Arthur C. Clarke wrote a short story about a huge matrioshka brain that sends out probes to the far reaches of the Universe to find out more information. I cannot recall the title, and was hoping someone else knew.
The story is set on a world without a sun, halfway between two galaxies. The world is covered with seas of liquid helium. The conditions permit superconductivity, which eventually evolves into a planetwide, computer-like intelligence.
The intelligence decides it should explore the two nearby galaxies, and sends a series of probes. The first probes fail as soon as they get close enough to be warmed by the stars. But eventually the intelligence learns that one of the galaxies is teeming with life--life that somehow exists at high temperatures.
The intelligence views this "non-mechanical" life as inferior to itself. It learns that there are other mechanical intelligences like itself, but they're in the minority, and they're under the control of the inferior life forms, who claim to have built the mechanical intelligences. It eventually decides to remedy the situation. The story closes with the indication that liberators sent by the intelligence are headed this way.
I've been unable to find any stories by Arthur C Clarke featuring matrioshka brains ... could you be thinking of Accelerando, which is by Charles Stross and not Arthur C Clarke (although it won the Arthur C Clarke award in 2006)? Quoting from its description on Wikipedia (emphasis mine):
As events progress in Accelerando, the planets of the solar system are dismantled over time to form a Matrioshka brain, a vast solar-powered computational device inhabited by minds inconceivably more advanced and complex than naturally evolved intelligences such as human beings. This proves to be a normal stage in the life-cycle of an inhabited solar system; the galaxies are revealed to be filled with such Matrioshka brains. Intelligent consciousnesses outside of Matrioshka brains may communicate via wormhole networks.
The notion that the universe is dominated by a communications network of superintelligences bears comparison with Olaf Stapledon's 1937 science-fiction novel Star Maker, although Stapledon's advanced civilisations are said to communicate psychically rather than informatically.