According to the USGS, six major geyser regions can be identified in the world: Iceland, Yellowstone in the United States, the Valley of Geysers in Kamchatka, the Taupō–Rotorua region of New Zealand, El Tatio in Chile, and Lake Bogoria in Kenya.

https://www.usgs.gov/media/images/map-showing-locations-major-natural-thermal-geyser-fields

For first comparison:

Geysers are rare because their formation requires a particular combination of geothermal heat, groundwater, permeable fractures, and a confined underground plumbing system in which water can become superheated before erupting at the surface.

According to the geometric interpretation presented here, the locations of all six major geyser regions can be related to prominent axes, ellipses, and major tectonic divisions shown on the map below.

Iceland, Yellowstone, and Kamchatka all lie in direct continuation of the principal axes of the Antarctic ellipse. New Zealand is located near the intersection of the minor axis of the Ring of Fire and its inner elliptical form. Kenya is associated with the Great Rift Valley of Africa, close to the Equator, while El Tatio in Chile lies on the outer rim of the elliptical form of the Ring of Fire. Thus, all six of the world’s most prominent geyser regions can be related to the principal geometric features described here.

In the case of Iceland, the accuracy level is tremendous:

1. Iceland – Geysir and Strokkur

Iceland contains one of the classic geyser regions of the world. The best-known examples are Geysir and Strokkur in Haukadalur. Strokkur erupts frequently, while the activity of Geysir has varied considerably through historical time.

The Icelandic geothermal systems are associated with intense volcanism, abundant groundwater, fractured volcanic rocks, and a high geothermal gradient. Water can circulate downward through fractures, become heated at depth, and rise again. In a geyser, restrictions within the underground conduit allow pressure to build until part of the water suddenly flashes into steam, producing an eruption.

Within the geometric framework shown here, Iceland lies in the direct continuation of the minor axis of the Antarctic ellipse. The continuation of this axis extends northward through the Atlantic region towards Iceland.

2. Valley of Geysers, Kamchatka

The Valley of Geysers in Kamchatka, Russia, is one of the largest and most concentrated natural geyser fields in the world. It contains numerous geysers, hot springs, steam vents, and other hydrothermal features within a highly active volcanic environment.

Kamchatka is located along a major subduction zone, where the Pacific Plate descends beneath the region. This produces extensive volcanism and provides the heat necessary for powerful hydrothermal systems. Groundwater circulates through fractured volcanic rocks and is heated at depth, allowing geysers to develop where the underground plumbing has the appropriate geometry.

Geometrically, the Valley of Geysers is particularly significant because Kamchatka lies in the direct continuation of the minor axis of the Antarctic ellipse on the opposite side of the Earth from Iceland. Thus, Iceland and Kamchatka are associated with opposite extensions of the same principal axis.

3. Yellowstone, United States

Yellowstone National Park contains the greatest concentration of active geysers in the world. Famous examples include Old Faithful, Grand Geyser, Castle Geyser, Beehive Geyser, and Steamboat Geyser.

The Yellowstone hydrothermal system is powered by an exceptionally large volcanic and geothermal system beneath the Yellowstone Plateau. Rainwater and snowmelt penetrate deeply into fractured rocks, where they are heated and subsequently rise through complex networks of fractures and conduits. In geysers such as Old Faithful, the shape of the underground reservoir and conduit permits pressure to accumulate and produces repeated eruptions.

Within the geometry examined here, Yellowstone lies in the direct continuation of the major axis of the Antarctic ellipse. This places one of the world’s most important geothermal and geyser regions along another principal axis defined by the Antarctic geometry.

4. New Zealand – Taupō and Rotorua

New Zealand contains several major geothermal areas, particularly within the Taupō Volcanic Zone, including the Rotorua and Whakarewarewa geothermal fields. Pohutu Geyser is one of the best-known active geysers in the region.

The Taupō Volcanic Zone is characterized by active volcanism, large caldera systems, abundant fractures, and powerful hydrothermal circulation. Hot groundwater rises through volcanic rocks and produces geysers, hot springs, mud pools, and steam vents. Some historic geysers in New Zealand have changed or disappeared as a result of natural changes and human use of geothermal groundwater.

