The Cosmic Cycles tool is a mathematical visualization and educational tool. It is not a scientific forecasting engine.
It has three modes. Cosmic (the default) overlays 22 periodic signals and 163 historical events across 60,000 years; that is what most of this reference covers. Atomic applies the same idea - searching for recurring structure - to matter instead of time: the chart of nuclides, the 17 Standard Model fields, the periodic table, and a particle‑building sandbox. Data shows measured series, such as sunspot counts and ocean temperature indices, with views that compare them against the model. See Historical Events, Atomic Mode and Data Mode below.
The convergence score shows where multiple cycle positive phases overlap. This is a defined mathematical metric - not a validated predictor of real‑world events. The chart superimposes 22 periodic signals from unrelated physical systems onto a common timeline. The resulting pattern is interesting to explore, but it does not constitute a forecast or discovery.
Key limitations:
Most cycles are modeled as sinusoids for simplicity. Several (Schwabe, ENSO, Bond events) are quasi‑periodic or chaotic in reality.
The tool is most accurate near the present (2000 CE). Short‑period cycles lose validity within decades. The Milankovitch periods hold for millions of years, but each is drawn as one sinusoid standing in for several orbital terms, so its timing drifts over tens of thousands of years.
The overlapping pattern of 22 cycles does NOT reveal hidden predictions. Volcanic eruptions, wars, and climate catastrophes are not caused by cycle convergence.
Lunar cycles
Lunar Perigee Precession (8.85 yr)
In plain terms: the Moon's closest point to Earth drifts all the way around its orbit every 8.85 years, and the strongest "supermoon" tides swell and fade with it.
TypeApsidal precession of the Moon's orbit
Period8.8504 years
PeriodicityTruly periodic
Physical effectAffects tidal range
Sinusoidal modelAppropriate
The Moon's orbit is an ellipse, and the point of closest approach (perigee) slowly rotates around Earth. One full rotation of the perigee takes 8.85 years. This modulates the strength of perigean spring tides; in high‑tide records the effect appears at half that period, about 4.4 years (Haigh, Eliot and Pattiaratchi 2011).
Saros Eclipse Repeat (18.03 yr)
In plain terms: nearly identical eclipses come back about every 18 years, each one shifted to a different part of the world.
TypeCommensurability of synodic, draconic, and anomalistic months
Period6585.32 days (18.03 years)
PeriodicityDiscrete recurrence
Physical effectProduces eclipse families
Sinusoidal modelSimplification - see note
The Saros is a discrete recurrence, not a continuous oscillation. The sinusoidal model used in the tool is a simplification. Each Saros series produces an eclipse every 18.03 years, shifting roughly 120 degrees in longitude. The cycle arises from the near‑coincidence of 223 synodic months, 242 draconic months, and 239 anomalistic months.
Lunar Nodal Precession (18.61 yr)
In plain terms: the tilt of the Moon's path slowly swivels over 18.6 years, raising and lowering how high the Moon rides and how strong the tides get.
TypeRetrograde precession of the lunar orbit's ascending node
Period18.6129 years
PeriodicityTruly periodic
Physical effectAffects declination range of the Moon and tidal amplitude
Sinusoidal modelAppropriate
The plane of the Moon's orbit is tilted about 5 degrees to the ecliptic. The line where these planes intersect (the nodes) rotates retrograde with a period of 18.61 years. At major lunar standstill, the Moon reaches its maximum declination; at minor standstill, the minimum. This modulates tidal amplitudes globally.
Metonic Cycle (19.00 yr)
In plain terms: every 19 years the Moon's phases line back up with the same calendar dates - which is why ancient calendars were built around it.
TypeCalendrical commensurability - 235 synodic months = 19 tropical years
Period19.00 years
PeriodicityResonance condition
Physical effectNone - lunar phases repeat on the same calendar dates
Sinusoidal modelSimplification - see note
This is a resonance condition, not a physical oscillation. Nothing sinusoidally varies with a 19‑year period. The Metonic cycle describes the fact that 235 synodic months (new moon to new moon) is almost exactly 19 tropical years, so lunar phases repeat on approximately the same calendar dates. Meton of Athens introduced it to Greek calendars in 432 BCE; Babylonian calendars had regulated their leap months with the same 19‑year cycle since about 499 BCE.
Solar cycles
Schwabe Sunspot Cycle (11.0 yr)
In plain terms: sunspots and solar storms build up and die down about every 11 years, though no two cycles are quite the same.
