Lebbeus Woods, the cult experimental American architect, died on Tuesday in New York, aged 72.

Born in Michigan in 1940, he worked for Eero Saarinen in the 1960s, but became best known for his conceptual work, which explored a kind of architecture "that gives us the opportunity to experience a type of space we haven't experienced before", through a vast body of intricate drawings and models.

Dynamic compositions of splintered surfaces and twisted wiry forms, his fantastical scenes depicted alternative worlds, glimpses into a parallel universe writhing beneath the earth's crust.

His dystopian visions were often set in disaster stricken cities – from Sarajevo to Zagreb, Havana to New York – and often adopted an almost medical metaphor, faceted accretions acting as "scabs" over the "wounds" of a building damaged by war and natural catastrophe. "Architecture should be judged not only by the problems it solves," said Woods, "but by the problems it creates."

Beyond inspiring a whole generation of architects, he also lent his talents to Hollywood, working briefly as the conceptual architect of Vincent Ward's ill-fated Alien III – abandoned in favour of David Fincher's much more successful Alien 3, which Woods later described as having "unremarkable sets" and "unrelenting grimness."

Woods' only built project was completed this year, the Light Pavilion within a vast complex of towers in Chengdu by Steven Holl – who explains more about the project below, along with a series of reflections from architects and academics, writers and critics who have been inspired by his work over the years.I distinctly remember meeting Lebbeus Woods a couple of decades ago at an Architecture Forum at the Royal Academy when I was working first-time around at Architectural Design as one of the most junior of assistant editors for Andreas Papadakis. Lebbeus was a very charismatic man in his prime. We were publishing a monograph on his work Anarchitecture: Architecture is a Political Act (1992), which contains some of his most potent images. Most of the Academy staff then were under 25 and Lebbeus was as happy to chat with us, probably more so, than with the other dignitaries at the RA.

Looking back at Woods' drawings now contained in that monograph – projects such as the Zagreb Free Zone and Berlin Free Zone – the rawness of their dystopian vision is no less extraordinary. He seemed to both capture the visionary qualities of Deconstruction while anticipating the all-engrossing preoccupation with cybernetics. For many decades, his images and his teaching have continued to fuel the imagination and aesthetic bite of architects and students alike. He will be sadly missed, but I have no doubt that he will remain a touchstone as one of the greatest Paper Architects.

Helen Castle

Editor, Architectural Design

Without Lebbeus, the world of architecture will be immeasurably poorer. He was on the side of architecture rather than building, the lifelong student rather than the architect. He reminded us that to believe in the existence of architecture you need to feel it. Elaborate drawings of found spaces full of whirring sticks and lines of energy were genuine attempts to materialise the experience of space. Who else could do this? Nobody!

Nigel Coates

Architect and designer

Lebbeus was one of the last of a generation of visionaries who dedicated a life in architecture to drawing an alternative world, one important for the present and the future. His singular mind and hand will be deeply missed.

Peter Eisenman

Architect and Professor of Architecture at Yale University

Lebbeus was a man of many gifts. He was an incisive, razor-sharp thinker, who sought out the flash points of political and social conflict and made them the bricks and mortar of his architecture. He was the most talented draughtsman of his generation – more than drawings, parallel universes flowed from his pencil. But his rarest gift – one that he cultivated throughout his life – was his generous, absorbent and humble mind. He didn't just teach; he never stopped learning. He was happiest with a crowd of young people around him, deep in conversation, every generational barrier cast aside: happiest not because they worshipped him as a hero, but because new worlds were unfolding in front of him. When we invited him to take part in Postopolis NYC, the first of a series of bloggers summits organized with Geoff Manaugh at Storefront gallery, he was so excited by the possibilities of the web that when he returned home he set up his own blog. The conversation that began that afternoon in Storefront will continue long after the sad day of his passing.

Joseph Grima

Editor, Domus magazine

It's a tremendous loss. Lebbeus was a very close friend and great architect. His visionary work explored the fantastic potential and dynamism of space with radical proposals and powerful drawings that were extremely influential. His Light Pavilion in Chengdu will be testament that our profession has lost a great voice.

Zaha Hadid

Architect

I met Lebbeus in February 1977. I arrived at Leb's small loft in TriBeCa to find him standing bent over an enormous black and white drawing of a Piranese-like urban vision. His cigarette had a long grey ash that was about to drop as he greeted me briefly and turned to show me the amazing drawing.

