Alice Anderson's 'Memory Movement Memory Objects': Everyday objects wrapped in copper wire

"Rapunzel, Rapunzel, let down your hair," calls the prince in the Grimm fairy tale. "Rapunzel was at first terribly afraid for she had never laid eyes on a man before." The image of a woman with hair so long that it can function as a kind of ladder is one of the most surreal of the Grimm fairy tales.

Rapunzel is an ingénue, isolated in a tower in a forest by a sorceress. The agony that she must have felt as the prince used her hair to drag his body up the tower is left out of the story. It seems surprising that it was not ripped out of her head at the roots. But magic is the point of fairy tales, which have always combined pleasure with pain.

Feminists have long investigated fairy tales as stories of female subjugation or resistance, with female archetypes who are often sweet or cruel, but lack full humanity. The sweet ones are condemned, then rescued, put to sleep, then woken up. The cruel ones are usually punished.

In 2010, the artist Alice Anderson draped a huge swathe of hair out of the upper story window of the Riflemaker gallery in Soho. Rather than a red flag to a prince, the masses of hair looked mutant. Anderson had bought the hair from a doll factory in China. It was the same fire-red colour as her own, which is long and beautiful and natural. The appearance of an artist, and particularly a female artist, is usually irrelevant, but Anderson's hair has formed the basis of her art. Her hair is her muse.

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Anderson's work has often been seen as a Freudian fairy tale. She was born in 1972 to an English father and a French-Algerian mother. As a child, she remembers being pointed at for her unusual hair. She would invent rituals to calm her anxiety while she waited for her mother to come home, making art out of strands of her own hair, as well as thread pulled from her clothes. In this way, she became an artist. She has since moved on to other materials. In 2011, she bound the entire exterior of the Freud Museum in Hampstead in thick copper cable, which was also the colour of her hair. This house on a quiet residential street, where Freud once lived, was taken hostage by Anderson's pseudo-hair. She was making a point to the man who had said that weaving by women was proof of genital deficiency. The art of weaving is historically "feminine". In another Grimm fairy tale, 12 huntsmen have to prove they are truly men by walking past a series of looms without getting excited. The presumption is that women would not be able to contain themselves.

Memory Movement Memory Objects, an exhibition of Anderson's new work, has just opened at London's Wellcome Collection. Anderson is a great choice of artist for the gallery, which is continually inventive and interdisciplinary. All of the objects on display are wound and bound in copper wire. The first half of the exhibition is wonderful, but the second half loses some of its majesty. All the works were made over the last three years. I would have preferred to see some of her older works too – the hair sculptures, and films starring uncanny looking dolls.

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The first room is the most impressive – a black 1968 Ford Mustang is spotlit in darkness. It is dramatic, like a scene from David Lynch's Wild at Heart. The interior of the car has been burnt out, rusted with copper. When I visited, Anderson herself was winding copper wire around and around the car, circling it like a predator circles its prey, enshrining it in denser and denser layers of shimmering lines of orange metal. The wires are so fine that they appear like the silk web of a spider.

Anderson calls this process mummification – the word may be a deliberate Freudian slip. Much of her practise has focused on the mother-daughter relationship. The act of binding seems to express the ambivalence of motherly love – cosseting and tender on the one hand, stifling and possessive on the other. It is both protective and destructive. This was expressed most powerfully in Louise Bourgeois's giant sculpture of a spider, with its sack of marble eggs, which she called Maman.

In the next room, the beauty and scale of Anderson's practise is revealed, with a series of works called Recognisable Objects. Each object is bound in copper and spotlit on a plinth, surrounded by darkness. Each is illuminated, both quiet and sacred. There is a holy air. However, most of the objects are ordinary: a plug, keys, a record player, a wide-screen TV. The copper wire too is ordinary – most commonly used for electrical wiring due to its tensile strength. Here it assumes the value of a precious metal.

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One of the most striking works is a bound staircase at the far end of the room that ascends all the way up to the ceiling then stops. This is a celestial escape or an existential "no exit". It goes to heaven or nowhere. As well as being beautiful, there is a paranoid and obsessive dimension to this aesthetic. The repetition goes on and on. Anderson has said she makes the work out of a necessity, "it's a way of living, it's a way of thinking, it's how you breathe, basically… there is something stronger than you."

The objects don't work so well under bright light – the copper can appear tacky. This is the case in a room full of sculptures of hybrid creatures called Assemblages. There is a hat-rack fused with a gun, which hints at human form; a skeleton slumped in a corner with leg bones coming out of its arm sockets. These are too fussy.

The works are most successful when they are simple and pure in form. An encased basketball assumes Zen gravity, a tangle of copper cable rope in another dark room is elegant and weird, a simple copper circle on a wall, spotlit, appears like a symbol from a cryptic system. Indeed, mummification was the Ancient Egyptian process of transporting the dead to the other world.

Most of the objects that Anderson binds in copper are defunct technological gadgets. In a corridor adjacent to the gallery, unbound objects await their fate: a VHS player, audio cassettes, DVDs, a cordless phone. She is making a comment about how much of our lives are preserved online, while physical objects are neglected. These once loved things are quickly discarded.

Once bound, the objects lose their purpose: the TV can no longer be watched, the plug can no longer provide electricity. They are beautiful, but useless on a practical level. They exist only to be looked at. In this way, Anderson seems to be making a complex point about being female.

Since 2012, Anderson has run a "travelling studio", whereby people are invited to bind objects alongside her. Rather than simply hiring assistants, this is an interesting way of turning a private ritual into a kind of communion. Visitors to the gallery can also help with binding – there are copper bobbins available, and dramatic black gowns to wear while you're doing it.

A strange element is the pulsing techno that can heard throughout the exhibition, coming out of a pair of bound speakers. Perhaps this rhythm emulates the rhythm of binding – but the objects would be better viewed in silence.

In a final series of works, Distorted Objects, Anderson reminds us of the destructive potential of her art. These objects have buckled and folded back on themselves under the strain of the copper. They are crippled. They are a warning against allowing oneself to be cocooned – by mother or anyone else.

'Memory Movement Memory Objects' is at the Wellcome Collection, London from 22 July to 18 October; wellcomecollection.org