'I wanted to dress rock stars,' Anna Sui declared at London's Fashion and Textile Museum, gesturing towards a 1992 Naomi Campbell grand finale dress with faux fur embellishments on display at its new exhibition, The World of Anna Sui.

Indeed, designer Anna Sui herself is a certifiable rock star. Sui decided she wanted to become a fashion designer at the age of four. She dedicated her life to the craft and left suburban Detroit for New York to redefine American fashion, starting with her pivotal grunge collection in 1993. There are now more than 300 Anna Sui stores in 35 countries. The designer’s encyclopedic knowledge of fashion history, dedication to the creative process, and playful, ostentatious elements are what makes her first retrospective especially striking.

A neat arrangement of Sui's inspirations opens the exhibition, leading you down a pristine hallway. Memorabilia that predates Sui's first fashion show is presented alongside imagery from designers that inspired her – Zandra Rhodes, Bill Gibb, Biba. Then you reach the wardrobe doors and enter into the main exhibition – Wonderland. For this, the museum has been transformed into Anna Sui’s space, reflecting her undiluted aesthetic. Rock-n-roll posters, black lacquered Victorian furniture, Tiffany lamps, purple walls inspired by Sui’s first store in New York and her childhood bedroom.

The Anna Sui store feel is perpetuated by the mannequins elevated on red podiums. Arranged by clothing themes ('archetypes') to show the stylistic tropes recurrent throughout her 30-year career – Americana, Androgyny, Fairytale, Grunge, Nomad, Mod, Punk, Schoolgirl and Surfer. Looks from collections 20 years ago are grouped with those from more recent seasons. Despite the range of designs, her signature outlandish style brings cohesion to the chaos.

By organising Sui’s looks thematically rather than chronologically, curator Dennis Nothdruft draws visitors' attention to the threads running through each individual outfit, and the thread running through the exhibition: the only constant in the outfits is inconsistency, with printed textiles, layering, power pattern clashes, colours, Sui has a uniform vision that redefines the concept of the term.

Anchored in American history and pop culture, each look was meticulously researched and incorporated elements contingent on her current passion. This is apparent in the display of mood boards in the upstairs space. At the exhibition opening the designer explained the board that became her S/S 17 Americana collection, describing how she’s inspired by dreams and fantasies, 'but also current events, and it becomes a mishmash of what’s going through my brain at that period of time'.

What distinguishes Sui from similar designers is her capacity to render inconceivable fashion choices into garments that are undeniably desirable: positive punk, pirate Marie Antoinette, rich hippie. Her collection colour palettes are inspired by psychedelic posters, she cuts up curtains à la Scarlett O’Hara, and has master milliners scalp stuffed animals and turn them into hats.

With more than 125 full looks, select cosmetics, collaborative projects, mood boards, photographs and cultural ephemera, The World of Anna Sui is as exhaustive as any artist’s first career retrospective. Fashion may well be the meeting point of self-expression, art, consumerism, and cultural history – but it’s also supposed to be fun, and fun is what Anna Sui does best.