The Delta Phenomenon
■ All markets repeat their turning-point sequences either directly or inversely.
■ The underlying driver is astronomical: Earth rotations, lunar orbits, and tidal cycles.
■ Time is the dominant organizing force; price merely reacts within these temporal windows.
■ The order is perfect; once the unique Delta solution for a market is identified, future turning points can be projected
■ The underlying driver is astronomical: Earth rotations, lunar orbits, and tidal cycles.
■ Time is the dominant organizing force; price merely reacts within these temporal windows.
■ The order is perfect; once the unique Delta solution for a market is identified, future turning points can be projected
without failure indefinitely, except for predictable adjustments at inversion windows.
The phenomenon was first identified by James Michael Sloman (also known as Jim Sloman, 1943–2015) through observation of recurring market patterns aligned with lunar cycles and tidal rhythms. In the early 1980s, Sloman presented his findings to J. Welles Wilder Jr. (1935–2021), the creator of the Relative Strength Index, Parabolic SAR, and Average True Range. After convincing Wilder that he had discovered long-term rotation solutions for various markets, and describing his system as "like having a road map into the future," Sloman sold the rights to Wilder for a substantial sum, reportedly $1.25 million, around 1983.
Term Delta Solution for Gold on a daily bar chart.
In the above daily bar chart of 1983 COMEX gold futures, colored vertical lines mark the Full Moons that serve as primary anchors for the timing cycle sequences or asset specific intermediate term Delta solutions. These colors—red, blue, orange, and green—repeat every four lunar months, or approximately 118 days, with each color corresponding to a specific month within that sequence. To calculate the predicted market turns, gold traders would use the tabulated legend in the upper right on the chart to count a specific number of days forward or backward from these Full Moon lines; for example, "Point 1 = Orange + 10 days" indicates that a turning point should occur ten days after the designated Orange Full Moon.
Wilder
then formalized and popularized the concept as the Delta Phenomenon,
naming it after the Greek letter Δ (symbolizing change or a gateway to
the unknown). He founded the Delta Society International to disseminate it through high-priced seminars, later software,
memberships (initially around $35,000), and proprietary materials.
In 1991, Wilder published "The Delta Phenomenon or The Hidden Order in All Markets," which remains the definitive text. In the book's prologue and promotional materials, Wilder explicitly credits George Marechal, reproducing his 1933 chart and stating that Sloman "rediscovered what I believe was Marechal's secret."
On the 15-minute cotton futures bar chart above, the repeating red, blue, orange, and green vertical lines serve strictly as calendar-day delimiters for visual reference. The core methodology is defined by the circled numbers (1 through 8), which identify a Short-Term Delta sequence spanning four calendar days. Under this system, the first full week shown is a "Red Week" because it begins with a "Red Day," followed by a "Blue Week," and so on.
Daily bar chart of the British Pound featuring Intermediate-Term Delta
(red circled numbers) and Medium-Term Delta (black framed numbers) solutions.
Short-Term Delta Solution for EUR/USD on a 5-minute bar chart.
for GBP/USD on a daily candle chart.
and 23-point Long Term (black) Delta solutions on a Gold daily bar chart.
Example of an Inverse Rotation in the (red) Intermediate Term Delta sequence in the S&P 500,
where Point 1 follows a Point 12 low in the Inversion Time Window (ITW) as a low.
where Point 1 follows a Point 12 low in the Inversion Time Window (ITW) as a high.
and 6-point Long Term (black) Delta solutions on a Nasdaq daily bar chart.
candle chart by shifting daily closes 118 calendar days into the future (blue line).
Wilder asserted that the Delta Phenomenon reveals "the basis of all market movement relative to time" and constitutes the "perfect order" underlying all freely traded markets (stocks, commodities, currencies, etc.). It is presented as enhancing any technical analysis method by providing precise timing for highs and lows. The system’s proprietary nature—coupled
with Wilder's marketing that emphasized secrecy and
exclusivity—generated significant interest alongside skepticism in
trading communities.