TypeMean sunspot cycle
Period~11.0 years (individual cycles range 9‑14 years)
PeriodicityQuasi‑periodic
Physical effectSolar irradiance variation, geomagnetic activity, radio propagation
Sinusoidal modelRough approximation - see note
The sunspot number curve is asymmetric: fast rise (~4 years), slow decline (~7 years). A sinusoid is a rough approximation that accumulates phase error within 2‑3 cycles. Grand minima (Maunder 1645‑1715, Dalton 1790‑1830) are NOT predictable from this model. They arise from nonlinear dynamo processes in the solar interior.
Hale Magnetic Cycle (22.0 yr)
In plain terms: the Sun flips its magnetic north and south each sunspot cycle, so a full magnetic round‑trip takes about 22 years.
TypeFull solar magnetic polarity reversal
Period~22.0 years (two Schwabe cycles)
PeriodicityQuasi‑periodic
Physical effectMagnetic field reversal, cosmic ray modulation
Sinusoidal modelRough approximation
The Sun's magnetic field reverses polarity roughly every 11 years, so a full magnetic cycle takes about 22 years. The same quasi‑periodic caveats as the Schwabe cycle apply. Named after George Ellery Hale, who discovered the magnetic nature of sunspots in 1908.
Gleissberg Cycle (88 yr)
In plain terms: the 11‑year sunspot cycle itself grows stronger and weaker over roughly a century.
TypeAmplitude modulation of the Schwabe cycle
Period80‑100 years (quasi‑periodic)
PeriodicityQuasi‑periodic
Physical effectLong‑term solar activity envelope
Sinusoidal modelSimplification - see note
The Gleissberg cycle describes how the amplitude of successive Schwabe cycles waxes and wanes over roughly a century. Physically, this should be a multiplicative envelope (modulating Schwabe amplitude), but the tool models it as an additive sinusoid for simplicity.
de Vries / Suess Cycle (210 yr)
In plain terms: a slower, roughly 210‑year swing in the Sun's activity, read from chemical traces left in tree rings and ice.
TypeSolar activity cycle detected in cosmogenic isotope records
Period205‑210 years (quasi‑periodic)
PeriodicityQuasi‑periodic
Physical effectModulation of galactic cosmic ray flux reaching Earth
Sinusoidal modelReasonable for the proxy record
Detected in cosmogenic isotope records (14C, 10Be). One of the more well‑established long‑period solar signals, but still quasi‑periodic. First identified by de Vries (1958) and Suess (1980).
Eddy Cycle (1000 yr)
In plain terms: a possible ~1,000‑year ebb and flow in the Sun's activity - real‑looking in the records, but not yet well pinned down.
TypeLong‑period solar activity cycle in cosmogenic isotopes
Period~1000 years
PeriodicityQuasi‑periodic, less well‑established
Physical effectLong‑term solar activity modulation
Sinusoidal modelSpeculative at this period
Named after Jack Eddy, who studied the Maunder Minimum and established that solar variability is real. A ~1000‑year periodicity appears in cosmogenic isotope records, but it is less well‑established than the Gleissberg or de Vries cycles. It may be part of a broader spectral feature.
Hallstatt Cycle (2300 yr)
In plain terms: an even slower, roughly 2,300‑year solar rhythm seen faintly in thousands of years of tree‑ring and ice records.
TypeVery long solar activity cycle in 14C records
Period2200‑2500 years
PeriodicityQuasi‑periodic, poorly constrained
Physical effectGrand minima clustering
Sinusoidal modelVery rough approximation
Detected in 14C records. Only 4‑5 complete cycles fit within the Holocene proxy record, so the period is poorly constrained. First identified by Damon and Sonett (1991). Named after the Hallstatt culture period, which happens to fall near one of the apparent cycle boundaries.
Planetary cycles
Jupiter‑Saturn Conjunction (19.86 yr)
In plain terms: the two biggest planets appear to meet in the sky about every 20 years - a striking sight, but with no real effect on Earth.
TypeSynodic period of Jupiter and Saturn
Period19.859 years
PeriodicityTruly periodic (orbital mechanics)
Physical effect on EarthNegligible - Jupiter's tidal force on Earth is under 10−5 of the Moon's, even at its closest
Sinusoidal modelAppropriate
These "great conjunctions" have been tracked since antiquity. Jupiter and Saturn appear close together in the sky roughly every 20 years. While the orbital mechanics are precise, the physical influence on Earth is negligible.
