
| Rule Wave 3 is always an impulse. Wave 1 is an impulse or a leading diagonal. Wave 5 is an impulse or an ending diagonal. | The subwaves of an impulse | None. This is why a three-wave “wave 3” forces a recount. |
| Rule A zigzag subdivides 5-3-5, and wave B never moves beyond the start of wave A. | Zigzags | Wave A may be a leading diagonal and wave C an ending diagonal instead of impulses. |
| Rule A flat subdivides 3-3-5, and wave B retraces nearly all of wave A (commonly defined as at least about 90%). | Flats | In an expanded flat, wave B goes beyond the start of wave A. In a running flat, wave C ends short of the end of wave A. |
| Rule A triangle has five subwaves, A to E, and each of them is corrective. | Triangles | A triangle appears just before the final wave of the next larger pattern, for example as wave 4, wave B or the last part of a combination. |
Guidelines (supporting, not decisive)
| Guideline | What it says | In the example |
|---|---|---|
| Guideline Alternation | If wave 2 is a sharp correction, wave 4 tends to be sideways, and the other way round. | (2) sharp, (4) sideways. Minor 2 deep, Minor 4 shallow. |
| Guideline Extension | Usually one of waves 1, 3 or 5 is much longer than the others. In stock markets it is most often wave 3. | (3) and Minor 3 are extended. |
| Guideline Equality | When wave 3 is extended, waves 1 and 5 tend toward similar length. | (1) is 30 points, (5) is 32. |
| Guideline Depth of corrections | Corrections, especially fourth waves, often end in the range of the previous fourth wave of one lower degree. | (4) ended at 160, inside the 154–162 range of Minor 4 within (3). |
| Guideline Channeling | Impulses often move within roughly parallel trend channels. | Not drawn here. |
| Guideline Fibonacci relationships | Waves often relate by ratios such as 0.618, 1 or 1.618. Wave 2 often retraces 50% to 61.8% of wave 1. Wave C is often close to wave A in length. | (2) retraced 60% of (1). In the scenario, (C) is drawn about equal to (A). |
A wave that ends near a Fibonacci ratio fits the count a little better. It does not prove it. With several common ratios and several possible starting points, some ratio lands near almost any turning point. Only the rules can rule a count out, and only later price action can confirm one.
Step 5 applied to View 2
Three counts fit the observed data in View 2. The table lists each one with the level or evidence that would separate them.
| Count | Reading | What would rule it out |
|---|---|---|
| Preferred | (5) ended at 192, which also completes Primary wave 3. An Intermediate-degree correction has started, and the drop to 183 is its first part, probably the opening of Primary wave 4. | A rise above 192 rules out a zigzag correction. It does not rule out an expanded flat, so on its own it weakens this count rather than ending it. A clear five-wave advance to new highs would favour the next count. |
| Alternative B | 192 was only the top of Minor wave 3 inside (5). The current dip is Minor wave 4, and one more new high is still due. | A drop below 168, the top of Minor wave 1 inside (5). Wave 4 cannot enter the territory of wave 1. |
| Alternative C | The whole rise from 100 is a higher-degree wave of a different kind, for example wave A of a larger zigzag, not part of a bigger uptrend. | View 1 shows a five-wave rise and a pullback before 100, which makes a counter-trend zigzag from there less likely. It is weakened, not ruled out, and only later price action can settle it. |
Common misunderstandings
Price moves all the time, and any chart has dozens of small turns. Labelling every one as its own wave quickly produces counts that satisfy no rule and say nothing useful. A wave is a swing that matters at the degree you are counting. Smaller turns belong to its subdivisions and only get labels when you study that lower degree on purpose. At very small scales, part of the movement is simply noise, such as a single large order in a thin market.
Switching from a daily to an hourly chart changes the magnification. The waves stay the same size. The hourly chart may reveal the subwaves of a daily wave, and those subwaves are one degree lower because they are parts of that wave. The bar interval is not the reason. A large wave can also be fully visible on an hourly chart if it covers only a few weeks, so the timeframe alone tells you little about degree.
Once a count is on the chart, it is tempting to protect it by calling a three-wave move a five, or by moving a pivot so that a rule still holds. The rules exist to prevent exactly this. If price crosses the invalidation level, the count is wrong, and switching to the alternative at that point is part of the method. Writing the invalidation level down before price gets there makes this much easier.
The rules exclude many interpretations but rarely leave just one. Two or three counts often fit the same data, as in the View 2 example above. Analysts usually rank them as a preferred count and alternates, and they watch the levels that would separate them. Later price action decides which one survives, and sometimes none of them does.
In hindsight, counts often look clean because the pivots can be chosen after seeing where price went. While the same structure was forming, it was far less clear. A count that explains the last year neatly gives no guarantee that the next move follows its script. Treat any expectation from a count as a scenario with a probability and an invalidation level, and keep risk decisions separate from how convincing the picture looks.
Checklist for your next chart
Tick the boxes as you work through a chart. Nothing is saved, so the list starts fresh each time you open the page.
Comprehension check
Three questions on nested wave structures. An explanation appears as soon as you choose an answer.
Sources and further reading
- Frost, A. J. and Prechter, R. R. Elliott Wave Principle: Key to Market Behavior. New Classics Library. First published 1978, 10th edition 2005.Standard reference for wave degrees, labelling, the rules and guidelines in φ 04, and the wave counts in φ 01.
- Prechter, R. R. (ed.). R. N. Elliott’s Masterworks: The Definitive Collection. New Classics Library, 1994.Contains Elliott’s original texts, including The Wave Principle (1938) and Nature’s Law (1946).
- Prechter, R. R. The Wave Principle of Human Social Behavior and the New Science of Socionomics. New Classics Library, 1999.Prechter’s later discussion of the wave principle as a self-similar, fractal-like model.
- Mandelbrot, B. B. The Fractal Geometry of Nature. W. H. Freeman, 1982.The general concept of fractals and self-similarity.
- Mandelbrot, B. B. and Hudson, R. L. The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward. Basic Books, 2004.Statistical scaling in market prices. Background for the “similar, not identical” point. It is not a test of Elliott Wave counts.
- Neely, G. Mastering Elliott Wave. Windsville Press, 1990.A more formalised approach to wave construction. Useful for seeing that practitioners disagree on details.