Closely related to the Composite pattern is the Flyweight pattern, which is needed when the number of components grows very large. In that case, the components themselves must for obvious reasons carry as little information as possible. Context or state information must then be passed as a parameter.
To give some more examples, suppose there exists a nice library for formatting text and images, but unfortunately with only a procedural interface. Then the Adaptor pattern may be used to provide a interface that suits you, by wrapping the original library.
The Bridge pattern is in some sense related to the Factory. In order to work with a platform-independent widget library, you need, as has been explained, a factory to hide the creation of widgets, but you also need to bridge a hierarchy of platform-dependent implementation classes to the more abstract platform-independent widget set.
When creating widgets to display text or images it may be very inconvenient to create a separate class, for example when adding scrolling functionality. The Decorator pattern allows you to insert additional functionality without subclassing.
Now think of a networked application, for example to be able to incorporate components that are delivered by a server. The library may provide a number of networking classes that deal with all possible communication protocols. To simplify access to these classes a Facade may be built, hiding the complexity of the original class interfaces.
Alternatively, remote components may be available through a proxy. The Proxy pattern describes how access may be regulated by an object that acts as a surrogate for the real object. Like composites and decorators, proxies may be used for recursive composition. However, proxies primarily regulate access, whereas decorators add responsibilities, and composites represent structure.