Rainer Werner Fassbinder lived fast, died young and left an awful-looking corpse, in 1982, at the age of 37. But not before writing, directing and producing dozens of movies, as well as plays, television series and the odd radio drama or book. Nonetheless, somehow, in between the endless chain of great subversive melodramas that made his name internationally in the mid-1970s, the director found time for this delirious, two-part conspiracy thriller.

BD, pronounced bédé, is short for "bande déssinée", the French equivalent of the comic-strip or graphic novel, which has long been accorded a popular affection and cultural standing well beyond that of its anglophone equivalent. Luc Besson says he was weaned on BD, which comes as no surprise to anyone familiar with his films. The only surprise is that it has taken him so long to direct an adaptation of one.

Neil Jordan’s smaller films have often betrayed a fascination with wispy visitants from the borderlands of gender. In The Crying Game the beautiful young call girl turns out, in one of cinema’s more jawdropping reveals, to be somewhat less she than he. Breakfast on Pluto found Cillian Murphy’s girly boy swishing around working-class Dublin in frocks and furs. And now comes Ondine, Jordan’s reimagining of the watery fable transplanted to the rugged shores of Cork.

Must rush, have to hurry: like the fretful White Rabbit with his pocket watch, fans have been eagerly anticipating the arrival of Tim Burton's Alice, which finally arrives in cinemas this week, albeit for a limited period following the controversial decision to push the film out quickly on DVD. Mindful of this, I hastened to the IMAX, Waterloo to catch it in 3D, larger than life and twice as natural, on the very biggest screen available. 30,000 people have already pre-booked tickets for Alice at the London IMAX. Is it worth the wait?

The action is set within a framing story. Alice, now aged 19, is about to be pushed by her widowed mother into an engagement to a smug upper-class twit. So down the rabbit hole she plunges to escape to a parallel life that she dimly remembers from her childhood dreams. Her adventures invoke Lewis Carroll's familiar line-up of fabulous creatures, even if these don't always appear quite in the order they do in the books.

The indispensable star cast - some seen caked in extraordinary make-up, others heard voicing CGI characters - includes Michael Sheen (the Rabbit), Alan Rickman (the Caterpillar), Barbara Windsor (the Dormouse), Stephen Fry (the Cheshire Cat), Timothy Spall (Bayard the Hunting Dog) and, not least, Johnny Depp, kitted out with an orange fright wig and green cat's-eye contact lenses as the Mad Hatter, and Helena Bonham Carter as a grotesquely distorted Red Queen.

Burton and Carroll, those twin dark fantasists, should have been a marriage made in heaven. But there's a third party in this union - Walt Disney Studios - and so things get a bit crowded. The director makes the point that the books are episodic, with Alice wandering through a suite of loosely linked encounters. To make the narrative more film-friendly, he sends her on a trite inspirational trip towards personal empowerment in the company of humorous, loveable sidekicks, courtesy of the screenplay by Linda Woolverton, a seasoned Disney alumna (Beauty and the Beast; The Lion King).

Mia Wasikowska looks gorgeous as Alice and gives a very spirited performance, but you sense Burton is secretly more interested in the Mad Hatter (when, after all, did he last create a great female character?); the role is vastly beefed up for the benefit of Depp, the director's long-time collaborator and male muse, who has, it must be said, tremendous fun with it. The climax is a by-numbers joust between Alice and the Jabberwock, a monster controlled by the Red Queen (the contradictory script endorses her rebellion against her mother, while requiring her reluctantly to embrace this pre-ordained destiny as dragon-slayer). It's all surprisingly ordinary.

Visually the film is eye-popping, though the luxuriant blue-tinged tropical Wonderlandscapes, with their strange creatures whizzing through the air would have been a good deal more impressive if I hadn't already seen Avatar to which this bears a marked family resemblance. The 3D isn't always all it might be either, especially in the "real-world" scenes, and, sitting near the front of the IMAX auditorium, I experienced ghosting at the fringes of my field of vision.

For a truly strange Alice you could do worse than to watch the first ever screen version, recently restored by the National Film Archive and available to view here. In 1903, this bizarre little nine-minute fragment, made decades after Carroll first published his original stories, represented the state of the cinematic art. Today it comes closer than all the extravagances of Hollywood to capturing their fragrant spirit. Curiouser and curiouser.

ALICE'S ADVENTURES ON STAGE AND SCREEN

Alice, Scottish Ballet. It should be a capital crime to attempt an Alice ballet - off with their heads

Alice's Adventures in Wonderland, Royal Ballet. Even the best butter would not help this plot-less evening

Alice's Adventures Under Ground, Barbican. Gerald Barry's crazy velocity berserks both Alice books in rude style

Alice in Wonderland, BBCSO, Brönnimann, Barbican. A curious tale gets a riotous operatic telling from composer Unsuk Chin

Alice Through the Looking Glass. Mia Wasikowska, Helena Bonham Carter and Johnny Depp back in inventive if unfaithful Carroll sequel

Jan Švankmajer's Alice. The great Czech animator's remarkable first full-length film

wonder.land, National Theatre. Damon Albarn’s Alice musical has fun graphics, but a banal and didactic storyline

Overleaf: watch the trailer to Alice in Wonderland

There is a sequence in which a monstrous tree of otherworldly dimensions, its boughs as sturdy as oaks, its twigs as vigorous as saplings, crashes spectacularly to earth in roaring, creaking, shattering, time-expanding slo-mo. In a film that’s full of them, this is very much the premier-cru money shot. Remember the last time the director, deploying the computer-generated forces of a sound-stage deity, downed another very large object? Back then it was a boat. This time it’s a piece of wood. Tiiim-ber-r-rr!!

They're back! Bella Swan and Edward Cullen (otherwise known as Kristen Stewart and Robert Pattinson) are once again smooching on a screen near you. I turned up one hour early for a showing of the new Twilight movie, and the damn thing was already sold out. Which suggests the film will do every bit as well as, if not better than, its predecessor, which made $383 million worldwide.