The position of the New Zealand geyser region is especially noteworthy in the present model. It lies on the minor axis of the Ring of Fire, close to the point where this axis crosses the inner ellipse of the Ring of Fire. The geyser region therefore occurs at an important geometric intersection within the circum-Pacific system.

5. El Tatio, Chile

El Tatio, in the high Andes of northern Chile, is one of the world’s major geyser fields. It contains numerous geysers, hot springs, fumaroles, and steaming geothermal pools. Individual eruptions are generally smaller than those of the largest geysers in Yellowstone or Iceland, but the number and concentration of geothermal features make El Tatio exceptional.

The heat source is related to Andean volcanism above the subduction zone along the western margin of South America. Water circulating through fractured rocks is heated by the volcanic geothermal system before returning to the surface.

In the geometry presented here, the Chilean geyser region lies on the outer margin of the Ring of Fire. Its position therefore corresponds directly with the major circum-Pacific tectonic and volcanic boundary.

6. Lake Bogoria, Kenya

The geothermal region around Lake Bogoria in Kenya contains hot springs, steam vents, and numerous small geysers. Although many of these geysers are considerably smaller than Geysir, Strokkur, or the major Yellowstone geysers, they operate according to the same basic hydrothermal principles.

Lake Bogoria lies within the East African Rift System, where the continental lithosphere is being stretched and fractured. This tectonic setting allows heat and fluids to rise relatively close to the surface and produces extensive volcanic and geothermal activity.

Its geographic position is particularly important in this comparison. The Lake Bogoria geyser field lies very close to the Equator and directly within the Great Rift Valley. It therefore represents the sixth major geyser region at the intersection of a major continental rift system with the equatorial zone.

Geometric Relationship of the Six Geyser Regions

The six major geyser regions occur in very different geological environments. Iceland is associated with an oceanic spreading system, Kamchatka and Chile with subduction-related volcanism, New Zealand with an active volcanic and plate-boundary region, Yellowstone with a major continental volcanic system, and Kenya with continental rifting. Nevertheless, all require the same fundamental conditions for geyser formation: a strong heat source, groundwater, fractured and permeable rocks, and an underground conduit system capable of retaining pressure.

When their geographic positions are compared with the geometry shown on the map, an additional pattern appears:

• Iceland lies on the northern continuation of the minor axis of the Antarctic ellipse.
• Kamchatka lies on the continuation of the same minor axis on the opposite side.
• Yellowstone lies in the continuation of the major axis of the Antarctic ellipse.
• New Zealand lies on the minor axis of the Ring of Fire, where it intersects the inner Ring of Fire ellipse.
• El Tatio in Chile lies along the outer margin of the Ring of Fire.
• Lake Bogoria in Kenya lies at the Equator within the Great Rift Valley.

All six locations are marked on the map below. The comparison is therefore not based only on the presence of geothermal activity. It shows that the world’s principal geyser regions occupy specific positions in relation to the major geometric and tectonic structures considered in this study.

The geometric relationships between the major geyser regions can be divided into several partly overlapping groups. It is important not to treat all of them as the same type of correspondence, because some are close point-to-line matches, while others involve larger tectonic or volcanic zones.

Iceland, the Valley of Geysers in Kamchatka, and Yellowstone form one group related to the geometric framework derived from the Antarctic Plate and the equatorial divisions. Geysir in Iceland is particularly interesting because it is not located directly on the principal axis at 19°37.5′W, but close to a subdivision line half a 1.5° interval farther west. This theoretical line lies at 20°22.5′W, while Geysir is at about 20°18′W. The difference is only about 0.075°, corresponding to roughly 4 km at this latitude. Thus, Geysir can be regarded as a close point-to-line correspondence within the subdivision system rather than as a direct match with the principal axis itself.

The Valley of Geysers and Yellowstone are also related to the Antarctic-derived geometry, but they have an additional and independent-looking relationship with the geometry of the Pacific Ring of Fire. In this second system, four major geyser regions occupy characteristic positions along the inner and outer margins of the Ring of Fire.

The Valley of Geysers in Kamchatka lies along the inner boundary of the Ring of Fire geometry. New Zealand, another of the world’s major geyser regions, is likewise associated with the inner boundary. On the opposite side of the geometric pattern, Yellowstone lies close to the outer boundary, while El Tatio in Chile is also located along the outer boundary.

