There's a minor commotion up ahead. Getting closer I see that it's caused by a ring-tailed lemur on a lead. It sits on its haunches in the crook of a girl's arm, gently licking her skin. A handful of schoolkids gather around, touching its fur, cooing. Lemurs aren't native to Mexico City; but it's a place where you can not only buy Bengal tiger cubs, but white Bengal tiger cubs, if you prefer. Or sugar gliders, or meerkats, or leopards. White meerkats or leopards, if you prefer. I watch the lemur and there's something vaguely unsurprising about seeing it on the corner of a residential street. Vaguely Aztec, the more I think – not a million miles from wearing bird-of-paradise feathers in a headdress. As if this valley had made its taste in accessories known to centuries of flowing tenants.
Aztec bling.
It must have been a stunning lake valley: 2,240m above sea level, held in the palm of 11 volcanoes, some active, some sleeping, some dead – and now a stunning city, with all but a corner of the lake system drained. Now humanity carpets the space between them as far as the eye can see. I'm at the end with the lemur, which is south-west, near the edge of the city where it starts rolling into hills, climbing towards the volcano Xitle, whose eruption spat the ground under my feet. I also grew up here, in Jardines del Pedregal, a resonant enough place to start a pilgrimage. Originally a 1940s eco-concept by modernist architect Luis Barragán, the district was an exercise in plumbing clean architectural lines through the nature of lava floes that bubbled and rolled here as rock. That was when the district was an outskirt; now it's a regular fancy neighbourhood, and while Barragán's work is all but invisible, there are still some gems behind the lava stone walls.
The plan is this: Mexico City is dissected by one of the world's longest avenues, Avenida de los Insurgentes, which runs from far out of town in the south, to way out of town in the north – and it's a few blocks from here, so I'll walk it. I admit I cheat some stretches, but it's in the spirit of the place, which anyway is vast; and comes from being over-entertained along the way, which is why I'm here.
On the short walk to Insurgentes it becomes clear that people have made with concrete what Barragán made of the lava floes. The city lives on cement, as if it also flowed down the mountains to settle in petrified squares – poor houses, rich houses, triple-decker freeways, malls, sculptures – all cement, clean and jagged, painted, naked or white, in between parks and clumps of nature; but the valley's sheer scale, along with the size of the sky, rescues it all. Slightly south of here, to the right along Insurgentes, sits the campus of the National Autonomous University of Mexico (Avenida Insurgentes Sur 3000, unam.mx), a modernist enterprise with world heritage status, boasting murals by Diego Rivera and David Siqueiros, plus a library by architect Juan O'Gorman. It is a beautiful campus, but I turn left and head north. Insurgentes is an avenue that veers rather than turns at any point, and where an occasional rise gives a view over the cityscape ahead, or a dip gathers you into a hall of mature trees, shadows, shopfronts, traffic and, since I left, a metrobus system that runs the urban length of the avenue, along what used to be the central reservation.
Mexico City has had to embrace radical change to keep moving, even licensing cars for use only five or six days a week, on a number-plate rotation. Speed isn't an issue for traffic cops here – circulation is, and you'll be just as firmly warned for dawdling. At traffic lights I see crews of vendors, entertainers and beggars poised to slip between the cars. One is a fire-eater. He's just a boy, carrying a bottle of paraffin; when the traffic stops he takes a slug from his bottle and spits a cloud of fire over the street. It's an unhealthy living; but it's a living, and you can't be here without immediately knowing your place on a spectrum of fortune.
A spectrum with ever-increasing extremes.
It's not a long walk to the intersection with Avenida de la Paz; another block to the left brings me to San Angel, the colonial neighbourhood with its flower markets, produce market, cobbled streets, and an old convent with human mummies on display. The sound of songbirds in stacks of wooden cages, and the smell of a million fresh flowers, plus coriander, wood smoke and dirty water, used to drag me exploring as a kid.
It's all still here, even El Bazar Sábado (Plaza San Jacinto, elbazaarsabado.com), a Saturday arts and crafts market that takes over the central plaza. Aside from the city centre, this southern end of town is probably the best pocket of Spanish colonial life; if I turned right at this intersection and walked east a mile or so I would come to Coyoacán, the rustic oasis where Frida Kahlo, Diego Rivera, and even the first conquistador, Hernán Cortéz, had their homes. Frida's blue house (Londres 247, Col. del Carmen, museofridakahlo.org.mx) is open to the public, and worth a visit. Cortéz's first house is open too; now it's the local police station, and maybe only that because no brothel wanted to use it. In a place so fond of monuments, you won't see a statue of Cortéz.
Looking around I see unique Mexican spirit reflected in everything. Spaniards brought a lot of change, but Mexicans chose what to keep, and weaved it seamlessly into their custom. It's as if nobody conquered here – but were themselves absorbed and conquered by Mexico.
