John Westbrooke looks back over a six-decade career at Tate Britain

This first thing you wonder on seeing this retrospective, the first in 28 years, is “Just how many David Hockneys have there been?”

He’s worked in a variety of media over the years (recently it’s been iPads), tried a wide range of styles, and tackled many different subjects. But the curators have pinned down one continuing concern: with the way an artist makes a permanent record of a fleeting impression we’ve picked up with our senses.

Our eyes can deceive us. The Model with Unfinished Self Portrait, for instance: a model curls up on a couch while behind him Hockney sits at a table sketching. But the unfinished self-portrait is actually a separate painting, which the artist propped up behind the model and recreated. Or Play Within a Play, in which a man is shown with his face and hands squished up against glass – real glass, it turns out, bolted to the canvas.

Hockney became famous early, with pop art works that were, and weren’t, overtly gay. Titles like We Two Boys Together Clinging are straightforward enough but what we’re seeing is not always so clear: one painting seems to involve sex, but with tubes of toothpaste, which might be caution, or humour, or just abstraction.

Soon, however, he settled on a form of naturalism and became a man of two worlds, England and California. He was one of many chroniclers of 1960s London – Mr and Mrs Clark and Percy remains one of the Tate’s most popular postcards – but when he turned up in Los Angeles, he realised it had scarcely been painted, and decided to become “the Piranesi of LA”.

How to paint a city that singularly lacked the dungeons Piranesi specialised in? He found the answer in geometry: the rectangles of street grids and of skyscrapers and domestic architecture, the triangles of sprinklers on lawns. Sinuous lines represented the surfaces of swimming pools.

The most famous of them all, and still a contender for Best in Show, is A Bigger Splash, from 1967: blue for the sky, another for the water, and the clean lines disrupted by a chair, a couple of palm trees, a diagonal diving board, and the great white splash where someone unseen has just jumped in.

Hockney spent some time in the 1960s and 1970s painting large double portraits, several of which are hanging in the show. They were prompted by his purchase of a camera, which could do a lot of things but, he decided, couldn’t show depth and weight as painting could.

The work was still essentially two-dimensional, and yet there’s a palpable tension between his subjects, a couple of whom look as if they’ve come to arrest their partners. In Christopher Isherwood and Don Bachardy, the former is glaring at the latter across a bowl of fruit. In the melancholic Portrait of an Artist (Pool with Two Figures) a man, fully dressed and ready to leave, watches another swimming.

If Hockney had taken early retirement at that point, his reputation as Britain’s best known and best loved artist would already have been secure. Remarkably, now pushing 80, he’s kept experimenting, working and thinking about how to represent things.

In 2001 he published a book, Secret Knowledge, which argued persuasively that western artists had for 600 years been using optical devices such as prisms and mirrors to produce more “realistic” images; some that he produced himself are on display and yes, you can see the difference.

But he’s also argued against the effectiveness of traditional perspective in art, and claimed that photography is fine as long as you don’t mind the split-second viewpoint of a paralysed Cyclops. In the 1980s he experimented with taking dozens of photos of a scene, all from different angles, and sticking them together as a collage, so that the viewer experiences not just a multiplicity of viewpoints, but the experience of passing time; the most striking of these, The Scrabble Game, shows people at different stages of putting words together.

In the south-west US and in his native Yorkshire, he painted illusionary road trips depicting in one image, or sometimes several gathered together, everything you might see in hours of driving. (Bigger proves not always to be better, though, and Yorkshiremen and Angelenos alike may struggle to recognise the lurid colours in some recent works.)

Though he’s now back in LA, the show ends firmly, and brilliantly, in Britain. One exhibit, The Arrival of Spring in 2013, gathers 25 charcoal drawings together, a reminder of how fine an observer and draughtsman the artist has always been.

For the other, The Four Seasons, he fixed nine HD video cameras to the front of a Land Rover and drove slowly through the Woldgate Woods in Yorkshire – then did it again, at three-month intervals. The nine videos, each shot from a slightly different angle and showing the same ride in four seasons, screen simultaneously on four walls of a room. It’s a mesmerising encapsulation of his search for ways of depicting space, depth and time. Goodness knows where Hockney goes next.

David Hockney, showing until 29 May 2017 at Tate Britain (then the Pompidou Centre in Paris and the Metropolitan Museum in New York); open till 8pm on Saturdays and 10pm on Fridays. Adults £17.70, concessions available.

www.tate.org.uk/whats-on/tate-britain/exhibition/david-hockney