This produces a striking two-by-two arrangement:

A further relationship is superimposed on this arrangement. New Zealand and Yellowstone are positioned in relation to the minor axis of the Ring of Fire ellipse. They are therefore not merely two geyser regions situated on different margins of the same geometric form; they also define, or lie close to, one of its principal axes.

Yellowstone and the Valley of Geysers are consequently of particular interest because they belong to both geometric groups. The Valley of Geysers is related both to the Antarctic-derived framework and to the inner boundary of the Ring of Fire. Yellowstone is related to the Antarctic framework, the outer boundary of the Ring of Fire, and the minor-axis geometry of the Ring of Fire. The recurrence of the same exceptional geothermal regions in more than one independently defined geometric relationship is more significant than a simple comparison of individual coordinates.

Kenya provides a different type of correspondence. Lake Bogoria lies very close to the equator within the Kenya Rift, which forms part of the eastern branch of the East African Rift System. The relevant geometric division also passes through the eastern rift system. Here the correspondence should therefore not be described as a geyser lying exactly on a single line. Rather, the subdivision line corresponds with a major tectonic zone, and the geyser field occurs within that same zone.

Iceland has a related connection with the equatorial subdivision system. Its major geothermal field at Geysir lies close to a longitude derived from one of the equatorial division points. In this sense, both Iceland and Kenya illustrate how the equatorial division system may correspond with major rifting and geothermal environments, although the geological expression is very different in the two regions.

These relationships can therefore be summarized as three overlapping geometric patterns:

1. Antarctic and equatorial geometry: Iceland – Valley of Geysers – Yellowstone, with Kenya providing an additional connection through the equatorial division and the East African Rift.
2. Inner and outer Ring of Fire geometry: Valley of Geysers – New Zealand on the inner boundary; Yellowstone – El Tatio on the outer boundary.
3. Minor axis of the Ring of Fire: New Zealand – Yellowstone.

The comparison is complicated by the fact that geyser regions differ greatly in size and geological setting. Geysir in Iceland can be compared quite precisely with a longitude, whereas Yellowstone is a very large volcanic and hydrothermal system, and Lake Bogoria is best understood in relation to an entire rift zone. For this reason, the significance of the pattern should not be judged solely by measuring the distance of each geyser from a single theoretical line. The more relevant question is whether the world’s most prominent geyser regions repeatedly occupy characteristic positions within a geometric framework that was defined independently of the geysers themselves.

At the Visitor Centre of Snæfellsjökull National Park, specimens of several different rock types found in Iceland are on display. Although Iceland is built predominantly of countless layers of basaltic lava, many other rock types also occur. Just as basalt differs from peridotite, which represents the Earth’s upper mantle, the other rock types have formed through different magmatic and geological processes.

In many cases, the cooling history of the magma is the most obvious factor controlling the final rock type. Rapid cooling, particularly beneath glaciers or in water, may produce volcanic glass and palagonite, while slow cooling beneath the surface allows coarse-grained rocks such as gabbro to crystallize. Rhyolite is much richer in silica (SiO₂) than basalt, and if rhyolitic magma cools extremely rapidly before crystals can form, it solidifies as obsidian.

This is a very informative exhibition and is highly recommended for anyone interested in Icelandic geology.

Viewed from the South Pole, the global system of plate boundaries reveals several striking geometric relationships between Antarctica, the Ring of Fire, and Iceland, as shown here:

The following observations summarize these relationships.

1. The Antarctic Plate can be approximated by an elliptical shape. Its minor axis extends from 60°S, 160°22.5′E to 60°S, 19°37.5′W, while its major axis extends from 45°S, 70°22.5′E to 45°S, 109°37.5′W.
2. These axes correspond closely with major plate-boundary systems. The major axis aligns with the Mid-Indian Ridge and the East Pacific Rise, whereas the minor axis follows the Mid-Atlantic Ridge and the western Pacific subduction system.
3. The Ring of Fire can likewise be represented by an ellipse whose minor axis crosses that of Antarctica at 64°S, 160°22.5′E. The opposite end extends through the equator and is found within the Yellowstone region.
4. The south coast of Iceland is located approximately the same angular distance north of the equator as the edge of the Antarctica Tectonic Plate boundary (sea floor) is south of it. Its overall elliptical geometry has the same orientation, with its minor axis lying along the longitude of 19°37.5′W.
5. The southern end of the Ring of Fire coincides with the point where an equatorial mantle convection-roll division (red line) reaches the Antarctic Plate. From there, the Antarctic segment of the Ring of Fire continues toward the endpoint of another convection roll (90° apart), where it intersects the Antarctic major axis.
6. The resulting geometry is consistent with the Ring of Fire extending between the equatorial convection-roll division points beneath eastern Indonesia and the west coast of South America. It coincides with the main deviation of the elliptical form of the Antarctic Tectonic Plate.
7. The illustration is schematic and is not drawn to scale, since it represents relationships on a spherical Earth using a two-dimensional projection.