Lebbeus and I began to meet every couple of weeks at a diner that served "all-you-can-eat-for-a-dollar" bean soup. Our ongoing philosophical discussions led to our sharing reviews in the design studios we were teaching.

In 1977, I began work on a project titled Bronx Gymnasium-Bridge that would become the first issue of Pamphlet Architecture. Lebbeus made the third issue with the project Einstein's Tomb. It was an amazing vision for a tomb about Albert Einstein – a strange architecture that would travel on a beam of light around the Earth. Today, I imagine that tomb is occupied by the spirit of Lebbeus.

The freedom of spirit in architecture that Lebbeus Woods embodied carried a rare idealism. Lebbeus had very passionate beliefs and a deep philosophical commitment to architecture. His designs were politically charged fields of reality that he created.

In 2007, when I first received the commission to realise a 3m sq ft urban project in Chengdu, China, I began studies to shape a new public space. The building fabric would not strive for iconic objects, but rather a simple architecture sliced by sunlight shaped space. "Buildings within buildings" are cut into this fabric, sitting in gaps that are 8-10 storeys in the air. I invited Leb to do one.

Lebbeus's Pavilion, constructed of huge beams of light, can be entered at several levels. Walking on sheets of glass suspended by steel rods, the view is infinitely multiplied via the polished stainless steel lining the four-storey gap in the building it occupies. It is a brilliant and engaging architecture. An experience there, especially at night, seems to dissolve the view of the city beyond.

This work merges art and architecture as they have merged in the past and are merging in the future. Next week, I will travel to Chengdu, walk into his Light Pavilion, stand suspended on steel rods and imagine Lebbeus's tomb has been launched – on a beam of light.

Steven Holl

Architect and Professor of Architecture at Columbia University

Like many people, I was devastated to learn that Lebbeus Woods passed away two nights ago, just as the hurricane was moving out of New York City and as his very neighbourhood, Lower Manhattan, had temporarily become part of the Atlantic seabed, floodwaters pouring into nearby subway tunnels and knocking out power to nearly every building – an event seemingly predicted, or forewarned, by Lebbeus's own work.

I can't pretend to have been a confidant of his, let alone a colleague, but Lebbeus's influence over my own interest in architecture is impossible to exaggerate and his kindness and generosity as a friend to me here in New York City was a reassuring thing to receive. I say this, of course, while referring to someone whose New Year's toast a few years ago to a room full of friends gathered down at his loft near the Financial District was that we should all have, as he phrased it, a "difficult New Year". That is, we should all look forward to, even seek out or engineer, a new year filled with the kinds of challenges Lebbeus felt, rightly or not, that we deserved to face, fight, and, in all cases, overcome – the genuine and endless difficulty of pursuing our own ideas, absurd goals no one else might share or even be interested in.

This was the New Year's wish of a true friend: someone who believes in and trusts your capacity to become what you want to be, and someone who will help to engineer circumstances in which that transformation might most productively occur.

If you were to walk through an architecture school today – and I don't recommend it – you'd think that the height of invention was to make your building look like a Venus flytrap, or that mathematically efficient triangular spaceframes were the answer to everything, every problem of space and habitability. But this is like someone very good at choosing fonts in Microsoft Word. It doesn't matter what you can do to the words in your document if those words don't actually say anything.

Lebbeus will be missed for his formal inventiveness: buildings on stilts, massive seawalls, rotatable buildings that look like snowflakes. Deformed coasts anti-seismically jewelled with buildings. Tombs for Einstein falling through space.

But this would be to miss the motivating absence at the heart of all those explorations, which is that we don't yet know what the world is, what the Earth is – whether or not there even is a world or an Earth or a universe at all – and architecture is one of the arts of discovering an answer to that question. Even flat-out fabricating an answer to this, meaning that architecture is more mythology than science. But there's nothing wrong with that. There is, in fact, everything right with that: it is exactly why architecture will always be more heroic than constructing buildings resistant to catastrophic rearrangements of the earth, or throwing colossal spans across canyons and mountain gorges, or turning a hostile landscape into someone's home.

Architecture is about the lack of stability and how to address it. Architecture is about the void and how to cross it. Architecture is about inhospitability and how to live within it.

Lebbeus Woods would have had it no other way, and – as students, writers, poets, novelists, filmmakers, or mere thinkers – neither should we.