"I asked a mathematician to make the following calculation: If there is not perfect order in the markets, what are the chances that one could know in advance that T-Bonds would make the highs and lows (in high/low rotation) as shown on the chart? The answer is one chance in 322 billion! To be exact, 1 in 332,687,692,541 that the turning points on the chart could have been known before they happened. Do investment bankers and financial institutions worldwide know this? Yes, some do, but try to tell this to your average banker and he will think you are some kind of a nut! I know, I've tried! But I have heard from a few people in major financial institutions (mostly in Europe) who read this book and believed it. In fact, they used the knowledge in the book to find the order in the European currency, bond and stock markets. Are these bankers telling anyone about the Delta order? Not hardly! They have something that gives them an edge in competition with other financial institutions. They are not about to let anyone else in on it!"Welles Wilder, 1991.
"How accurate are the Delta turning points? For all twenty-five commodities, which include over 200 years of observing the Delta phenomenon, the average accuracy for all Intermediate-term points is as follows:[1] 51 % of the time the projected Delta turning points will occur within two days of the projected day.The average accuracy rating (AR) for all Delta intermediate turning points is 27. This means that the average distance of every Intermediate-term Delta turning point from the projected date is 2.7 days. I know it sounds incredible to make the statement that all Intermediate turning points in the future will maintain this accuracy. I was convinced of this only after researching this phenomenon over two hundred years of daily data and over three hundred years of weekly and monthly data."
[2] 68% of the time the projected Delta turning point will occur within three days of the projected day.
[3] 81% of the time the projected Delta turning point will occur within four days of the projected day.Welles Wilder, 1991.
The basic assumptions are that all freely traded financial markets repeat directly or inversely:
- Every 4 revolutions of the Earth = every 4 Days = Short Term Delta (STD).
- Every 4 revolutions of the Moon around the Earth = every 4 synodic Lunar Months (of 29.5306 Calendar Days each) = 118.1224 CD = Intermediate Term Delta (ITD)
- Every complete Tidal Cycle = every Lunar Year = 12 x 29.5306 CD = 354.3672 CD = Medium Term Delta (MTD)
- Every 4 revolutions of the Earth around the Sun = every 4 Solar Years = 1,461 CD = Long Term Delta (LTD)
- Every complete total interaction of the Sun, Moon and Earth = Metonic Cycle = 235 Lunar Months = 6,939.691 CD = every 19 Years and 5 Hours = Super Long Term Delta (SLTD).
- Direct vs. Inverse Rotation: The rotation determines the market's structural orientation. In a Direct rotation, Point 1 is established as a high; in an Inverse rotation, Point 1 is a low. This initial placement dictates the sequence of all subsequent turning points in the series.
- Inversion and Inversion Time Window (ITW): Inversions are restricted exclusively to the Inversion Time Window (ITW). The ITW is a recurring period characterized by a precise, fixed frequency. It spans from the final Delta turning point of the previous series to the second turning point of the new series. Outside of this specific window, inversions cannot occur.
- In-Between Point (IBP): An In-Between Point (IBP) is an auxiliary turning point that may only manifest within the ITW. Its presence dictates the rotation of the series: Single IBP: If one IBP occurs on either side of Point 1, it triggers an inversion, causing a change in the expected rotation. Double IBP: If IBPs occur on both sides of Point 1, two inversions take place. Because these inversions effectively "cancel" each other out, the original rotation remains unchanged. Practical Application: For example, a common Intraday (ITD) solution for the S&P 500 typically identifies 12 turning points within a four-lunar-month cycle. However, when IBPs are present, this same series can expand to include up to 14 turning points.
Wilder asserted that these mechanics account for apparent “failures” in other cycle systems. Once solved, the framework projects dates far into the future (decades or centuries) with calendar-day precision, requiring adjustment only for the ITW.
