2D Plate Tectonics Simulator: Euler Poles, Plate Boundaries, Hotspot Chain and Seafloor Age Lab

Presets

Live readouts

Graphs

Plate speed vs distance from its Euler pole

Boundary-normal rates: divergent and convergent

Seafloor depth and heat flow vs age

Hotspot chain: volcano age vs distance from the plume

Magnetic polarity stripes vs distance from the ridge

Numerical checks

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How to use

The map shows the synthetic planet: plates in their own colours, land lighter, new crust forming in blue gaps and crust being consumed in orange overlaps. Yellow arrows show plate velocity, crosses mark Euler poles, the white star is a mantle plume and the coloured dots are the volcano chain it leaves on the plate above. Drag the Time slider or let it animate. Select a plate and move its Euler pole or rate; click the map for a local speed. Space pauses, R returns to t = 0. Things to try: (1) move to t = -150 Myr and +150 Myr; (2) select the Africa-like plate and move its pole to the equator: the speed profile changes; (3) put the pole of the India-like plate far away and look at which boundary closes; (4) place the plume under different plates and compare the chain spacing with the speed readout; (5) change the ridge half-rate and reversal frequency and read the stripe width; (6) set all speeds to zero and see every boundary rate vanish.

The science

The lithosphere is broken into rigid plates that move over the weaker asthenosphere. On a sphere, the motion of a rigid plate is always a rotation about some axis through the centre of the Earth (Euler's theorem). The point where that axis pierces the surface is the plate's Euler pole. This page uses a synthetic Earth-like planet with eight plates and illustrative poles and rates of the right order of magnitude (a few cm/yr); it is not a reconstruction of the real Earth.

Plate velocity. A plate that rotates at angular rate ω about a pole has the surface velocity

v(r) = ω × r, |v| = ω R sin Δ, 1°/Myr at Δ = 90° = 11.1 cm/yr

where Δ is the angular distance from the pole. Speed is zero at the pole and largest on the great circle 90° away, so different parts of one plate move at different speeds and a boundary can change from spreading to shearing to closing along its length. The first graph shows this curve for the selected plate; click the map to read the local speed.

Boundaries. Two plates A and B with poles k_A, k_B move relative to each other with v_rel = ω_Bk_B × r − ω_Ak_A × r. Projecting it on the boundary normal gives divergent (positive, mid-ocean ridge, blue), convergent (negative, trench or collision, red) or, when the tangential part dominates, transform motion (yellow). The map is built by rotating each plate's pattern back to its own frame: where no plate covers a pixel there is a gap (new oceanic crust forms there), where two overlap crust is destroyed or piled up. This is only a kinematic cartoon: area is not conserved in the drawing, because the real process (ridge accretion and subduction) is not simulated.

Seafloor. New oceanic lithosphere cools as a half-space, so its depth grows with the square root of age, d = d_ridge + 2 ρ_mα(T_m − T₀)/(ρ_m − ρ_w) √(κt/π) ≈ 2500 + 350 √t m (t in Myr, valid to about 70 Myr; Parsons and Sclater, 1977) and heat flow falls as q ≈ 473/√t mW/m². The check in the page evaluates the cooling coefficient from rock properties (ρ_m = 3300 kg/m³, α = 3×10⁻⁵/K, ΔT = 1300 K, κ = 10⁻⁶ m²/s) and compares it with 350 m/√Myr.

Magnetic stripes. The field reverses at random times (a Poisson process, a few per Myr in the last tens of Myr). Crust formed at a ridge records the polarity of its time, so with half-spreading rate u the polarity alternates with distance x = u · age; a faster ridge gives wider stripes. This is the Vine-Matthews-Morley evidence for seafloor spreading.

Hotspot chain. A plume rooted in the deep mantle stays put while the plate moves over it, so a volcano formed at time −T has been carried by the plate's rotation: its distance from the plume satisfies cos d = cos²Δ + sin²Δ cos(ωT) (Δ = distance from the Euler pole). The chain's age grows linearly with distance, with slope 1/v; a bend in the chain marks a change in the Euler pole.

Numerical checks run in the page. (1) a rotation is rigid (angles preserved); (2) the finite-difference speed at 90° from the pole equals ωR; (3) the distance moved at 52° from the pole matches the spherical law of cosines; (4) rotations about one axis add; (5) the half-space cooling coefficient; (6) the Poisson stripe width; (7) the 60 Myr hotspot volcano position; (8) the boundary classification covers every sample.

Simplifications. Constant Euler poles for hundreds of Myr; plates are rigid caps with no deformation zone; no mantle convection, slab pull or ridge push is computed (the rates are inputs); synthetic continents; the stripes graph is a single ridge; the age-depth law is not used for flexural isostasy; no sea-level or erosion.