triangle (2009) explanation

First of all, it's important to realize that there's quite a bit going on behind the scenes. If Jess is the reason her son spills paint, making her change out of her dress, why is she never in her dress on the boat (there should exist a Jess who's son was not surprised by her out the window, who does not spill paint that gets on her dress). They even make a point to say, when they first set off, that originally she had planned on bringing her child. Just like there should be a Jess with the Sundress on, there should be a Jess that brought her son (who didn't die in a car accident) along.
Truth be told, there is an answer. A pretty solid one at that. I recommend watching the movie again, paying attention to the recursions occurring, but it's still a conclusion that's pretty out there. I tied together my own discoveries in the film and what I've found from other's interpretations from sites like IMDB, since this is -not- a well known movie and there isn't much discussion to be found out there.

Clue #1 - The mention of Sisyphus. Sisyphus wanted to test his wife to see if she loved him, so he told her that, once he died, she was to take his corpse and throw it in the center of town. The idea was that, if she truly loved him, she would not be able to go through with the task. When she indeed throws his corpse out, Sisyphus convinces Persephone, the queen of hell, to let him leave hell for a day to confront his wife. He promises to return back to hell the next day. He decides not to return, and is then dragged back to hell. For his punishment he was made to roll a huge rock up a steep hill, but before he could reach the top of the hill, the rock would always roll back down again, forcing him to begin anew.

Clue #2 - How many versions of Jess are on the ship? There must be at least two: the Jess who kills Victor without seeing her double, and the Jess who, when about to attack Victor, see her double. But if you watch a bit more carefully, there must be at least three:
One Jess dies on the ship and is killed/thrown overboard by another Jess
One Jess jumps overboard and does not mention that she's saving her son as she's going over
One Jess jumps overboard and does mention that she needs to save her son as she's going over

Clue #3 - Sisyphus's punishment was meant to be custom tailored, while Jess's situation seems pretty extreme for someone who's just a crappy mom.

Clue #4 - The clock on the boat matches her clock, the symbol on the drum on the boat matches the symbol on the drum in the marching band, and her house number/the room she uses on the boat are both 237 [the room where the power in The Shining originates from].

Clue #5 - The movie ramps up the saturation after Jess's car crashes, as she's talking to the driver. This same over-saturation is used, though subtly, when the boat sinks.

Clue #6 - Her watch is set to 8:20 or so, while everyone else has 11:30. If you make a conservative estimate that they left port around 9:00, and remember that it's mentioned Jess slept for a few hours on the boat, neither time could be correct.

Clue #7 - At the beginning, Jess is ready to go in her sun dress. We know this because she says, "come on honey we're gonna be late". But she's always wearing jean shorts and a tank top on the ship. If one "Tank Top Jess" is stabbed, and thus doesn't make it back to the beginning of the loop to kill the "Sun Dress Jess", and change the outcome, where are the additional Jesses boarding the ship coming from? In addition, the next Jess's son should not have been surprised by a double, so why would she not have a Sun Dress on?

Clue #8 - If she originally died in "a car crash", why are there car keys on the ship? The Jess that watches the car crash didn't take them out of a crashed, upside down car's ignition.

Clue #9 - At what point does her memory erase? If it's the nap in the taxicab, how can one of them know she needs to save her son while going over the rail? She'd forget every time.

The explanation:
Jess, along with her friends, are in a triple-depth recursion hell after dying at sea, Heather being the only survivor. The cab driver at the end of the movie is death, and this eternity of violence is her punishment for murdering her son, Tommy. Crazy, but that's less of a stretch than you might think.

The full explanation:
This all begins with the fact that Jess is in hell. There's a lot of proof of this:
-Her promise to return to the Taxicab mirrors the promise Sisyphus made with death. That along with the mention of Sisyphus in the movie should be enough to convince you she's in hell.
-Room 237 is very indicative of the same type of evil in the Shining
-The clock on the boat matching her watch, the symbol of the drums matching on and off the boat show that they're manifestations of reality in her hell
-The time on Jess's watch is the time she died. In the current iteration, her watch says 8:20, which is a reasonable time for her car crash to occur (especially if they leave port around 9). Greg's watch says 11:30, which is the time he died (the time the boat sank)
-We see her original death without realizing it. Victor and Greg died in the storm without lifejackets, Sally and Downey were stuck inside, and Heather, if you watch carefully, is pulled out of the ship through the window. She survives, which is why she is not present in their hell. The screen shortly becomes oversaturated as the boat tips over. This oversaturation is the same as the next time we see Jess die, in a car crash.
So, what did Jess do to deserve a hell so terrible? Watch the beginning and end once more. The camera sure focuses on her putting a corpse into the duffel bag, doesn't it? Consider what would have happened if she did not ring the doorbell. It is at this point that the original Jess finally snaps, killing Tommy, stuffing him into the duffel bag and then driving to the harbor. This, too, is supported by more evidence you would suspect:
-Victor says that the Sisyphus's punishment was severe, asking what he did to deserve it. We should be asking the same question, does being a shitty mom relate to this violent of a hell?
-It's much more likely that the violent murder of her son (to be free of his burden) is reflected in her killing everyone on the boat to get back to her son.
-The cab driver, obviously representing death or the devil, tells Jess point blank that nothing can be done to save the boy. As I'll explain, every first iteration through the cycle she ends up murdering Tommy herself, and every second and third iteration he dies in the car crash.


The Cycle:
The easiest way to understand the three cycles Jess goes through is to start at the end of the third cycle. At this point, Jess is murdered by her past self. This means that she will not go back in time to murder herself. This is how the cycles play out (I think I eventually figured out that I was wrong about which Jess kills which Sally, but the idea that one Jess kills her son and escapes, one Jess we see in the movie, and the Jess that gets her head clipped (your bloody faced Jess) is the same Jess that ends up getting killed I think I proved correct):

Cycle 1: Jess the son murderer
Jess murders Tommy, undistracted by doorbell, and changes out of blood-soaked sundress. She drives herself to the harbor, and boards the boat with keys in pocket. She drops her keys, which are picked up by Cycle 2 Jess. When having an encounter with Victor, she is interrupted by Cycle 2 Jess storming through. She encounters Cycle 3 Jess, and just before killing Cycle 3 Jess (who she may think is Cycle 2 Jess who almost shot her), learns that she was attempting to save her son. Cycle 1 Jess murders Sally who crawls into the same place as always, and then escapes the ship, telling Cycle 2 Jess that she needs to save her son. Cycle 1 Jess then interrupts herself from murdering Tommy, kills what would have been a reoccurring Cycle 1 Jess, thus becoming Cycle 2 Jess.

Cycle 2: Jess in the Movie
Cycle 2 Jess dies in a car accident, and is brought back to the harbor by the driver. When having an encounter with Victor, she kills him, and encounters Cycle 1 Jess about to kill Victor. As we see in the movie, Jess shoots Sally in the Theatre AND murders Sally who crawls into the same spot as always, and picks up the keys dropped by Cycle 1 Jess, dropping them for Cycle 3 Jess to pick up. She jumps off the ship, without telling Cycle 3 to save her son, and interrupts Cycle 1 Jess from murdering Tommy, becoming Cycle 3 Jess.

Cycle 3: Jess the murdered
Cycle 1 Jess is interrupted before murdering Tommy. Comes across dying Sally and tells her that she is not the murderer. Cycle 3 Jess's head gets clipped when she attempts to later kill Sally in the Theatre, and finally dies to Cycle 1 Jess's crowbar.