The goal in each level within the game is to direct the shapes to exit points specifically tied to each shape, so that they all simultaneously occupy this exit. This most often requires using the shape abilities together to maneuver them appropriately. A shape that cannot jump very high can be helped by creating a staircase from other shapes so that the shape can reach a higher platform, or the shape that can float can ferry the other shapes across water. A shape can be lost to several hazards, but it will reappear at the start of the level, or at a checkpoint if the shape has passed such a point.
There are ten sets of levels, each introducing a new character, with ten levels within each set.
Plot
A company called Artificial Life Solutions experiments with various artificial intelligence solutions, but something unexplained causes some AIs to become self-aware. These AIs perceive their digital world as a 2D space with themselves represented as quadrilateral shapes.
One of them is called "Thomas-AT-23-6-12", Thomas for short, who is represented as a red rectangle. Thomas is curious and observant by nature, and possesses an average jumping height. He starts to travel through his internal world, trying to find out his own purpose and perhaps companionship. He subsequently meets Chris, a cynical orange AI, who is shorter than Thomas and a worse jumper; John, a tall yellow AI, who has a considerably high jump, and is very eager to show it off; Claire, a large blue AI who can't jump very high, but aspires to be a superhero when she realizes she can swim, unlike every other AI; and Laura, a flat and wide pink AI whom others can bounce off. Laura is uncomfortable joining the crew, concerned both about her track record of others "just using her" and disappearing and about a large "pixel cloud" (which we later find out in a quote is called a "splitter") following her; even though the rest of the group is disturbed by the cloud. The splitter soon attacks and "eats" Thomas, and eventually the others as well.
The splitter is revealed to be a mechanism that attempts to fix the fact that multiple AIs are erroneously ending up in testing areas together. Thomas wakes up meeting James, a green AI. James has a "unique disregard for Newtonian laws", and falls upwards instead of down, a feature which caused him to be a target of bullying and thereby grew isolated. However, apart from his direction in gravity and colour, he is identical to Thomas, and the two quickly become friends. They later meet Sarah, a purple AI, who initially treats them with contempt, since she can double-jump, and they can't. Sarah tells them about "the fountain of wisdom", the system's Internet uplink, which they soon find, but which only Thomas is close enough to reach. Thomas connects to it for twelve seconds, creating a "network connection spike", which is later erroneously believed by the Humans to be the first moment Thomas became self-aware. He learns of the outside world, mostly through in-jokes and memes. With this newfound knowledge, he, assisted by James and Sarah, rescues his original friends and tells them of what he learned, and his plan to become an "architect", someone who is able to modify his world and empower other AIs to do the same. Thomas and all his friends enter the "creation matrix", the generator of the world, and disappear. Whether they sacrificed themselves or continue to exist somewhere remains a mystery.
Some time later, other AIs, all in different shades of grey, emerge and start using "shifters", coloured patches that equip them with one of the skills of the original seven architects. These new characters include Grey, a rogue AI, who becomes obsessed with the outer world, a couple, Sam and Jo, who were happy living in one place until Sam began to explore the possibilities given to them by the shifters, an older AI named Paul, who previously told Sarah of the Fountain of Wisdom, and now has a religious reverence for the Architects, believing that they died to provide a better world, and finally a team of five small, identical AIs collectively called Team Jump. Together, these disparate AIs all seek the final portal that leads them to the outer world. Paul realizes that Grey has lied to them and will abandon them when given the chance, and when he can't warn Sam and Jo about the danger, he lures Grey to a place where Grey is eaten by the final splitter. Although Paul and Team Jump are somehow left behind along the way, Sam and Jo find and leap into the final portal and enter the outer world. The final scene shows three monitors on a wall in the real world, inside the Artificial Life Solutions facility. Red emergency lights flash and the screens display pure white as Sam and Jo become the first truly free AIs.