Jupiter‑Saturn‑Neptune / Jose Cycle (178.7 yr)
In plain terms: the giant planets nudge the Sun around the solar system's shared center of gravity on a ~179‑year cycle; claims that this steers the Sun or the weather are not accepted.
TypePeriod of solar barycentric motion
Period178.7 years
PeriodicityTruly periodic (orbital mechanics)
Physical effectDisputed - see note
Sinusoidal modelAppropriate for the orbital component
The Sun orbits the solar system's center of mass with a ~178.7‑year modulation driven primarily by Jupiter, Saturn, and Neptune. The claimed link to solar activity (the Charvatova/Jose hypothesis) is not accepted by mainstream solar physics. At the base of the Sun's convection zone, the accelerations that planetary tides and the Sun's motion about the center of mass produce are about a thousand times smaller than those already observed there (de Jager and Versteegh 2005).
Jupiter‑Saturn Triangle (59.58 yr)
In plain terms: three of those 20‑year meetings trace out a slowly turning triangle across the sky over about 60 years.
TypeRotation of great conjunction positions through the ecliptic
Period59.58 years (3 x 19.86)
PeriodicityTruly periodic
Physical effectNone independent of the conjunction cycle
Sinusoidal modelAppropriate
Three consecutive great conjunctions rotate through approximately 120 degrees of ecliptic longitude, forming a triangle pattern. The full triangle takes about 60 years to complete. This is a geometric consequence of the synodic cycle, not an independent phenomenon.
Climate cycles
Bond / Dansgaard‑Oeschger Events (1470 yr)
In plain terms: the North Atlantic has lurched between warm and cold spells roughly every 1,500 years - though whether that is a real clock or just chance spacing is debated.
TypeQuasi‑periodic abrupt climate shifts in the North Atlantic
Period~1470 years
PeriodicityDebated - possibly stochastic
Physical effectAbrupt shifts: Dansgaard‑Oeschger warmings in the last glacial period, Bond cold events in the Holocene
Sinusoidal modelPoor - these are abrupt events, not smooth oscillations
A ~1470‑year spacing was reported in Holocene North Atlantic ice‑rafted debris (Bond et al. 1997), whose peaks mark cold events, and in the Dansgaard‑Oeschger warmings of the last glacial period recorded in Greenland ice cores. Ditlevsen et al. (2007) argued the spacing is consistent with a stochastic process. The mechanism is unknown. These are abrupt events (a Dansgaard‑Oeschger warming arrives within decades and fades over centuries), NOT smooth oscillations. The sinusoidal model is a rough approximation.
ENSO Envelope (5.0 yr)
In plain terms: El Nino and La Nina shift weather around the globe every few years, but never on a schedule you can set a clock by.
TypeEl Nino‑Southern Oscillation
Period2‑7 years (broad spectral peak, ~5 year center)
ENSO is driven by ocean‑atmosphere coupling in the tropical Pacific and is unpredictable beyond roughly 1‑2 years. The 5‑year sinusoid used in the tool is a rough center‑of‑spectrum approximation. Real ENSO events are irregular in timing, amplitude, and character (El Nino vs La Nina are not symmetric).
Pacific Decadal Oscillation (25 yr)
In plain terms: the North Pacific Ocean drifts between warm and cool patterns over a couple of decades, affecting salmon runs and droughts.
TypeMulti‑decadal SST pattern in the North Pacific
Period20‑30 years (quasi‑periodic)
PeriodicityQuasi‑periodic - debated as true oscillation vs red noise
A recognized climate mode, named by Steven Hare and described by Mantua et al. (1997). Decadal‑scale shifts in North Pacific SST patterns. Some researchers question whether it is a true oscillation or low‑frequency variability. The 25‑year period is a representative midpoint of the 20‑30 year range.
Atlantic Multidecadal Oscillation (70 yr)
In plain terms: the North Atlantic does much the same over roughly 60‑80 years, nudging Atlantic hurricanes and European weather.
TypeMulti‑decadal SST oscillation in the North Atlantic
Detected in SST records by Schlesinger and Ramankutty (1994). A 60‑80 year oscillation correlating with European climate and Atlantic hurricane activity. Mann et al. (2020) questioned whether the AMO is a true internal oscillation or a response to external forcing.
