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Britain, 1970 - a new radio telescope, designed by the young scientists John Fleming and Dennis Bridger under the supervision of Professor Reinhart, has been built at Bouldershaw Fell. Shortly before its official opening, the telescope picks up a signal from the distant Andromeda Nebula. Examining the signal, Fleming realises that the signal is a computer program.

Fleming is permitted to use the computer facilities at the London Institute of Electronics, where he is aided by Christine. Using the computer to decode the message, Fleming realises that the message contains a set of instructions for the construction of another more advanced computer. The message also contains another programme for the computer to run, and data to process. Bridger meanwhile, has sold out to an international conglomerate called Intel, represented by the sinister Kaufmann. The British government decides to build the computer at a military establishment at Thorness in Scotland. The computer is switched on and begins to output its first set of instructions.

The team at Thorness is joined by the biologist Madeline Dawnay. The computer is outputting instructions for the creation of living cells. Fleming becomes nervous, worried that whatever life-form they are creating may not have humanity's best interests at heart. Dawney proceeds with the experiment, however, synthesising a primitive protoplasmic life-form. In the meantime, Bridger's leaking of Thorness' secrets has been discovered. Bridger is confronted by Ministry of Defence agent Judy Adamson; fleeing he tumbles over a cliff to his death.

It is now 1971 and the protoplasmic lifeform, now nicknamed "Cyclops" on account of its giant eye, continues to grow. Fleming has become ever more sceptical about the project, certain that the computer has its own agenda. He comes to realise that two terminals positioned either side of the computer's main display have the ability to affect the brainwaves of those who stand near it. His warnings are not heeded, however, and Christine, mesmerised by Cyclops and by the machine, is compelled to grasp the two terminals - she falls to the floor, killed by a massive electric shock.

Following Christine's death, the computer outputs a new set of instructions - this time for the creation of a complete human embryo. Fleming is horrified and demands that it be killed. He is ignored. The embryo rapidly grows to maturity; everyone is stunned when it is revealed to be a clone of the deceased Christine. The creature - which they name "Andromeda" - quickly learns to communicate and is brought before the computer. The computer, realising its instructions have been carried out, destroys Cyclops as it has been superseded by Andromeda.

Andromeda is put to work developing a program to enable Britain to intercept orbital missiles which a foreign power is firing over British airspace. Using the missiles designed by Andromeda, they are successful in destroying one of the missiles. The Government is now determined to make full use of Andromeda, not just for defence but also to aid industry. Fleming continues to make trouble and has his access to the computer revoked. He is horrified to discover that the Government has made a trade deal with Kaufmann and Intel for the rights to a new enzyme that Andromeda has developed that heals injured cells. By this stage, Dawnay is also beginning to have doubts about Andromeda - she agrees to aid Fleming by entering a program into the computer to convince it Andromeda is dead. The program is quickly discovered and reversed by Andromeda. However, the computer soon exacts its revenge - it corrupts the formula for the enzyme, making Dawnay and her assistants sick.

It is 1972 and the message from the Andromeda Nebula has stopped transmitting. Fleming has been able to determine the correct formula to counteract the effects of the enzyme and save Dawnay. Fleming, Dawnay, Reinhart, and Judy now agree that Andromeda must be stopped - however, the military now has control over the project. Andromeda tries to kill Fleming but fails; she confesses to Fleming that she is a slave of the computer, which is working to take over humanity. Fleming takes an axe to the machine, destroying it. Now free of the machine, Andromeda is able to burn the instructions for building the computer so that the machine cannot be rebuilt. She flees with Fleming to one of the islands near the base. Pursued by soldiers, they hide in a series of caves on the island. However, Andromeda is apparently killed when she falls into a deep pool. The dejected Fleming is brought back to Thorness by the soldiers.