Plate Tectonics, Explained

After reading this you will know how three simple boundary types (convergent, divergent, transform) produce every mountain range, ocean and trench in the toy, how the elevation rates are computed, and how to read the relief view without over-trusting a cartoon.

What the toy actually does

A planet's rigid outer shell is broken into a handful of plates. Each plate drifts across the surface at its own speed and direction. The toy tracks one number per surface cell: elevation. Nothing else. Where two plates meet, the toy looks at their relative velocity and decides what the boundary is doing, then it raises or lowers the crust nearby at a rate chosen to match real geology.

Here is the hook. Take two continental plates closing on each other at a combined 7 cm/year. Neither can sink, because continental crust is too light. So the crust between them buckles and stacks. Run that for 50 million years, which is 50 seconds at the toy's default speed, and you get a belt of high ground. That is the toy's version of the Himalayas: India rammed Asia, and the crust had nowhere to go but up.

The rest of the geology is the same story with the sign flipped or the buoyancy changed. Pull the plates apart and the crust drops and floods. Slide them past each other and you get a fault line with almost no elevation change.

When this model helps, and when it misleads

Use the toy to build intuition about why features sit where they do: why trenches and volcanic arcs come in pairs, why mid-ocean ridges run down the middle of young oceans, why mountain belts are long and thin rather than round blobs. Those patterns fall straight out of boundary classification, and the toy makes them visible in seconds.

Do not use it to predict a real planet. The plate motions here are prescribed by you or by a random re-roll. On Earth they emerge from mantle convection, slab pull and ridge push, none of which the toy solves. The elevation changes are heuristic rates, not a stress-and-strain calculation. Treat every number as illustrative.

The one rule: relative velocity sets the boundary

Consider a short segment of boundary between plate A and plate B. Let \vec{v}_A and \vec{v}_B be their velocities, and let \hat{n} be the unit vector pointing across the boundary from A into B. The single quantity that decides everything is the relative velocity projected onto that normal:

Here v_{\perp} is the closing speed across the boundary. A negative value means the plates approach (convergent). A positive value means they separate (divergent). A value near zero, with the plates instead sliding along the boundary, means transform. The along-boundary component v_{\parallel} = (\vec{v}_B - \vec{v}_A) \cdot \hat{t}, using the tangent vector \hat{t}, is the grinding speed of a transform fault.

The classification rule the toy uses is simple. Pick a small threshold, say 0.5 cm/year. If v_{\perp} \lt -0.5 the boundary is convergent. If v_{\perp} \gt 0.5 it is divergent. Otherwise it is transform.

Turning boundary type into elevation change

Each boundary type drives a local rate of elevation change \tfrac{dh}{dt} that falls off with distance d from the boundary:

Here k is a tuning constant with a sign, |v_{\perp}| is the closing or opening speed, d is distance from the boundary in cells, and \sigma sets how wide the affected band is. For convergence between two continents, k is positive: the crust rises. For divergence, k is negative: the crust drops and later floods. For a convergence where ocean meets continent, buoyancy sends the ocean plate down, carving a trench (large negative k on the ocean side) while pushing up a volcanic arc a fixed distance behind (positive k on the continent side).

A worked example from the demo defaults

Load the demo, which uses the field defaults, and watch one continent-continent boundary. Suppose plate A moves east at 3 cm/year and plate B moves west at 4 cm/year, with the boundary running north-south so \hat{n} points east.

The chart below shows the uplift rate as a function of distance from that boundary, the bell-shaped falloff from the formula.

Explore the boundary threshold yourself

The whole geology hinges on one comparison: is the closing speed big enough to count as convergent or divergent, or small enough to be transform? Change the closing speed and watch the boundary flip type and the relief respond.

Reading the relief view

The main display is a hypsometric relief map: color encodes elevation. Greens and browns are land, deepening blues are ocean, white caps are the highest peaks. Learn to read boundaries by their signatures rather than by the overlay alone.

Long thin bright ridge

A collision belt. Continent-continent convergence. It grows taller the longer you run and the faster the closing speed.

Deep blue line next to a bright line

A subduction pair: trench plus volcanic arc. The trench is the ocean plate diving, the arc is melt rising behind it, typically offset by a few cells.

Central valley in a spreading blue field

A mid-ocean ridge inside a young rift ocean. New crust forms at the center and ages outward, so it sits higher in the middle and sinks with distance.

Sharp offset with flat elevation

A transform fault. Little uplift or subsidence, just lateral grinding.

Toggle the velocity arrows to confirm what you are seeing. Two arrows pointing at each other means convergence; a bright ridge should follow. Arrows pointing apart means divergence, and a rift should be dropping. Arrows sliding parallel means transform.

Common mistakes when reading the sim

The first mistake is reading absolute plate speed instead of relative speed. A plate racing east at 10 cm/year next to a plate also going east at 10 cm/year has v_{\perp} = 0: nothing happens at that boundary, no matter how fast both are moving. Only the difference across the boundary drives geology.

The second mistake is expecting a trench wherever two plates converge. Trenches only appear when ocean meets continent (or older, denser ocean meets younger ocean). Continent-continent convergence has no subduction, so you get a mountain belt and no deep trench. Buoyancy, not speed, decides who dives.

The third mistake is trusting the exact heights. The k and \sigma values are tuned to look right, not measured. A ridge reaching "8 km" in the toy is a scale cue, not a prediction. Compare shapes and relationships, not raw numbers.

The fourth mistake is forgetting the time scale. One second is a million years. A boundary that looks frozen for a few seconds may be a slow convergent belt that needs 30 or 40 seconds (30 to 40 Myr) to show a visible range.

How this fits with the other simulations here

The plate toy is a prescribed-motion model: you set the drivers, and structure follows. That contrasts with the emergent-pattern sims elsewhere on the site. If you want landscapes that carve themselves without any plates, the River Erosion model rains on a surface and lets water do the work. For patterns that self-organize from local rules, the Forest Fire Model shows how growth and lightning settle into a critical balance, and Schelling's Segregation Model shows sharp blocks emerging from mild preferences. For the dynamical-systems side, coupled rates that oscillate rather than build, the Predator-Prey Simulator uses the Lotka-Volterra equations, and the SIR Epidemic Simulator tracks a wave that rises and burns out.

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