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Modern sculpture rarely surprises us any more. The idea that modern art can only be seen in museums is mistaken. Even people who take no interest in art cannot have failed to notice examples of modern sculpture on display in public places. Strange forms stand in gardens, and outside buildings and shops. We have got quite used to them. Some so-called 'modern' pieces have been on display for nearly fifty years.

In spite of this, some people--including myself--were surprised by a recent exhibition of modern sculpture. The first thing I saw when I entered the art gallery was a notice which said: 'Do not touch the exhibits. Some of them are dangerous!' The objects on display were pieces of moving sculpture. Oddly shaped forms that are suspended from the ceiling and move in response to a gust of wind are quite familiar to everybody. These objects, however, were different. Lined up against the wall, there were long thin wires attached to metal spheres. The spheres had been magnetized and attracted or repelled each other all the time. In the centre of the hall, there were a number of tall structures which contained coloured lights. These lights flickered continuously like traffic lights which have gone mad. Sparks were emitted from small black boxes and red lamps flashed on and off angrily. It was rather like an exhibition of prehistoric electronic equipment. These Peculiar forms not only seemed designed to shock people emotionally, but to give them electric shocks as well!

Why not use with each other there? What is the difference between them?

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The verb attract is transitive and, in active voice sentences, normally takes the two things that are attracted as subject and object. There is no need to use a preposition.

A magnet attracts iron filings.

The sentence that you quoted is reflexive, and works the same as an active voice sentence: again, no preposition is required.

A magnet and iron filings attract each other.

When attracted is used in passive voice, there is no subject: it is possible to attach the agent (the subject in the active voice version) using the normal agent-preposition by. According to this NGram graph, the preposition to is, however, more widely used.

Iron filings are attracted by a magnet.
Iron filings are attracted to a magnet -more common.

with can be used in the sense using though, as this NGram graph shows, its usage is very uncommon. Here is an example

Iron filings can be attracted with a magnet.

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