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Lego Turing Machine: The building blocks of computing in play

By · June 22, 2012, 1:38 AM PST

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  • The Turing Machine is a theoretical model of how computation takes place. It dates from 1936 and inspired the pioneers who created the modern digital computer. The machine was described in a paper, On Computable Numbers, written by British mathematician Alan Turing.

    Researchers at the Centrum Wiskunde & Informatica (CWI) or Centre for Mathematics and Computer Science in Amsterdam in the Netherlands decided to demonstrate the principles of the machine's operation by building a Turing Machine using a Lego Mindstorms NXT set.

    The machine is part of the Turings Erfenis exhibition at the centre, which is running until October to mark the centenary of Turing's birth.

    Photo: Centrum Wiskunde & Informatica

  • The Lego machine is based on the theoretical device set out by Turing in his paper.

    Turing described the hypothetical machine as being able to move backwards or forwards over a strip of infinite tape, which is divided into cells. The machine could read, write or erase symbols inside each cell.

    The machine would be controlled by a series of rules that tell it whether to move the tape, how to manipulate a cell's contents and which rule to jump to next.

    In the Lego Turing Machine each cell on the building-block tape, seen above, is made of a black switch, which can be switched on to represent a symbol or turned off to represent a blank cell.

    Photo: Centrum Wiskunde & Informatica

  • As the Lego machine moves along the tape, it checks the contents of each cell using a light sensor. The sensor detects the light reflected from each cell to check whether it contains a black switch, representing a symbol, or a white Lego block, representing a blank cell. The Lego tape is made up of 32 cells.

    Photo: Centrum Wiskunde & Informatica

  • A rotating beam with two orange arms mounted above the Lego tape can flip the black switches in both directions - either inscribing a symbol on the tape or erasing it.

    Photo: Centrum Wiskunde & Informatica

  • The machine reads from the Lego tape.

    Photo: Centrum Wiskunde & Informatica

  • Here you can see the machine representing the computation of 2 + 2.

    Photo: Centrum Wiskunde & Informatica

  • And here the machine is representing the result of the 2+2, which is of course 4.

    Photo: Centrum Wiskunde & Informatica

  • The movement of the Lego tape and the operation of scanner are controlled by a series of corkscrews and rotors.

    Photo: Centrum Wiskunde & Informatica

  • A side view of the machine.

    Photo: Centrum Wiskunde & Informatica

  • Another close-up of the machine.

    Photo: Centrum Wiskunde & Informatica

The Turing Machine is a theoretical model of how computation takes place. It dates from 1936 and inspired the pioneers who created the modern digital computer. The machine was described in a paper, On Computable Numbers, written by British mathematician Alan Turing.

Researchers at the Centrum Wiskunde & Informatica (CWI) or Centre for Mathematics and Computer Science in Amsterdam in the Netherlands decided to demonstrate the principles of the machine's operation by building a Turing Machine using a Lego Mindstorms NXT set.

The machine is part of the Turings Erfenis exhibition at the centre, which is running until October to mark the centenary of Turing's birth.

Photo: Centrum Wiskunde & Informatica

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By Nick Heath

Nick Heath is a computer science student and was formerly a journalist at TechRepublic and ZDNet.

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