[Welles Wilder’s "Delta Phenomenon" (1991) and Steve Copan’s "Market Matrix" (2004) both posit a perfectly ordered market sequence dictated by solar-lunar cycles. They share a core architecture involving repeating temporal frames—ranging from intraday to long-term—that define high and low turning points with mathematical precision. Both frameworks utilize the concept of rotation and an Inversion Time Window (ITW) to manage phase shifts caused by In-Between Points (IBP). While Wilder’s original 1991 work focused on proving the existence of this hidden celestial order, Copan’s 2004 re-make refined the system into a more granular "Matrix." Copan’s version introduces specific entry and exit protocols and modern technical filters designed to navigate the increased noise of contemporary electronic markets, essentially acting as a practical trading overlay to Wilder’s foundational discovery of cyclical symmetry.]
More Chart Examples (IDT, MTD, LTD, SLTD)
Practical implementation and application requires solving the unique “Delta solution” (or reference configuration) for each market or instrument:
■ Compile historical price data (daily or appropriate timeframe).
■ Overlay candidate cycle intervals and identify alignments of actual major highs/lows with projected points.
■ Determine the reference date for Point 1, the rotation (direct/inverse), and any recurring inversion pattern.
■ Validate across multiple cycles and timeframes for consistency.
■ Project forward: Add integer multiples of the cycle length to generate future turning-point dates.
■ Overlay candidate cycle intervals and identify alignments of actual major highs/lows with projected points.
■ Determine the reference date for Point 1, the rotation (direct/inverse), and any recurring inversion pattern.
■ Validate across multiple cycles and timeframes for consistency.
■ Project forward: Add integer multiples of the cycle length to generate future turning-point dates.
■ Manual calculation is labor-intensive (accounting for weekends, holidays, and exact lunar periods), which led the Delta Society to offer specialized software. Once solved, traders mark expected turning dates on charts (typically with ±1-day tolerance) and anticipate directional changes.
Trading usage:
■ Treat Delta dates as high-probability reversal zones rather than exact signals.
■ Enter or exit positions near these windows, confirmed by price action, volume, or complementary indicators.
■ Higher-timeframe Delta points provide directional bias for lower-timeframe trades.
■ Multi-cycle confluence (e.g., STD and ITD alignment) strengthens conviction.
■ Inversion windows require heightened caution and verification.
■ Enter or exit positions near these windows, confirmed by price action, volume, or complementary indicators.
■ Higher-timeframe Delta points provide directional bias for lower-timeframe trades.
■ Multi-cycle confluence (e.g., STD and ITD alignment) strengthens conviction.
■ Inversion windows require heightened caution and verification.
■ The methodology is swing-oriented and time-centric; it forecasts when a turn is likely but not the magnitude or exact price. Wilder explicitly stated it is not a standalone system but a timing overlay that elevates the success probability of existing methods.
Short-Term Delta Solution for the S&P 500, NASDAQ, DJIA, and R2K
Short-term Delta works exactly like the other time frames. Each market has its own series, and inversions occur in exactly the same way. However, short-term Delta has 2 or 3 turning points per day. The following charts show the rotation of the Short-Term Delta Solution for the S&P 500, NASDAQ, DJIA, and Russell 2000.
Short Term Delta (STD) Solution for the S&P 500 | Tepid
How
to solve any market for Delta? I have never encountered a freely traded
market that lacked a Delta solution. If Delta is indeed the basis of
all market movement, it follows that every market possesses its own
interlock—a total interaction of the sun, moon, and earth across each of
the five Delta timeframes.
Solving
a new market may initially seem daunting; however, it becomes easier as
your mind learns what to look for. While I have seen one or two
Directors struggle to grasp the concept, most learn it without much
difficulty, and some become exceptionally proficient.
The Methodology: Once you have overlaid the colored lines, place up to three charts vertically on a large table. Align them so the colored lines form a single vertical axis. Next, identify major low points flanked by large price moves; these are the best clues for locating Point (1).
Keep in mind that each series may move in the opposite direction of the adjacent one. If you find a significant point between two colors that acts sometimes as a high and sometimes as a low, you have found the same point in the series—a vital clue to the rotation. Regardless of the timeframe, the series must complete every four colored lines.
I begin by observing the charts for several minutes, allowing my mind to absorb the overall picture without forcing a solution. I then identify a significant point located in the same position on two different charts. By placing an index finger on each, I can trace the same numbered point across both. As I move to the next significant point, my fingers will either move in unison or in opposition.