Earth cycles
Chandler Wobble (1.186 yr)
In plain terms: the Earth wobbles on its axis like a slightly off‑balance top, a tiny sway about every 14 months that even fades away for years at a time.
Physical effectSmall latitude variations: with the annual wobble, the pole moves up to about 0.3 arcseconds (about 9 m)
Sinusoidal modelPoor - amplitude varies and was nearly zero around 2005‑2006
Discovered by Seth Carlo Chandler in 1891. The wobble is stochastically excited by atmospheric and oceanic processes, and its amplitude varies unpredictably. A fixed‑amplitude sinusoid cannot represent this behavior. The wobble was nearly undetectable around 2005‑2006.
Axial Precession (25,772 yr)
In plain terms: the Earth's axis slowly traces a giant circle over about 26,000 years, so the "North Star" changes across the ages.
TypeLuni‑solar precession of Earth's rotation axis
Period25,771.5 years (IAU)
PeriodicityTruly periodic
Physical effectPole star drift, seasonal shift relative to orbit
Sinusoidal modelAppropriate
This is the "pole star drift" - Polaris will not always be the North Star. Earth's rotation axis traces a cone with a period of about 25,772 years. For climate forcing, what matters is "climatic precession" (~21,000 yr), which combines axial precession with orbital apsidal precession.
Climatic Precession (21,000 yr)
In plain terms: that same slow wobble decides whether Earth is closest to the Sun in summer or in winter - a key pacemaker of the ice ages - on a roughly 21,000‑year beat.
TypeCombined effect of axial and apsidal precession on insolation
Period~21,000 years (~19 and ~23 kyr components)
PeriodicityTruly periodic
Physical effectControls timing of perihelion relative to solstices - drives ice age insolation forcing
Sinusoidal modelAppropriate
The actual Milankovitch precession forcing that appears in paleoclimate spectra (Hays, Imbrie, and Shackleton 1976). Climatic precession combines the ~25,772‑year axial precession with the apsidal precession of Earth's orbit to produce dominant periods near 19 and 23 kyr. The tool uses 21 kyr as a representative single period.
Obliquity Cycle (41,000 yr)
In plain terms: the Earth's tilt nods between 22.1 and 24.5 degrees over 41,000 years, making the seasons milder or harsher.
TypeVariation of Earth's axial tilt
Period~41,000 years
PeriodicityTruly periodic
Physical effectAxial tilt varies between 22.1 and 24.5 degrees
Sinusoidal modelAppropriate
A well‑established Milankovitch parameter described by Berger (1978). The tilt of Earth's axis oscillates between 22.1 and 24.5 degrees. Higher obliquity means more extreme seasons in both hemispheres. The current tilt is about 23.44 degrees and decreasing.
Eccentricity Cycle (100,000 yr)
In plain terms: Earth's orbit stretches from more round to more oval and back over about 100,000 years - the slowest of the big ice‑age drivers.
TypeVariation of Earth's orbital eccentricity
PeriodMultiple components at ~95, ~100, ~125, and ~405 kyr
PeriodicityTruly periodic (superposition of several terms)
Physical effectModulates total annual insolation and precession amplitude
Sinusoidal modelSimplification - the tool shows only the ~100 kyr component
The dominant "pacemaker" of Pleistocene glacial cycles. Earth's orbital eccentricity has multiple spectral components; the tool models only the ~100 kyr term. The "100 kyr problem" - why glacial cycles lock to the weakest Milankovitch forcing term - remains one of the major unresolved questions in paleoclimatology.
Validity range
Not all cycles in the tool maintain accuracy over the same timescales. The sinusoidal model diverges from reality at different rates depending on the underlying physics.
Planetary, LunarSet by orbital mechanics, so the periods hold across the tool's span. The catalog rounds them (18.61 years for 18.6129), which puts the far ends of the timeline up to about a quarter cycle out.
MilankovitchThe periods hold for millions of years, but each sinusoid stands in for several orbital terms (Laskar et al. 2004), so its timing drifts over tens of thousands of years.
Hallstatt, Eddy, de VriesSeen in proxy records through the Holocene (about the last 11,700 years). The phase is poorly constrained outside those records, and the Eddy period itself is uncertain.
Gleissberg (88 yr)Valid ~400 years back (telescopic era), ~100 years forward. Period is loosely constrained.
