In case you didn’t know, we live in a ‘post-minimalist’ age, sculpturally speaking. Not a maximalist age, though some of the works in the Hayward’s new sculpture show are huge – an age of revolution against neatness.

Who’s to blame for this call to disorder? Women. The two prime movers of this movement, if you can call it that, could not be more different, but both rebelled against minimalist geometry. As a student at Black Mountain College in the late 1940s, Ruth Asawa travelled to Toluca, Mexico, and saw villagers looping wire to make baskets for eggs. It struck her as a way of drawing in three dimensions and later, after becoming a mother of six, of working from home.

Some of the artists here seem to take a perverse delight in making their medium do the impossible

Over the years, her distinctive hanging ropes of lobed wire forms grew increasingly intricate and involuted, turning inside out so that smaller forms appeared nested within. Lynda Benglis, meanwhile, found a simpler way of subverting the rectilinear by sculpting with poured latex and polyurethane foam: ‘I like things to flow,’ she said. Both women took inspiration from the natural world: Benglis from the rivers, swamps and crawfish mounds of her native Louisiana; Asawa from ‘observing plants, the spiral shell of a snail, seeing light through insect wings, watching spiders repair their webs in the morning’.

The 19 other artists in this 60-year survey fall roughly into the camps of Benglis or Asawa. The Benglis tendency culminates in the lumbering, lopsided sculptures of Phyllida Barlow, defiantly dirty protests against clean lines that seem to shout: ‘Don’t ever call me aesthetic!’ The Asawa tendency expresses itself in a desire to elevate base materials through craft. In his ‘Blooming Matrix’ series (2018), Choi Jeong-hwa creates elegant ‘stupas’ from junk and industrial parts – a Shard-like pinnacle is assembled from faucet handwheels and a totem is composed of red plastic tubs and funnels – while Tara Donovan’s ‘Untitled (Mylar)’ (2011) is a glittering agglomeration of carefully furled pompoms of polyester film that spills out over the gallery floor like a froth of giant bubbles or a rampaging virus.

‘Sottobosco’ by Holly Hendry. Credit: Jo Underhill. Courtesy of the Hayward Gallery

Rather than go with the flow, some of the artists here seem to take a perverse delight in making their medium do the impossible. Martin Puryear makes Alaskan yellow cedar look as pliable as silk and Matthew Ronay gives carved lime wood the texture of velvet. Ronay’s gangly, brightly coloured forms might have been dreamed up by Dr Seuss on acid, but they are rooted in nature. ‘I started to realise that all these things that you think you invented, nature thought of them first,’ he says. ‘Beautiful textures, colours, divine geometries.’

Natural history used to have a supporting role in sculpture, confined to swags; now it’s playing the lead. Marguerite Humeau’s honeycomb structures and termite mound shapes don’t just look organic, they contain beeswax, wasp venom and termite mushroom culture. With a saxophone soundtrack mimicking the hum of insects, her gallery sounds like a beehive – as well as smelling like one. There’s something disturbing about this faintly odorous installation in a dimly lit room; in another century, Humeau might have been burned as a witch.

A critic complained the art on show was not sufficiently conceptual. So what?

No scent comes off the crocheted yellow tendrils filled with turmeric, clove, cumin, pepper and ginger that dangle above the stairwell in Ernesto Neto’s ‘Iaia Kui Dau Ara Naia’ (2021). The contents must have passed their smell-by date.

Although the show is full of works that look capable of motion, only one of them – ‘Shylight’ (2006-14) – actually moves. This ‘performative sculpture’, an array of harebell-shaped lamps that slowly open their silk and steel shades while descending from the ceiling like fairies on wires, is inspired, like all the work of Dutch collective DRIFT, by movement in nature. But not every inspiration in the show is biological. The idea for the black mushroom cloud billowing up the gallery wall in Olaf Brzeski’s ‘Dream – Spontaneous Combustion’ (2008) came to the artist in a cloud of soot while cleaning his studio chimney.

Hayward director Ralph Rugoff has a knack for choosing exhibitions that breathe life into the gallery’s brutalist spaces, and with When Forms Come Alive he’s done it again. A fellow critic at the press view complained that the art on show was not sufficiently conceptual. So what? It’s phenomenological rather than logical. My one regret is that a show of work so temptingly tactile is full of notices prohibiting touch, except, that is, in the project space off the lobby, where the taut pimply skin of Eva Fabregas’s ‘Pumping’ (2019) – an XXL intestine stuffed with massage balls – thrums like a rumbling stomach to the subwoofers on the electronic soundtrack. Whisper it, but here the gallery attendants have been given mixed messaging on touching. Slip round the back and you could just cop a quick feel.