For example, if one finger is on a high while the other is on a low, but then both move to a high point to maintain the correct distance from the color line, you have found your first clue to the inversion.
Finally, mark your best guess for Point (1) on all three charts. Trace the series chronologically, numbering each point until you have completed the sequence through the four colored lines. While this often begins as a process of trial and error, the solution emerges as you move through the colors. Once you correctly place Point (1), the rest of the sequence typically falls into place.
The Methodology: Once you have overlaid the colored lines, place up to three charts vertically on a large table. Align them so the colored lines form a single vertical axis. Next, identify major low points flanked by large price moves; these are the best clues for locating Point (1).
Keep in mind that each series may move in the opposite direction of the adjacent one. If you find a significant point between two colors that acts sometimes as a high and sometimes as a low, you have found the same point in the series—a vital clue to the rotation. Regardless of the timeframe, the series must complete every four colored lines.
I begin by observing the charts for several minutes, allowing my mind to absorb the overall picture without forcing a solution. I then identify a significant point located in the same position on two different charts. By placing an index finger on each, I can trace the same numbered point across both. As I move to the next significant point, my fingers will either move in unison or in opposition.
For example, if one finger is on a high while the other is on a low, but then both move to a high point to maintain the correct distance from the color line, you have found your first clue to the inversion.
Finally, mark your best guess for Point (1) on all three charts. Trace the series chronologically, numbering each point until you have completed the sequence through the four colored lines. While this often begins as a process of trial and error, the solution emerges as you move through the colors. Once you correctly place Point (1), the rest of the sequence typically falls into place.
Inversion Free Delta Solutions | Russell L.
Russell L. presents a detailed technical analysis of cyclic patterns in stock indices, focusing on two primary time frames: 32 lunar months and 32 calendar years.
These cycles are applied to major indices, including the Nasdaq 100, Dow Jones Industrial Average, and S&P 500, with the objective of identifying recurring swing highs and lows without the inversions observed in certain standard Delta Society time frames (such as the 4-lunar-month interval). The approach relies exclusively on the timing of swing points relative to full-moon reference dates, without incorporating price levels or magnitude projections.
■ The 32-lunar-month solution comprises 88 distinct turn points across the complete cycle. Each lunar month is delineated by a full-moon day (marked by vertical lines on the charts and numbered sequentially from 1 to 32). Turn points are derived from four historical series and expressed as the average number of days past the relevant full-moon day.
■ The 32-year cycle is presented as a complementary, self-explanatory longer-term framework. It aligns market behavior across exact 32-calendar-year intervals (e.g., 2007 with 1975, 1943, and 1911).
■ The 32-year cycle is presented as a complementary, self-explanatory longer-term framework. It aligns market behavior across exact 32-calendar-year intervals (e.g., 2007 with 1975, 1943, and 1911).
The appropriate time frames for Inversion Free Delta Solutions are:
Short Term Delta = 32 calendar days
Intermediate Term Delta = 32 lunar months
Medium Term Delta = 96 lunar months
Short Term Delta = 32 calendar days
Intermediate Term Delta = 32 lunar months
Medium Term Delta = 96 lunar months
Long Term Delta = 32 calendar years
For reasons unknown by me, the non lunar month time frames
also have no inversion if they are multiplied by 8.
Automated Trading Using Delta Points | Slawomir Bobrowski
The method presented below is based on two of the several principles upon which Welles Wilder supported his Delta Phenomenon model. These two principles are: First, the Middle Term Delta (MTD) is based on a market cycle which repeats each Lunar Year; second, equity price characteristics allow for the identification of the Turning Point One location within the Lunar Cycle, thus helping to verify the existence of market inversions.
My approach to Delta points trading differs from Welles Wilder's methodology in that it is fully algorithmic and driven by a computer program which uses trade yields as the main criteria for Turning Point locations. The presented program simulates the trading of MTD setups.