Schwabe, HaleValid ~50 years back, ~20‑30 years forward. Phase accumulates error within 2‑3 cycles.
ENSO, PDO, AMO, Bond eventsThe sinusoidal model is a rough approximation at any timescale. These are chaotic or stochastic systems.
Chandler WobbleValid ~10 years in either direction. Amplitude is stochastically excited and varies unpredictably.
Convergence score
The convergence score at any point in time is a weighted average over the visible cycles in which each cycle counts only while it is positive, so the score runs from 0 to 1. The weights come from the selected mode. When many cycles happen to be in their positive phase together, the score is high; when few are, it is low.
This shows mathematical overlap, NOT physical conjunction or prediction. Superposing unrelated physical phenomena (polar wobble + orbital eccentricity + sunspot number + ENSO) has no established scientific predictive value. The cycles operate through completely different physical mechanisms at completely different scales.
Historical events overlaid on the chart are provided for context and interest. They do not imply that cycle convergence caused those events. Correlation in a chart is not causation - especially when 22 overlapping signals make it almost certain that some cycles are in positive phase during any historical event.
Historical events
The timeline overlays 163 historical events across its full 60,000‑year span (30000 BCE - 30000 CE). Each carries a one‑word subtype and a 1‑2 sentence note, and belongs to one of four categories you can toggle independently in the Historical events group of the Settings sidebar (or hide entirely).
PoliticalStates, dynasties, wars, treaties, religions, and scientific or cultural milestones - the human record.
EcologicalThe biosphere: pandemics, famines, agricultural milestones, and climate regimes such as warm periods, megadroughts and glacial transitions.
GeologicalVolcanic eruptions, earthquakes, tsunamis, impacts, and floods.
AstronomicalSupernovae, eclipses, comets, Miyake solar‑proton events, grand solar minima, and great conjunctions.
Dates before about 2000 BCE rest on radiocarbon and other physical dating (ice‑core layers, tree rings, volcanic ash) and on reconstructed chronologies, and carry real uncertainty; the notes give the method where it matters. The four events past the present are orbital projections (such as when sunlight peaks at far northern latitudes, or when Vega becomes the pole star).
These events are context, not evidence. An event sitting near a convergence peak is coincidence: with 22 overlapping signals, some cycle is in positive phase during virtually any year. Nothing in the cycle model caused any listed event. See Convergence Score.
Weight modes
The tool provides four weighting modes that change how each cycle contributes to the convergence score.
Physical:Physical impactWeights cycles by their measurable physical effect on Earth. Milankovitch cycles and tidal forces score highest. Cycles with negligible physical forcing (Jupiter‑Saturn conjunction, Metonic) score lowest.
Cultural:Cultural visibilityWeights cycles by how noticeable they are to human observers. Eclipses, sunspots, and ENSO score highest. Long‑period Milankovitch cycles (invisible on human timescales) score lowest.
Combined:Physical + CulturalTakes the maximum of Physical and Cultural weights. A cycle matters if it has real physical forcing OR is culturally visible - whichever is greater.
Raw:Equal weightAll cycles weighted equally (1.0). Useful for seeing pure mathematical overlap without any interpretive weighting. Every cycle contributes the same amount to the convergence score.
Atomic mode: the matter axis
The tool's second mode hunts for the same repeating structure in matter that the cosmic side finds in time. Instead of scanning across years, it scans across the building blocks of atoms - how many protons and neutrons sit in a nucleus, and how many electrons surround it. It starts from the 17 most basic particles we know of, climbs up to atomic nuclei, and ends at the chemical elements, with each layer built out of the one below.
Scope: almost everything you see in Atomic mode is calculated, not measured. The nuclear pictures come from one classic formula that treats a nucleus like a wobbling drop of liquid (the semi‑empirical mass formula), plus a small, deliberately simple stand‑in for the quantum "shells" that protons and neutrons fill. Real measurements are used only to tune that formula - its handful of constants and a short list of known decay rates. So treat the heavy, never‑yet‑made nuclei as the model's best guess, not as fact.
17 Fields
What it isThe smallest known building blocks of everything: 6 quarks, 6 leptons, 4 force‑carrier particles, and the Higgs. The numbers come from the Particle Data Group, the field's standard reference.
Three viewsA grid: each card shows a bar for the particle's mass and dots for the forces it feels (strong, electromagnetic, weak). A mass ladder: the same particle shows up in three ever‑heavier copies, the heaviest over a hundred billion times heavier than the lightest. An interaction web: lines join each force‑carrier to the particles it acts on, switchable force by force.
