Underwater Caustics Simulator (2D)

Water Surface

Wave amplitude 3.0 cm

Wave speed 1.0×

Pool

Water depth 1.2 m

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Live Readout

Peak floor brightness

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Max ray deflection

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Refraction angle range (θ₂)

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How it works

The water surface is built from five sine-wave components of different wavelength, direction and phase speed, so its height field h(x,y,t) never simply repeats. At every point the local surface slope (∂h/∂x, ∂h/∂y) tilts the surface normal away from vertical.

A dense grid of parallel sunlight rays strikes the surface from directly above. Each ray bends at the interface according to Snell's law, n₁ sin θ₁ = n₂ sin θ₂ with n₁ = 1 (air) and n₂ = 1.333 (water), so the refracted ray tilts toward the local normal and continues in a straight line down to the pool floor.

Where the surface curves like a lens (a trough or crest), nearby rays converge onto almost the same floor point — that is a bright caustic line. Where the surface curves the other way, rays spread apart and the floor goes dark. This sim traces thousands of rays every frame and accumulates where they land, so the bright network you see is a true ray-density map, not a painted texture. Raising the amplitude steepens the slopes and sharpens the caustics; raising the depth lets rays travel further after refracting, so the same slopes spread the pattern out and blur it.