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LIFE is an element that implements various cellular automata rules. All these different rules can be found in the Life menu.
All buttons in the Life menu create a particle of LIFE, but with a different ctype which indicates which cellular automata rule that particle is following.
Powder Toy also has one other CA rule which isn't listed here, since a separate element is used - WireWorld ( WWLD).
Link to Wiki: Conway's Game of Life
This element is essentially Conway's Game of Life from way back when. It's been used to make enormous computing machines in the past, and now it's in Powder Toy. Even though the window size of Powder Toy limits it from being able to make enormous machines, all kinds of interesting things can still be made.
The basic premise is that on every frame, every pixel is calculated and the computer checks for the number of neighbors around each cell. If a cell is surrounded by two or three living cells, it continues to live on the next frame. However, if an empty cell is surrounded by exactly three live cells, it comes to life on the next frame. The result is the bacteria-like behaviors that GOL particles display.
GOL formations that remain static and do not change over time are called still-lives. Particles that change over time but remain stable (not exploding or anything). Certain formations have the ability to move across the screen but do not 'explode' in any way, these are thus called gliders. For more Information, check the wikipedia page.
The following names are essentially GOL, but using different functioning rules. Also, rules like star wars, Frog, Frog 2, have a extra number on the end. That number is the amount of frames an alive cell can keep itself alive without dying.
The same as GOL but with one extra rule. High Life particles survive if surrounded by 2 or 3 particles, and come to life if surrounded by 3 or 6 particles. Because of the extra "6", there is an interesting spaceship and replicator that is unique to Highlife. Other than that, high life and GOL are very similar 
Assimilation particles survive if surrounded by 4, 5, 6, or 7 particles, and come to life if surrounded by 3, 4, or 5 particles. The result is a diamond-generating ruleset that can usually perfectly regenerate into its original shape if a large portion is deleted. Diamonds of ASIM can also absorb "fizzy" patterns, which makes them larger.
2X2 particles survive if surrounded by 1, 2, or 5 particles, and come to life if surrounded by 3 or 6 particles. The result is particles which tend to make surprisingly geometric patterns when produced in even squares or lines. These oscillators can be made with 2X4 rectangles, 2X8 rectangles, 2X12 rectangles and so on.
Day and Night particles survive if surrounded by 3, 4, 6, 7, or 8 particles, and come to life if surrounded by 3, 6, 7, or 8 particles. The result is an exotic particle who's physical properties are exactly inversed both in floodfilled areas and empty ones. In other words, the same patterns can appear inside of a solid block of Day and Night as outside of it, hence its name.
Amoeba particles live up to their name, sloshing around figuratively speaking, producing a peculiar mess of splashy patterns. The result is what looks surprisingly like... Amoebas. Amoeba particles survive if surrounded by 1, 3, 5, or 8 particles, and come to life if surrounded by 3, 5, or 7 particles.
One cool property demonstrated by amoeba is that whenever one draws a perfectly straight light form left to right, or up to down, a fractal traingle is produced.
Move particles don't move anything... besides themselves. They survive if surrounded by 2, 4, or 5 particles, and come to life if surrounded by 3, 6, or 8 particles. The result is a particle that makes patterns that are adept at... moving. The patterns its makes tend to die off rather quickly from random soup, however.
Pseudo Life produces patterns that look superficially like normal GOL, hence its name. Particles of Pseudo Life survive if surrounded by 2, 3, or 8 particles, and come to life if surrounded by 3, 5, or 7 particles.
Diamoeba particles are peculiar indeed. They're like a half-way step between Amoeba and Assimilation particles, producing irregular diamond shapes that lean towards gently disappearing on their own. They can survive when surrounded by 5, 6, 7, or 8 particles, and come back to life if surrounded by 3, 5, 6, 7, or 8 particles.
An interesting rectangular pattern is created when creating a perpendicular straight line.
34 Life particles are an exploding-type particle that can be used to make certain types of useful patterns, but tend towards exploding randomly bigger and bigger if made much larger. 34 Life particles survive if surrounded by 3 or 4 particles, and come to life if surrounded by 3 or 4 particles (hence its name.)
Long Life particles actually don't resemble normal Life particles, being an alien type all their own. They tend to generate diamond shaped oscillators that essentially become stable and never die. Long Life particles survive when surrounded by only 5 particles, but come to life when surrounded by 3, 4, or 5 particles.
Stains particles are an exploding-type pattern that tends to splash outwards from its point of origin in predictable patterns in solid fill. Stain particles survive when surrounded by 2, 3, 5, 6, 7, or 8 particles, and come back to life when surrounded by 3, 6, 7, or 8 particles.
An exploding rule in which every cell dies in every generation. It has many simple orthogonal spaceships, though it is in general difficult to create patterns that don't explode.
An exploding rule that crystalizes to form maze-like designs.
An exploding rule in which patterns tend to expand forever, producing a thick "goo" as it does so.
A stable rule that forms centers of pseudo-random activity separated by walls.
A simple exploding rule that forms complex patterns from even a single live cell. Expands rapidly by itself.
An exploding rule in which every pattern is a replicator.
However, this is not a unique property of the rule string, as many others like Fredkin and Replicator 2 replicate, though they are not included in The Powder Toy
The reason why every pattern in this rule is a replicator is complicated, but here is the link,
Similar to diamoeba.
It is the only life variant in TPT that can survive with 0 surrounding cells.
The 6 at the end means that if a Star Wars particle dies, it stays for 6 frames, and dissapears, instead of going away instantly. The 'dying' particle is not counted as a neighbor, and nothing can be born into that space until it dies. The dying particle will also turn from a dark blue to a much brighter blue as it dies.
Like Star wars, a LOTE pixel will survive for an extra 4 frames after it 'dies', those pixels will change color from a red to a yellow when this occurs.
BRAN particles tend to form 'glider'(those things that look like spaceships) formations consisting of a 2 pixel by 2 pixel square and various trailing pieces. It is very hard if not impossible to make stable patterns
FROG formations sometimes result in gliders that move slowly across the screen, somewhat like frogs
Similar to FROG, but less stable.
How it works
All kinds of GOL particles use Temperature to display in heat mode how long it's been since a particle has been born. A LIFE particle is always born at the highest possible temperature, and gently falls to the lowest temperature until it's destroyed by any means. In other words, the newer a particle is, the hotter it will be. Watch GOL on heat view and you will see that older particles slowly fade to blue while newer ones remain pink.