Build a Nucleus
Add or remove protons and neutrons and watch everything update at once: which element it is, a ring diagram of its electrons, whether it would hold together, and the quark‑and‑electron "recipe" that makes it. Add a neutron to lead, or keep adding until the nucleus can no longer hold together - it is a quick way to get a feel for which combinations survive and which fall apart.
Particle Forge
Build a particle out of quarks and antiquarks. The same rules nature uses decide whether your combination is allowed: the electric charges have to add up correctly, and the quarks have to combine into complete, color‑balanced groups - a lone quark or a half‑finished set is not allowed. If it works, the tool names it from the real particle zoo (proton, neutron, pion, kaon, and friends) and drops it onto the Eightfold Way - a triangular map physicists use to sort these particles by their properties. Particles with names show their true measured mass; a valid but unnamed combination shows a rough estimate, clearly marked as a guess. The lesson: a proton is just one recipe (two up quarks and a down), not a building block of its own.
Island of Stability (Chart of Nuclides)
Every possible nucleus, from hydrogen on up, is a square in a grid. The color shows how it would fall apart, and the brightness shows how long it would last. The bright diagonal stripe is the "valley of stability" - the combinations that hold together. The dark zone past the heavy elements is the "sea of instability," and the bright patch beyond it is the predicted "island of stability," where a special neutron count (184) might let some super‑heavy nuclei survive far longer than their neighbors.
Shell‑strength sliderSets how strong that special‑number effect is. Nobody knows the right value - expert estimates vary widely - so it is left as a knob: the island's brightness is an open question.
Model dropdownRespected models disagree on where the island's center sits - element 114, 120, or 126. The markers jump when you switch models: this is a prediction, not a measurement.
Where it stops being trustworthyThe math is only checked against real data up to element 106. The first island is already a guess beyond that, and the faint second island in the far corner (around element 164) is flagged as pure speculation. Nothing past element 118, oganesson, has ever been made.
Binding Curve
How tightly each particle in a nucleus is held, plotted against how big the nucleus is. The peak sits near iron and nickel (56 to 62 particles): lighter nuclei release energy when they fuse together, and heavier ones release energy when they split apart. Nickel-62 is the most tightly bound nucleus, and iron-56 has the lowest mass per particle. It is why fusion in stars stops yielding energy at the iron peak, why fusion powers stars, and why fission powers reactors.
Periodic Table
The familiar table, but the layout is worked out in code from the rule for the order electrons fill their shells - not copied from a picture. Color it by the usual chemical families, or by where in the universe each element is made (the Big Bang, cosmic rays, dying small stars, exploding massive stars, exploding white dwarfs, neutron capture (stellar interiors, supernovae, and neutron‑star mergers), or a laboratory). It even predicts that the not‑yet‑made element 119 would sit in hydrogen's column - the same "this pattern repeats" idea the cosmic side uses, now in chemistry.
Universe Lab
Turn the dials on the five numbers inside that nuclear formula - in effect, the "constants of nature" for a made‑up universe - plus a pressure knob (the crushing gravity inside a dying star). The whole chart of possible nuclei regrows into the matter of a universe that may never have existed. Everything here is hypothetical; "reset" brings you back to ours.
For the underlying physics, the in‑tool "Learn more" links point to the Particle Data Group, the IAEA Live Chart of Nuclides, and the free Feynman Lectures.
Data mode: measured series
The third mode holds real measurements, kept apart from the mathematical catalog so neither passes for the other. Each dataset is a snapshot taken from its publisher, not a live feed, and its source, license, citation and retrieval date stay on screen while it is shown.
SeriesAny dataset over its full span. A scaled model overlay is available but off by default, drawn fainter and labeled as scaled, so the sum of sine waves is never mistaken for the measurement.
RecurrenceOne series embedded in a delay space (Takens), drawn as a recurrence plot with the standard recurrence quantification measures (RR, DET, L, Lmax, DIV, ENTR, LAM, TT, Vmax) and a windowed DET strip along the diagonal.
Cross‑RecurrenceAny two sources, measured or model, aligned on the years they share and compared as a cross‑recurrence plot. Set measured polar motion against the model's Earth profile, which over these decades moves almost only with its 1.186‑year Chandler term, and the model visibly fails to track the measurement.