Seabed Caustic Patterns

Pictured by M. Rasid Tugral. Bright lines, nearly always paired with bright domains of light between them and always pin-sharp. They flicker and roam over the seabed - ever changing yet somehow familiarly structured. The transparent sea was 30-50cm deep. Image ©M. Rasid Tugral

The curved water surface refracts - but does not 'focus' - the sun's rays

The shifting seabed light patterns are a two dimensional slice through a 3D cluster of ever moving and changing light sheets - caustic sheets.

The caustic sheets are boundaries between different optical regions of space. On one side the sun's rays refracted by the water's wavy surface do not cross each other. On the other side the rays do cross.

Rays cluster at the edges of the ray crossing regions producing the very bright and always sharp caustic boundaries.

Seabed lines are often paired with a bright area between them. The brighter area is a ray crossing region. Typically, a convex wave region refracts light to produce two caustic sheets joined at top at a cusp and then slowly separating with depth.

The understanding of the intersection and behaviour of caustics falls into the domain of a comparatively recent branch of pure mathematics, ‘catastrophe theory'.

Catastrophe theory deals with the behaviour of critical points on a map.   The name arises because these critical points are ones of stability. Transition from one stable point to another can, in the practical world, have dire consequences.   For example, engineers apply catastrophe theory to the stability of bridges.   One stable point on their map is the desired bridge structure.  Twisted girders in the river are another stable point.   The discontinuity in behaviour representing bridge collapse is the catastrophe.

The same mathematics describes how rays from a refracting (or reflecting) surface behave because rays of light from a surface to the eye define a map. Caustics mark discontinuities in space, optical catastrophes. The theory predicts that they are stable and occur naturally. A rippling stream or swimming pool generates their sharp and ordered forms without special preconditions – they just happen. Compare that to the effort needed to create a camera lens. The lens focus is unstable in that any minor perturbation – a change in distance to the focusing screen or an error in a lens element position – destroys the focus into a blur. Caustics - Nature’s focussing - stay sharp. They are stable – human focussing is not.

A deep result from catastrophe theory is that caustics are not infinite in their variety. There are only seven stable elementary forms. These severe restrictions on form give rise to their remarkable order and to a high specificity in the way they cross and interact. Although ever changing, their shifting patterns remain sharp, familiar and ordered.

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