The purpose of this figure is to illustrate the geometric relationship between the global systems of mid-ocean ridges and subduction zones. In particular, it emphasizes that the Mid-Atlantic Ridge and the western Pacific subduction system occupy opposite sides of the same great-circle plane.

Several important features are intentionally omitted for clarity. These include the subduction system along the west coast of South America, the inner boundary of the Ring of Fire, the San Andreas Fault in California, and the Alpine Fault of New Zealand. Each of these plays an important role in the overall tectonic framework but would unnecessarily complicate the present illustration.

For reference, it may be helpful to compare the upper illustration with the more conventional one below. The Greenland–Iceland–Faroe Ridge Complex (GIFRC) is another manifestation of the symmetry around the 19°37.5′W axis of longi

The symmetry around the axis is obvious. A bit more complicated version below:

This shows how the two ridges are symmetrical around the Icelandic abyss, with D and E being the end points of the major axis. B and C are also on the periphery of the abyss, on the end points of the same convection roll. https://www.lyellcollection.org/doi/full/10.1144/sp447.14

Extrapolating the mid-ocean ridges, showing that they meet at the central point of the elliptical form of the Icelandic plateau, and marking the divisions of the Greenland and Faroe Ridges respectively, also contributes to realizing the symmetrical aspect of the structure as a whole.

Because the Antarctic Plate, like other tectonic plates, consists of both continental and oceanic crust, it is treated here as a single tectonic unit.

When the Antarctic Plate is examined in relation to the South Pole and the surrounding plate boundaries, a remarkable geometric pattern emerges. The Pacific–Antarctic Ridge, forming the southern continuation of the East Pacific Rise, and the Southwest Indian Ridge are situated almost exactly opposite one another across the South Pole. A straight line can therefore be drawn from the Pacific–Antarctic Ridge triple junction, across the South Pole, to the triple junction where the Southwest Indian Ridge meets the Antarctic Plate.

A second line, drawn perpendicular to the first and also passing through the South Pole, intersects two major subduction systems: the South Sandwich Trench in the South Atlantic and the Puysegur–Hjort subduction system south of New Zealand. The South Sandwich Trench also lies close to the southern continuation of the Mid-Atlantic Ridge, which extends northward approximately parallel to this same line.

Using these two perpendicular lines as the major and minor axes, an ellipse can be constructed that closely resembles the outline of the Antarctic Plate. Two additional major plate-boundary systems also meet or approach the elliptical outline: the Peru–Chile Trench along the western margin of South America and the ridge system extending southward from Africa into the Indian Ocean.

Although the geometric fit is not exact everywhere, much of the Antarctic Plate boundary follows the ellipse closely. The principal deviation occurs within the Pacific sector, where part of the plate boundary trends approximately parallel to the major axis rather than following the elliptical curve.

When the major and minor axes are extended northward, another part of the same pattern becomes visible. The two ends of the major axis point toward the East Pacific Rise and the Mid-Indian Ridge, while one end of the minor axis aligns with the Mid-Atlantic Ridge. The opposite end coincides with the southern endpoint of the minor axis of the Ring of Fire. It also meets the southern end of the principal mantle-convection division line proposed in this study, which is associated with subduction along the western Pacific margin.

The same geometric framework can therefore be traced from the South Pole to the principal tectonic divisions near the equator and to the geometry of the Ring of Fire. Major spreading ridges, subduction zones, triple junctions, and axis endpoints repeatedly occur along the same projected lines and intersections. Together, these relationships form a distinct and internally consistent large-scale pattern centred on the South Pole.

Reasons for the Geometric Regularity of Mid-Ocean Ridges and Subduction Zones

Having derived a system of mantle convection rolls from the known thermal structure and layering of the Earth, it is natural to examine the global distribution of mid-ocean ridges and subduction zones in light of these results.

