A German Enigma coding machine on loan from Mick Jagger and a 1950 computer with less calculating power than a smartphone but which was once the fastest in the world, are among the star objects in a new exhibition at the Science Museum devoted to the short, brilliant life and tragic death of the scientist Alan Turing.

'We are in geek heaven,' his nephew Sir John Turing said, surrounded by pieces of computing history which are sacred relics to Turing's admirers, including a computer-controlled tortoise that had enchanted the scientist when he saw it at the museum in the 1951 Festival of Britain. 'This exhibition is a great tribute to a very remarkable man,' Turing said.

'My father was in awe of him, the word genius was often used in speaking of him in the family,' he said, 'but he also spoke of his eccentricity, of how he cycled to work at Bletchley wearing a gas mask to control his hayfever so the local people he passed dreaded that a gas attack was imminent.'

The exhibition, marking the centenary of Turing's birth, tackles both the traumatic personal life and the brilliant science of the man who was a key member of the codebreaking team at Bletchley Park, and devised the Turing Test which is still the measure of artificial intelligence.

Turing was gay, and in 1952 while working at Manchester University, where he had a relationship with a technician called Arnold Murr.