Although I started out inside the metropolitan area, there's still a sense of the city growing up as I move towards the centre. Shaded restaurants and boutiques of the south give way to glimpses of glass and steel through the trees, not least from the 52 floors of the World Trade Center, once the Hotel de México. In its shadow, minding out for cracks and dips in the pavement, I enjoy the micro-life of the streets. This is a city that wears its heart and life on its sleeve: here a couple getting passionate on a bench, there a man being honked at for wheeling a piano down the road; in a courtyard garden a family dressed as nobles marks a coming-of-age. Seeing me reach for a camera, they pose, then pull me in for a picture together, to mark the coincidence of our passing.
It's upbeat and bright, the energy of the place – and it feels lucky.
Traffic fumes are mixed with passing food smells from stalls and cafes; you can withstand the first six, then you start lingering through them until you have to stop. As it's one of those cities where honking in traffic is recreation, I wait for a snarl of cars to pass before asking a food stall attendant how he thinks the place has changed.
"Well," he muses, "it's not like the stories you hear from the north."
And that's right: blood from the drug wars tends to stain the whole country, but Mexico City feels safer than when I roamed it as a kid. This isn't a drug war town. It couldn't be. And the police force has vastly expanded in the past three years, mounting a New York-style blitz on crime – no small feat in a megacity, much less the biggest sprawl in the western hemisphere. Patrol cars are everywhere – and I haven't been bitten for a bribe even once.
Along the avenue you notice how much the written words of a place are also a telling decor, street names such as Tlacoquemecatl mixing with San Lorenzo, California and Holbein, showing gradients of culture similar to those on the faces passing by – open and earnest faces descended from pilgrims to these volcanos. After passing Parque Hundido and the City of Sports stadium complex, the avenue flows into a different kind of downtown, becoming an overpass in places as it crosses vital arteries headed east and west. Still, trees, colours and culture hold sway: the valley is spacious enough, low-rise enough, to feel that nothing is on top of you.
Then Colonia Roma looms, and an edgier, more urban cafe culture emerges. A block or two back from Insurgentes the pavements are alive with restaurant tables, bars, parasols, music and chatter – this is how I imagine the streets of a modern Latin American country; you could play a tango here, a salsa, cumbia or merengue, and any of the nations to the south would claim the street as its own. My walking day ends here, friends wait in a cantina, and the hotel is nearby.
The next morning I cheat a few blocks and start at the Covadonga cantina (Calle Puebla, 121), a couple of blocks off Insurgentes. Once the Club Asturias, and reputed to serve a different snail recipe every week, the place looks like a sprawling Spanish bar of the 1950s, with uniformed waiters bustling, and dominoes bashing on to tables as old Spaniards tuck into brandy. It comes as no surprise that since independence, almost two centuries ago, a noble core of Spanish descendants kept a grip on key posts in industry and government here. Whenever I came to the Covadonga I used to imagine they were all in here at once, throwing dominoes and shouting at the heart of the cultural maelstrom they helped create. I don't know if they are all here – it just looks like it. And the snails are still good.
Steadied in this way, I rejoin Insurgentes for the short journey to its crux, past the landmark of Metro Insurgentes underground station, a sunken wagon wheel with a pedestrian plaza and avenues flying off it as spokes. Past this lies the entrance to the Zona Rosa – the Pink Zone – reputedly so named by the great Mexican artist Jose Luis Cuevas, who said the district was too timid to be called red, but too frivolous to be white. The Zona Rosa was fashioned by the city's europhile elite after the revolution; they named its streets after European cities, and built gracious European residences for themselves and the émigrés among them. Then, mid-20th century, it lived a bohemian phase, becoming something like Colonia Roma today – until finally, when I was still a local resident, clubs with boys and girls moved in; and although this is considered a prime tourist zone today, they're still here. It's one of those places where the best-looking street-girls are boys but, this being Mexico, you can hire a lad to point out which are which.
A few blocks ahead, Insurgentes crosses the city's showpiece avenue, Paseo de la Reforma, which has just crawled out of Chapultepec park and grown robust with monuments and gardens. This, for Insurgentes, is officially the heart of town. Here Insurgentes Sur becomes Insurgentes Norte, and the city begins to reach towards northern hills, through poorer neighbourhoods, outskirts, heavy and light industrial zones, and on to the pyramids of Teotihuacan, or further still, 18 hours' drive away – the border that everyone makes such a big deal about. I haven't walked the whole distance of the avenue, perhaps only a third of it, from one edge to the middle – but in a place so saturated with meaning, it's plenty.
Only one last visit seems fitting, further north off Insurgentes – the Basilica of Our Lady of Guadalupe (Plaza de las Américas 1, Villa de Guadalupe, virgendeguadalupe.mx), home of Mexico's own virgin. Because in 1531, within a decade of the Spanish conquest, a native Mexican, Juan Diego Cuauhtlatoatzin, saw the virgin appear over Tepeyac hill, and had her image burn into his apron. The apron with her image hangs inside the basilica, but I'm not here for that.
Instead I look back from here, across the megalopolis I barely crossed, with all that I found charming – and remind myself that since 1531 a great number of people do this walk on their knees.