“Keep Austin weird” is, according to a brochure I happened to read some time ago, this city’s strapline. It sounds somehow artificial, not only because it was coined, as it turned out, by a group of lobbyists named the Independent Business Alliance; but, also, because it is objectively hard to put my finger on what, exactly, makes this place “weird”.

Sprawl spreads unchecked all around a city centre ringed by highways. A flourishing of skyscrapers of questionable sizes and shapes sprouts where you'd expected the centre to be, with hotel chains – W, Fairmont, Hilton, JW Marriott, Sheraton, Four Seasons, Hyatt – so ubiquitous to generate sympathy for the only two banks – Bank of America, Chase – that dared flying their flag there.

But, perhaps, there is something. It’s not the 6th Street bars strip, for every city has one, and it’s not even SXSW, because of the same reason, albeit less frequently. It’s not the Texan Lone Star, merged with the Gay Pride rainbow flag, fluttering above a closed for the day.

It’s an Ai Weiwei sculpture made of hundreds of chrome bicycles, dizziness-inducing in its splendour. It’s a girl jogging along the lake embankment, a T-shirt proclaiming, “I support planned parenthood” written across her chest. It’s the fact that I’m the only one to take notice of it.

In a world of Madrids and Berlins, I’m doubtful whether Austin would make it on the list, but when your peers are Fort Worth or Birmingham then perhaps, yes, Austin is “weird”, in an American teenager sort of way.

Downtown’s ordinate grid of streets descends in good order from Texas’ State Capitol to the lake. The Capitol itself is what you’d expect from such a building and, a welcome change from the usual white-plaster cliché, is granite-burgundy. Built by migrants and convict labour, it’s flanked by a monument to the emancipation of Texas’ African Americans. I take my turn to photograph it after Indian families and groups of Stetson-wearing Latinos. As the shutter whirrs and buzzes I think at the black tour guide I’d heard lecturing a group of Asian tourists on 6th Street of how, when he was a boy, the Ritz was the only theatre allowing black punters.

Turtles, cormorants and seagulls jostle for space on a floating barrier on the lake, next to the beautiful lakeside walk. The walkway, sneaking in and out of the vegetation, didn’t feel very Texan, or at least it didn’t seem to fit very much with my own preconception of the state – desert, pump-jacks and 10-lane-speedways. Chinese tourists snap photos of each other against the skyline; tiny mamacitas chirp Christmas greetings into phones plugged to their ears, wishing love to “Mi hermosa”. Three friends in hats, leather gilets and trucker moustache inspect the crab shack.

“Move over bitch. Get out of the way you son of a bitch” yells a homeless man as he careens on a bicycle a good three meters away from us.

The median income for a family in Austin is $54,091 per annum. In spite of that, 14% of the population here lives below the poverty line. According to an estimate, one Austin resident every thousand is estimated to be homeless.

To see how big one in a thousand is, all I had to do was to look at the I-35 overpass by the Shell petrol station just south of the Sheraton Hotel. Whilst three men beg by the slip road, another hundred or so sleep rough beneath the Interstate. Another contingent does the same by the Salvation Army’s office, one block off 6th Street’s bars.

On Christmas Day it’s only us on the pavements. Us, and men and women politely asking for a dollar. I haven’t been enough on these shores to be numbed by the dimensions of the problem of homelessness in the world’s biggest economy, so I quite can’t shake the image away. In my mind, the figures huddled in sleeping bags beneath the overpass merge with the footage of scared villagers taking shelter in their cars after an earthquake in Umbria, uncertain of whether an aftershock will send their medieval homes crumbling down. But no tremors shake the Texan land whilst I’m there.

A remembrance tree laden with origami and two plaques spearhead the efforts to raise awareness on the problem. But it’s deeply laden with meaning, I reflect, that a Bible has been left on a bench next to them. As if it was meant to say that only Him could solve the problem. And, perhaps, not even Him.

Dogs are the undisputed masters of the piece of lake shore straddling between the Hyatt and the rusting bridge where somebody’d risked his neck to stand on a narrow, crumpling ledge to spray-paint two Pac-Man ghosts and the rather cryptic message “I’ve got ninja style kung-fu grip”. Oblivious to its meaning – or perhaps all too aware of it, but unwilling to share it with this visitor – Alsatians battle with Labradors to retrieve bright plastic Frisbees, spaniels go sniffing setters’ butts and pugs oversee proceedings as if they’d already figured everything out a long time ago, something I always suspected but never quite been able to demonstrate.

Meanwhile, an ersatz Rodriguez jams with another guy that could pass for a young Tony Hawk impersonator.

Keep Austin weird.