This is NOT a back-testing process. It is a simulation of the trading process where the computer makes a decision ahead of the trading day and the respective market Turning Point. More on the simulation and algorithmic order placement can be found in the section titled “ABOUT ANALYTICAL TOOLS & METHODS” provided below.
The subject simulation covers the trading of SPDR S&P 500 (SPY) from 2007-09-24 through 2010-06-25, which represents three Lunar Years; it also covers the market collapse of 2008-2009, when most investors lost at least 30% of their holdings' value.
My approach to Delta points trading differs from Welles Wilder's methodology in that it is fully algorithmic and driven by a computer program which uses trade yields as the main criteria for Turning Point locations. The presented program simulates the trading of MTD setups.
This is NOT a back-testing process. It is a simulation of the trading process where the computer makes a decision ahead of the trading day and the respective market Turning Point. More on the simulation and algorithmic order placement can be found in the section titled “ABOUT ANALYTICAL TOOLS & METHODS” provided below.
The subject simulation covers the trading of SPDR S&P 500 (SPY) from 2007-09-24 through 2010-06-25, which represents three Lunar Years; it also covers the market collapse of 2008-2009, when most investors lost at least 30% of their holdings' value.
[...] The conclusion drawn from the results presented in Figure 3 is straightforward: A trader using our algorithmic program to trade SPY during these three critical years would have seen a profit of 452.15%, whereas an investor who remained long in the SPY during the same period would have suffered a loss of 29.3%.
The Moon's Biological Effects | Michael Bevington
The debate about how far the Moon causes biological effects has continued for two millennia. Pliny the Elder argued for lunar power “penetrating all things”, including plants, fish, animals and humans. He also linked the Moon with tides, confirmed mathematically by Newton. A review of modern studies of biological effects, especially from plants and animals, confirms the pervasive nature of this lunar force.
However calculations from physics and other arguments refute the supposed mechanisms of gravity and light. Recent space exploration allows a new approach with evidence of electromagnetic fields associated with the Earth’s magnetotail at full moon during the night, and similar, but more limited, effects from the Moon’s wake on the magnetosphere at new moon during the day. There is now evidence for mechanisms such as calcium flux, melatonin disruption, magnetite and cryptochromes. Both environmental and receptor variations explain confounding factors and inconsistencies in the evidence. Electromagnetic effects might also account for some evolutionary changes.
Further research on lunar biological effects, such as acute myocardial infarction, could help the development of strategies to reduce adverse effects for people sensitive to geomagnetic disturbance (HERE).
The
reason for the tidal effect is the ecliptic path of the Moon around the
Earth and the Earth’s daily cycle of 24 hours. Through this mechanism,
the Moon affects our daily lives. It also affects the biological clocks
and the mental attitudes of all living organisms through a mysterious
mechanism. The force of the Moon’s gravity on the Earth is 2.5 times
more than the Sun’s, and for that reason alone it affects us that much
more. Humans, animals, and plants change under the Moon’s light. Nothing
stays the same in terms of thoughts and attitudes.
Two phases of the Moon are most
important: The new Moon and full Moon. During full-Moon periods,
the Earth’s magnetic field is filled with extra ionization and
biological life is influenced more. As the number of positive ions
entering is temporarily higher, humans and animals feel repressed. Some
scientists say humans are bombarded by a wider spectrum of
electromagnetic waves during full Moons.
The Earth is negatively loaded normally, but during full Moons it is loaded with positive particles. This is because the Moon reflects the Sun’s energy to the Earth. As humans are also negatively loaded, they are influenced by this change and feel repressed. Sensitive people are influenced more by full Moons. People who are restless may give exaggerated responses and make themselves and others uneasy. They may behave in a way they always wanted, and their attitudes become sharper. In some extreme cases, they may go mad. People who tend to be violent may give harsh responses. It is well known that suicides, accidents, and heart attacks increase during full moons.
The Earth is negatively loaded normally, but during full Moons it is loaded with positive particles. This is because the Moon reflects the Sun’s energy to the Earth. As humans are also negatively loaded, they are influenced by this change and feel repressed. Sensitive people are influenced more by full Moons. People who are restless may give exaggerated responses and make themselves and others uneasy. They may behave in a way they always wanted, and their attitudes become sharper. In some extreme cases, they may go mad. People who tend to be violent may give harsh responses. It is well known that suicides, accidents, and heart attacks increase during full moons.
