Along the shores of Sri Lanka, the tsunami that has killed more than 140,000 people first appeared as a rapidly rising tide -- a phenomenon more akin to a quickly filling bathtub than a bona fide wave.
To the east, on the Thai islands of Phuket and Phi Phi, the same tsunami made landfall as a train of intense, cresting waves that washed ashore with brutal impact.
And on the little islands of Diego Garcia and Mauritius, east of Madagascar, that very same wave -- barreling across the Indian Ocean at about 400 mph -- wreaked virtually no damage as it washed by, according to officials.
Like the mercurially morphing villain in the movie "Terminator 2," a tsunami can have many faces.
Why the apparent capriciousness? The answer, scientists said, lies in a few rules of physics that govern the behavior of waves as they travel through water.
Last month's disparities started when a plate of Earth's crust slipped abruptly beneath an adjoining slab of rock under the seas just west of Sumatra. Unlike an asteroid impact, which would send out concentric circles of energy in all directions equally, this geologic event was primarily a sideways motion. That meant that from the start, the waves it sent east and west carried much more energy than those headed north or south, said Steven Ward, a geophysicist at the University of California at Santa Cruz, who has generated a detailed computer model of the tsunami's progression (visible at www.es.ucsc.edu/~ward/indo.mov).
That reality -- along with the fact that shorelines happened to be closer to the east and west of the epicenter than to the north or south -- helps explain why vulnerable countries to the far north and south, such as Bangladesh and Mauritius, suffered relatively little, compared with Sri Lanka to the west and Thailand to the east.
Yet Sri Lanka and Thailand experienced the tsunami very differently, even though they both lay along that dangerous east-west axis. Those differences, scientists said, point to the most important determinant of a tsunami's personality as it comes ashore.
"Basically, it's the shape of the bottom," said Jeffrey Weissel, a senior research scholar at Columbia University's Lamont-Doherty Earth Observatory in New York.
In a nutshell, Weissel and others said, land masses that poke abruptly from the deep ocean experience tsunamis as diffusely rising tides, while those bounded by shallower seas get hit by higher, steeper and often more destructive waves.
At the core of this truth -- as with most truths in physics -- is an equation: v = square root (g times h), where v is the wave's velocity, g is the force of gravity and h is the depth of the water. In plain English, as the water gets shallower, waves slow down.
That is a common-sense observation, but one with an unexpected consequence: These slower waves end up packing extra punch.
There are two keys to understanding why. One is that a tsunami is not just one wave but a train of waves, typically half a dozen or more, each a little weaker than the one ahead of it but all packing tremendous energy. The waves are generally a few feet high in deep ocean, and their wavelengths -- the distance between the swells -- can be a mile or more.
When a tsunami's leading wave slows down as it enters shallower water, others behind it -- still in deep water -- do not. They pile on from behind, shortening the distance between waves and adding to the height of the leading waves, said Andrew Ingersoll, a professor of planetary science at the California Institute of Technology in Pasadena.
The second key, Ingersoll said, is that the slowing of waves in shallow waters is simply a reflection of how waves behave in limited space. It is not because of friction on the ocean bottom. That is important because it means that, although the wave is slowing, it is not giving up energy. All that energy is being rearranged within a slower but newly steepened wave, not to be released until it hits buildings, trees, people and anything else in its way.
"The total energy is the same, but it's concentrated," Ingersoll said.
With those rules in hand, a look at the Indian Ocean's bottom geography explains a lot about what happened Dec. 26. The ocean, it turns out, is quite shallow off Thailand's west coast, with huge expanses less than 500 meters (1,640 feet) deep. So shallow and wave-slowing are those waters that last month's tsunami hit the Thai coast well after it hit the east coast of India, which is more than twice as far away but lies across deeper seas.
When the slow, steep, closely packed waves hit Thailand and Sumatra, they did so with brutal force. By contrast, the string of waves that hit Sri Lanka -- a giant island that rises steeply out of water that is as much as 3,500 meters (11,500 feet) deep -- were low, broad and still spaced far apart. Although the damage was still great as those big swells flowed rapidly ashore, they were so broad as to be perceived as rising and dropping tides rather than as waves.
"It looked more like a storm surge without the wind," said Weissel of Columbia.
Some islands suffered hardly any damage despite being directly in the tsunami's track, highlighting other features that can affect wave behavior.
Facilities on the island of Diego Garcia, for example, which is British but is home to a U.S. military base, "were not affected," according to the Navy. Although some skeptics have suggested the military may be downplaying damage at the sensitive installation, scientists said it was plausible that the island escaped harm because of two protective features: the sturdy ring of coral reefs surrounding it and the extremely deep Chagos Trench just to the east, which may have disrupted some of the wave forms as they approached the island.
Environmentalists this week were quick to pick up on the wave-deflecting benefits of coral reefs. Friends of the Earth said the tough natural barriers, many of which are suffering from the effects of pollution and warming oceans, are among the best ways to protect coastal communities from the risk of future tsunamis.