Light: Beer–Lambert
Water absorbs light exponentially: I(z) = I0 · e^(−K·z·m). K differs by colour. Clear tropical water is roughly K≈0.37/m for red (650 nm), 0.065/m for green (550 nm) and 0.022/m for blue (450 nm). Red falls to 2.5% by 10 m and is gone by 20 m, which is why a red fish turns grey-brown at depth and everything drifts to blue. m = 1/cosθw lengthens the slanted sun path (Snell’s law, n=1.33), so a low sun is absorbed sooner. Water clarity adds extra absorption (plankton, sediment).
Zones
The photic (sunlit) zone is bright to about 10% of surface light; the euphotic zone ends at 1% of surface light, where photosynthesis stops paying for itself (about 150 m here, shallower in turbid water). Below it is the dim twilight (dysphotic) zone; the formal twilight zone is usually quoted as 200–1000 m, so 200 m is only its upper edge.
What you see
Each pixel is the sunlit surface colour attenuated per channel on the way down and again on the way to your eye, plus a blue veil of scattered light. Your eye adapts, so the screen exposure rises with depth (up to 5x); the graph shows the true light. Near the surface a moving caustic pattern is added. The torch adds light that only has to travel a short distance, so it brings red back at close range.
Schools: boids
Each fish follows three local rules (Reynolds 1987): cohesion (move toward neighbours), alignment (match their heading) and separation (avoid collisions), plus avoidance of floor, surface and predators. Cohesion is measured from the nearest-neighbour gap in body lengths; polarization is the length of the mean heading vector (1 = all parallel). Under threat fusiliers pull in, swirl around the school centre and form a bait ball.
Predators and the dilution effect
A hunting predator stalks, then makes a short burst at one fish. Chance of a catch per strike is p = p0 · e^(−n/8), where n is the number of other fish within 2.5 m of the target: dense schools confuse and dilute attackers, so a tight bait ball loses fewer fish per strike than a loose school. Catches are removed and prey slowly recruit back.
Coral bleaching
Corals live near their heat limit. Sea surface temperature follows a seasonal cycle (27.5±1.5 °C, summer maximum MMM = 29.0 °C). Hotspot = SST − MMM; only hotspots of at least +1 °C count toward degree heating weeks, DHW += HotSpot/7 per day, with a ~12-week memory. Using NOAA-style levels, around 4 °C-weeks bleaching is likely and around 8 °C-weeks mortality is likely. The warming slider shifts the whole year; roughly +1 to +2 °C over the summer maximum triggers it. Heat fades with depth (thermocline), so deeper corals are partly protected. Branching corals are more heat-sensitive than brain corals. Growth scales with available light, so shading by depth slows it.
Simplified
Flat sea surface, no waves in the physics, no turbidity layers, no currents. Speeds, strike bursts and recovery times are scaled for readability; counts are small; fish do not breed, they recruit at a fixed rate; the reef-fish capacity link to live coral is a simple proportion. Bleaching is shown per colony with a single heat model rather than species-level genetics or symbiont shuffling.