It has been a dozen years since the first Animal Crossing, and there's still nothing quite like it. These are perhaps Nintendo's warmest and most human games; part town-builder, part life simulator, each an evolving paradise for its players. New Leaf casts you as the mayor of a town populated by anthropomorphic animals, which over time grows and adapts to your decisions and style. But not in-game time; New Leaf works in real time.

This is not a game you sit down with for a few hours on the weekend; it's something you check in on, even for 10 minutes, every day. If you get a house extension, for example, it will be ready tomorrow – literally. This principle certainly has its quirks, and closed shops can be frustrating, but is essential to how New Leaf's ecosystem works; the bugs, fish, and many other surprises tie into the day and time.

Very few games pace themselves like this, but Animal Crossing goes even further – its unit of composition is weeks rather than days, as your town slowly grows from bare grass and a few scattered houses into a bustling and character-packed world. The seasons are tracked, as are public holidays, and special events commemorate big days with a party. Many features don't come to the fore until you've been playing for a while, such as the Island – a remote vacation spot with rare tropical species and challenges. Even later you can join Club Tortimer and begin visiting the Island alongside players worldwide, waving and showing off costumes across the language barrier.

This is a special kind of online game, a communal happiness devoid of cynicism, and one only possible within Animal Crossing's disarming style. The game is so named because of its residents; in my town I've a few vain sheep, a weightlifting sparrow, a self-doubting crocodile, a trendy fox, and that's not even the half of it. This surreal proposition is realised with character design that resembles papercraft, set against a rolling horizon of 3D popups. It makes the world feel like a small globe, and the springy weight of New Leaf's landmarks against this is just gorgeous.

You can donate bugs, fish and fossils to the museum for display, and build up an outstanding collection – as well as hear great truths spoken

There's plenty to do: bug-hunting, fishing, fossil-hunting, fruit-collecting, swimming, popping balloons with a slingshot. All of Animal Crossing's interactions are one-button affairs, with depth in particular items like the bug net or fishing rod – which are still easy to use, but depend on subtle wielding for the rare specimens. Selling stuff you've collected, from bugs to bananas, is generally the aim, because if one thing matters in New Leaf it's money. Bells are the currency of Animal Crossing, and bells you must have in abundance to get things done.

Bells can be spent on clothes, items, or furnishings, donated to a city project (like a new bridge), saved in the bank, or used to pay off your home loan. If this sounds depressingly like real life, well it is. But at least Tom Nook, the Tanooki estate agent who will rinse you of bells time and again, remains a fantasy figure – the honest capitalist.

And though money is a big part of New Leaf, the overall game doesn't have the traditional structure this suggests. There are set milestones as your town grows, like expanding your house or new businesses, but the game doesn't ever really 'end' with a full stop. It depends on what you want to do. Perhaps it's over when your town's laid out perfectly, or when your home's full of Nintendo icons, or when the museum collection is complete. It's a question of personal satisfaction;the important thing is, it never feels unfinished along the way.

Games are all about systems and, in the case of Animal Crossing, part of its genius is in how well this is hidden. The surface is surreal but, as you have more conversations, exchange letters and get to know these characters, they push such odd buttons. One will produce a letter you sent them weeks ago, saying they look at it when they're down. One might visit the town of a friend, and return with a cheeky report. Another will put up a painting you gave them, and talk about it all the time. With such little tricks the inhabitants of New Leaf gain rounded edges, become convincing personalities, almost seem real. It is the product of not just great writing, but meticulous attention to detail.

At times it leaves you open-mouthed. To go to the island you hire a Kappa – a mythical Japanese beast – called Kapp'n to sail you over, and every time he sings a different sea shanty. A real-life friend visited my town and we went to the island together. On the way over Kapp'n sang about how it was great to spend time with your buddies, however you could. The singsong rhyming is like a children's poem, and tugs at that part of you while the sentiment speaks to the adult, one of the most bewitching and beautiful virtual creations I've seen.

There is nothing like Animal Crossing. A vivid ecosystem built around exploration and surprise, its characters convince some credulous part of you that they are more than algorithms. Its creatures and their habits become second knowledge. The town grows to accommodate the way you play. There's soon a routine, online buddies, special visits to catch something unusual, and a slight unease about the next mortgage payment. New Leaf is a world on a cartridge slightly bigger than a stamp, one full of beautiful, wise and hopelessly optimistic observation of humans as social animals. It is a magical creation.