Yayoi Kusama made a spectacular entrance to her Tate Modern exhibition this morning, sporting a day-glow orange wig, a red puffa jacket, and a red skirt adorned — like her wheelchair — with her signature polka dots. Freshly arrived from Japan, the grande dame was seeing the show for the first time, and she looked quietly pleased as curator Frances Morris pointed out some of her artworks and memorabilia. "See, this is your plane ticket, from when you flew to Seattle in 1957." Kusama nodded, taking it all in. In a room full of her early accumulation sculptures, she even shed a small tear, discretely wiped with a polka-dot handkerchief.

What this exhibition demonstrates so brilliantly, though, is that there is much more to Kusama's work than her dots. The show retraces the journey of a woman whose psychedelic visions have been from very early on combined with a restless taste for experimentation and a fierce determination to succeed. The paintings and works on paper realized in the late 1940s and early 1950s, while she was still living in her hometown of Matsumoto, are saturated with Surrealist influences; shapes redolent of Salvator Dalí's, Joan Miró's, and Roberto Matta's crop up again and again in the dark purples and browns of Kusama's first palette. But her affinities with Surrealism run deeper than formal resemblances. The artist's production is an exploration of her own subconscious, a voyage into herself — one she is eager to share. By the late 1950s, Japan had become too small for Kusama's ambitions. She writes in her autobiography: "For art like mine, art that does battle at the border of life and death, questioning what we are and what it means to live and die — [Japan] was to small, too servile … and too scornful of women. My art needed a more unlimited freedom, a wider world."

And off she went, to Seattle first, where she had a solo show at Zoe Duzanne Gallery, and then, six months later, to New York City. Around that time, she wrote to another grande dame, Georgia O'Keeffe, asking her advice on how to develop a career in the States. (The answer, which came in a letter included in the exhibition, was stern: "When you get to New York, take your pictures under your arm and show them to anyone you think might be interested.") Although some early works bear motifs that were to become the artist's trademark a decade later, it was in New York that Kusama developed what could be considered her early mature work. For the "Infinity Net" paintings — that she developed , some say, as a response to the then prevailing abstract expressionism — the artist repeated hundreds of white scalloped brushstrokes on black backgrounds, delimiting in the process round zones of colour. These works appear meditative on two levels: for the artist during the mind-numbingly repetitive making process, and as objects of contemplation, the canvases quietly pulsating through their accretions of white paint.

This very principle of accumulation defines Kusama's work; it transcends the real, turning the banal into the phantasmagoric. Her accumulation sculptures, covered with soft white fabric phalli or bananas, charge the atmosphere with a humorous eroticism. Kusama calls these works the "Sex Obsession" series, as if to go to the bottom of her own emotions, she had to lose herself in their representations, on the verge of being defeated by their numbers. In the 1963 "Aggregation: One Thousand Boats Show" held at Gertrude Stein Gallery in New York, and recreated at Tate, she covered a small boat and oars with white phalli, the ensemble presented in a dark room wallpapered with pictures of the boat itself. There's a dizzying echo between the piece and its jewel-box-like room, a sense of disorientation through repetition that Kusama has now cultivated to a very fine art.

During the heyday of flower power, the artist gave free rein to her love for performance: she paraded in NYC in full Japanese regalia, convinced her pals to paint dots on each others during her "Body Festivals," and posed, naked, burning the American flag on Brooklyn Bridge. Some of these moments are recorded in the film "Kusama's Self-Obliteration" (1967). In 1973, she went back to Japan, and in 1977 voluntarily admitted herself to the psychiatric hospital where she still lives today. The confinement, far from hampering her creativity, seems to have focused it. At this stage of her career, the installations gradually became more disciplined, either gathering a multitude of small elements like in the hand-sewn "Clouds," or presented in boxes, as if mimicking the artist's own physical situation. The motifs in her paintings from that period and the years that followed also appear more complex, more intense, more precisely executed.

The exhibition's grand finale is "Infinity Mirrored Room" (2000-2012) a large-scale installation of tiny coloured bulbs glowing in the dark, and repeated at infinitum by the reflective walls. It's mesmerizing — it is conceived to be so, and thus perhaps lacking some of the freshness of Kusama's most recent paintings on show both in the penultimate room and at Victoria Miro Gallery. In this latest body of work, Kusama undercuts her own rules, incorporating figurative elements to some of her signature motifs, and nodding, in turns, to outsider art, cartoons, and her past self. At 82, she's up for a challenge. Once again.

To contact the writer of this story, write to Coline Milliard at cmilliard[at]artinfo.com