According to the model, the upper mantle contains convection rolls that are approximately 1.5° wide in the east-west direction, aligned with the Earth’s rotation. In the deeper mantle, the larger convection rolls span approximately 15° in width. Consequently, the principal upwelling zones occur at intervals of 30° around the equator.

A comparison with the mapped distribution of plate boundaries, mid-ocean ridges, transitions between continental and oceanic crust, and major subduction systems reveals a striking correspondence: these major tectonic boundaries repeatedly occur at approximately 30° intervals along the equator. This geometric regularity is, by itself, a remarkable observation. The existence of this pattern cannot reasonably be disputed, since the global plate boundaries are among the best-mapped geological features on Earth.

The same regularity also emerges from the Earth’s internal structure. When convection rolls with equal height and width are placed within the known mantle layering, the geometry naturally accommodates 24 rolls in the lower mantle, or twelve counter-rotating convection pairs. This arrangement produces twelve principal upwelling zones spaced 30° apart around the globe.

The derivation is most straightforward along the equator. From these equatorial upwelling points, the principal mid-ocean ridges and subduction zones extend northward and southward. In the following discussion, the focus is placed primarily on the Southern Hemisphere.

On the southern hemisphere, the principal spreading ridges are conspicuously aligned in a north-south direction. This applies to the East Pacific Rise, the South Atlantic Ridge, and the Central Indian Ridge. Southward, these ridges merge into the circum-Antarctic spreading system that surrounds Antarctica.

Two of these junctions exhibit particularly striking symmetry: the connection between the East Pacific Rise and the Antarctic Ridge occurs near 110°W, while the corresponding connection between the Central Indian Ridge and the Antarctic Ridge lies near 70°E. These locations are separated by almost exactly 180°, meaning that a straight line connecting them passes directly across the South Pole.

One might be tempted to dismiss this as a coincidence. However, the broader pattern is far more difficult to ignore. Along the equator, major tectonic boundaries appear repeatedly at intervals of approximately 30°. Moving eastward, one encounters the East Pacific Rise, the western margin of South America, the eastern margin of South America near the Amazon mouth, the Mid-Atlantic Ridge, the western margin of Africa, the East African Rift System, the Central Indian Ridge, the western margin of Indonesia, and the eastern margin of Indonesia—each separated by roughly 30° of longitude.

From a statistical perspective, such a systematic arrangement is unlikely to arise by chance alone. It strongly suggests that an underlying large-scale control governs the distribution of these tectonic features, and the mantle convection-roll model provides a possible physical explanation for that control.

It is important to recognize that continental drift and the mantle convection pattern are not contradictory processes. Plate motions continuously rearrange the continents, so the surface expression of the underlying convection system changes through geological time. Nevertheless, the convection geometry itself may remain comparatively stable, while its surface manifestations evolve. We obviously cannot wait tens of millions of years for the continents to assume a new configuration before investigating whether such a fundamental geometric pattern exists.

A second remarkable relationship emerges when a line is drawn across Antarctica perpendicular to the line joining the East Pacific Rise and the Central Indian Ridge. The endpoints of this second line fall very close to the subduction system south of New Zealand on one side and the South Sandwich subduction system on the other. The South Atlantic Ridge lies close to this same axis.

These four reference points define an ellipse surrounding Antarctica that corresponds surprisingly well with the overall geometry of the Antarctic Ridge system. Two additional tectonic elements also fit naturally within this framework: the South American subduction zone and the spreading system extending southward from Africa.

An even more intriguing relationship appears when this Antarctic ellipse is compared with the ellipse defined by the Pacific Ring of Fire. The Ring of Fire itself displays a pronounced elliptical geometry, with its minor axis extending from Yellowstone, through the eastern side of the San Andreas Fault system, to New Zealand on the western side of the Pacific. When this axis is extended southward, it intersects the endpoint of the minor axis of the Antarctic ellipse.

These observations establish geometric relationships that link the principal spreading ridges and subduction systems of the Earth into a single coherent framework. Whether this remarkable regularity reflects the influence of large-scale mantle convection remains a question for continued investigation. However, the geometric relationships themselves are systematic, internally consistent, and sufficiently striking to warrant careful examination.