Collapse may refer to:

Collapse! is a series of award-winningtile-matching puzzle video games by GameHouse, a software company in Seattle, Washington. In 2007, Super Collapse! 3 became the first game to win the Game of the Year at the inaugural Zeebys.

Gameplay

The classic Collapse! game is played on a board of twelve columns by fifteen rows. Randomly colored blocks fill the board, rising from below. By clicking on a group of 3 or more blocks of the same color, the whole group disappears in a collapse and any blocks stacked above fall down to fill in the vacant spaces. If a whole column is cleared, the elements slide to the center of the field. If one or more blocks rise beyond the top row of the board, the game is lost. If the player manages to survive a specified number of lines without losing, they win the level and are awarded points for successful completion.

A level usually begins with a few rows of blocks using a starting set of colors (typically red, green, blue, white, and yellow.). One after the other, new blocks are added to a "feed" row below the board. When the feeder row has filled, all of its blocks are moved up, to the active board, shifting the field of remaining blocks higher. During the course of a level, the rate of new blocks entering the feed increases. New colors may also be introduced, making it more challenging for the player to find groups that are large enough to be collapsed.

In Riemannian geometry, a collapsing or collapsed manifold is an n-dimensional manifold M that admits a sequence of Riemannian metrics g_i, such that as i goes to infinity the manifold is close to a k-dimensional space, where k < n, in the Gromov–Hausdorff distance sense. Generally there are some restrictions on the sectional curvatures of (M, g_i). The simplest example is a flat manifold, whose metric can be rescaled by 1/i, so that the manifold is close to a point, but its curvature remains 0 for all i.

Examples

Generally speaking there are two types of collapsing:

(1) The first type is a collapse while keeping the curvature uniformly bounded, say .

Let be a sequence of dimensional Riemannian manifolds, where denotes the sectional curvature of the ith manifold. There is a theorem proved by Jeff Cheeger, Kenji Fukaya and Mikhail Gromov, which states that: There exists a constant such that if and , then admits an N-structure, with denoting the injectivity radius of the manifold M. Roughly speaking the N-structure is a locally action of a nilmanifold, which is a generalization of an F-structure, introduced by Cheeger and Gromov. This theorem generalized previous theorems of Cheeger-Gromov and Fukaya where they only deal with the torus action and bounded diameter cases respectively.