Jupiter brain

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A Jupiter brain is a theoretical computing megastructure the size of a planet. Unlike a matrioshka brain, a Jupiter brain is optimized for minimum signal propagation delay, and so has a compact structure. Power generation and heat dissipation are formidable concerns for a Jupiter brain implementation.

While a rigid solid object the size and mass of a rocky planet or gas giant could not be built using any known material, such a structure could be built as a low-density lattice with a mass comparable to a large moon or a small rocky planet but a far larger volume, or as a solid but non-rigid structure with the mass and density of a planet (as long as the internal heat gradient is carefully controlled to prevent convection).

[edit] Fiction

Earth is a form of Jupiter brain in The Hitchhiker's Guide to the Galaxy by Douglas Adams. Built by the Magratheans and commissioned by mice, it is frequently mistaken for a planet by its inhabitants (who are part of the program to determine the question of "Life, the Universe and Everything", given the answer 42 found by Deep Thought).
In addition, Marvin the Paranoid Android from the same series complains of having a "brain the size of a planet" but not having any use for it, and thus being terminally bored. He may be indulging in hyperbole, but in the DVD edition of the 1981 television series it is implied that his brain is indeed the size of a planet; it's just not inside his body.
In Life, the Universe and Everything, also by Douglas Adams, Hactar is a planet-sized computer who was ordered to construct a weapon of universal destruction. However, he found the idea distasteful and deliberately introduced a flaw into the design he came up with. When his masters learned of this, they pulverized Hactar, greatly diminishing his powers but failing to destroy his consciousness in the process.

One of the main "characters" in Ken MacLeod's The Cassini Division is the planet Jupiter, which is the home of transhumanists who uploaded their personalities.

In The Well of Souls series by Jack L. Chalker, the Well of Souls is a Jupiter brain which is tasked with maintaining the physical state of the current universe.

In Revelation Space by Alastair Reynolds, the neutron star Hades is a Jupiter brain which stored the minds of and so preserved the corporeally extinct race of the Amarantin.

In The Last Question by Isaac Asimov, the Multivac predecessor is the size of a planet.

In The Dark Side of the Sun by Terry Pratchett, the First Syrian Bank is a sentient computer/planet, composed of silicon formations that have gradually evolved into natural synapses.