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I want a word or phrase that means a group of PCs that distribute their processing power equally. For example, when one computer is in sleep and another is active, the active computer can be boosted by the asleep computer. I don't think "cloud computing" is the right word because of what I've seen that means a computer that processes on a data center, over a cloud. Also, it usually means there is some "central control", where one computer sends out processing jobs to other computers. However, I want a word that means every computer can access the network and talk to every other computer.

To reiterate: what's the word/phrase used when a group of computers can distribute their processing power across the whole group?

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It's a cluster.

A cluster is a group of independent servers (usually in close proximity to one another) interconnected through a dedicated network to work as one centralized data processing resource. Clusters are capable of performing multiple complex instructions by distributing workload across all connected servers.

Clustering improves the system's availability to users, its aggregate performance, and overall tolerance to faults and component failures. A failed server is automatically shut down and its users are switched instantly to the other servers. (source: business dictionary)

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Try VOLUNTEER computing -

Volunteer computing is a type of computing in which computer owners donate their computing resources (such as processing power and storage) to one or more "projects".

Also you must know, if you don't already, that it belongs to a class of distributed computing. In the broadest sense of the term, distributed computing just means that something is shared among multiple systems which may also be in different locations. 

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When there's no central control it's sometimes called a mesh. If there's some particular node directing traffic and collecting results, it might be called a farm.

  • It could be a render farm. If you are processing data this will increase bus speed. This is done by Daisy chaining the computers. – user15266 May 11 '16 at 22:41

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