The word “lunatic” describes people who go crazy at
those times, because psychotic behavior increases during full Moons. At
the full-Moon phase, the Moon is at the “magnetic tail” created by
particles swirling around the Earth. The Moon reaches that point in four
days, and this sometimes creates an imbalance in the Earth’s magnetic
field. In the new-Moon phase, the Moon enters between the Sun and the
Earth, and its physical body obstructs the particles coming from the
Sun, and some geomagnetic disturbances are experienced.
During
full Moons, our creativity also peaks. It is the time to give birth to
new things. Everything now becomes evident. Instead of acting alone,
this period gives us the energy to act together. Consequently, full
Moons allow us to integrate and exchange love instead of conflict and
diversity. As I emphasized before, the Sun, the Moon, and the planets
are the universal powers that emit electromagnetic waves. We respond to
these energies in the light of our consciousness and awareness level.
Louise McWhirter's Theory of Stock Market Forecasting
Louise McWhirter outlined her theory in 1937 in her book Astrology and Stock Market Forecasting. She proposed that the US stock market and broader economic activity correlate with the 18.6-year cycle of the Lunar North Node as it moves through the zodiac signs. The North Node, a point where the Moon’s orbit intersects the ecliptic, moves retrograde (backward) through the zodiac, spending about 1.5 years in each sign.
McWhirter’s central claim is that the North Node’s position in specific zodiac signs corresponds to distinct phases of economic and stock market activity. Her model, based on data from 1850 to 1938, suggests the following correlations:
- Aquarius (Low Point): The North Node in Aquarius marks the bottom of economic activity and stock market performance, often coinciding with recessions or depressions. For example, she noted Aquarius transits during low economic periods, such as the Great Depression’s nadir in 1933.
- Leo (High Point): The North Node in Leo, roughly 9.3 years later (half the cycle), signals peak economic activity and stock market highs. She predicted a recovery peak in November 1942, which aligned with wartime economic stimulus.
- Transition Phases:
- Scorpio and Libra: A transition from normal to above-normal activity, often marking the start of economic expansion (e.g., 2012–2015).
- Cancer and Gemini: Above-normal activity but trending toward normal, indicating a slowdown from the peak.
- Taurus: A pivot point where the economy shifts from normal to below-normal, often a precursor to slowdowns (e.g., 2003–2004).
- Capricorn and Sagittarius: Below-normal activity, moving toward normal, signaling recovery from lows (e.g., 2009–2011).
- Pisces, Aries, Virgo: Additional phases with nuanced effects, such as approaching lows (Pisces), falling below normal (Aries), or rising higher (Virgo).
McWhirter argued that the North Node’s 18.6-year cycle reflects long-term business cycles, with four critical points tied to the fixed signs (Aquarius, Taurus, Leo, Scorpio). She also considered:
- NYSE Natal Chart: Transits to 14° Cancer (Ascendant) and 24° Pisces (Midheaven) of the NYSE’s chart (May 17, 1792, 7:52 AM, per her rectification) were significant for market turns.
- New Moon Analysis: Short-term market trends could be timed using New Moon aspects to planets connected to the NYSE chart.
- Secondary Factors: Other astrological cycles (e.g., Jupiter-Saturn 19.86-year cycle, 19-year Metonic cycle) and non-astrological influences (e.g., central bank policies) could modify the North Node’s effects by up to 20%.
- She accurately identified the 1933 economic low (North Node in Aquarius) and forecasted a 1942 peak (North Node in Leo), which materialized with WWII-driven growth.
- Her cycles aligned with housing market trends, such as lows in 2009 (North Node in Capricorn) and projected peaks in 2020 (North Node in Cancer).
However, her theory isn’t universally consistent:
- Some periods, like 2012–2014 (projected as above-normal), didn’t clearly reflect expected market strength, possibly due to other cycles or interventions like quantitative easing.