John Conway first theorized that it would be impossible to create a forever-expanding universe using these rules, which was proven wrong by a team at MIT, creating the “glider gun,” which is featured in the third gif.
Since then, thanks to computers, people all over the world have added new designs to the database, creating amazingly complex designs.
For example Andrew J. Wade created a design which replicates itself every 34 million generations! Furthermore it is also a spaceship (permanently moving pattern) and not only that, it was also the first spaceship that did not travel purely diagonally or horizontally/vertically! These types of spaceships are now appropriately named Knightships.
The simulation has some interesting properties, for example it has a theoretical maximum speed information can travel. Or simply, light speed - as that is the limit in our own universe. The limit is set to 1 cell per generation - after all how can you create something further than 1 cell away in one generation if you can only effect your immediate neighbours? And yet you can get things like the ‘stargate’ (Love the name, huge SG fan here.) which allows a space ship to travel 11 cells in just 6 generations.
Some smart people have even designed calculators, prime number generators and other incredibly complex patterns.
You can create your own patterns here: http://www.bitstorm.org/gameoflife/
All gifs were made from this video: https://www.youtube.com/watch?v=C2vgICfQawE