To the average eye Barcelona's attacking play is a kaleidoscope in which gifted footballers pour into space at whichever angles they fancy. Not quite. Unlike Arsenal, Catalan experts sniff, Barça's flowing forward play is strictly governed by a grid system so that when they lose the ball the whole team is already in position to win it back.

Manchester United face organised art at Wembley: structured creativity. Pep Guardiola, the Barcelona coach, is fond of rhetorical flourishes about the club's duty to entertain, their passion for ingenuity. But in this phase of the club's history – which can trace its origins to the Dream Team of 1992 – Guardiola has added a dimension that would have been anathema to Johan Cruyff's conjurers.

Barça apprentices are taught to see the pitch as a field of eight boxes, all of which must be occupied. Seeing a vacant area, a Barcelona player will slide into the void to restrict the options of the opponent should he find himself in possession. So graduates of their La Masia academy learn to think two ways at once. Even as they attack, they lay the ground to defend. And from the back, a high percentage of their forward moves start from Víctor Valdés, the goalkeeper, or Gerard Piqué, the Franz Beckenbauer of a team who have increased their possession ratio in Champions League games from 61.1% in 2006-07 to 73.3% this season.

Sergio Busquets is another starter/stopper. "Part of my role is to shuttle between the defence and attacking lines to make sure the ball circulates well and quickly. Often this pivotal position starts the play," Busquets says. "Defensively I'm also an intermediate between our back four and the midfield and I try to mark and press so I can isolate the opposition striker from their midfield. I'm a team player who needs to work a lot and sacrifice myself for the success of the group."

Barcelona's mystique is not founded, of course, in mathematical calculation. It stems from the sense that the Camp Nou is really one of Gaudi's unofficial artistic projects. Through the brilliance of Lionel Messi, Xavi Hernández and Andrés Iniesta, Barça have acquired a global array of diehard followers who reach for the cudgels at the faintest criticism of tiki-taka, or of the practice of rolling around on the ground, clutching one's unhurt face.

This mostly commendable adoration expresses a deep appreciation of football as it should be played, and in this respect Barcelona are hardly slow to promote themselves as guardians of the flame, even while selling their shirt sponsorship to the Qatar Foundation, from a country now embroiled in an alleged Fifa corruption scandal. The "Més que un club" (more than a club) boast is increasingly pervasive. This week a Barcelona official told the BBC: "Barça belong to 190,000 members and we will never be the property of a millionaire from Russia or the United States."

Yet José Mourinho's nemesis in Spain are ruthless on and off the pitch, where they have scored 144 times in La Liga, the Champions League and Copa del Rey, and are so superior to their contemporaries that their brilliance almost confers an obligation to win the European Cup every year: an expectation that weighs heavily on Guardiola.

Cruyff is adept at playing the spiritual godfather of the 30-year Barça tradition, and when the talk turns to their first European title, won at Wembley in 1992, Guardiola lets the old man claim his bragging rights. "They were pioneers and we cannot compete with that no matter how many trophies we win," Guardiola says. "We will never equal the period of the Dream Team as they were the first to break up the long period without success. [Louis] Van Gaal, [Frank] Rijkaard and I have added things but none of this would have happened without the Dream Team."

Cruyff's crushing 4-0 defeat by Milan in Athens in 1994 was a trauma Guardiola's side appear unlikely ever to experience, because their defensive work is so zealous. Europe's leading managers will say as one that Barcelona "hound" the ball back from teams who spoil their pretty patterns (or "sterile domination", in Arsène Wenger's view).

Sir Alex Ferguson says: "Guardiola has created a different philosophy for Barcelona. I think the Cruyff era laid the foundation for the width they used in their game and using the full size of the pitch. If you look at their midfield players over the last 20 years, they have all been small. What has changed is the pressing and the areas in which they press the ball. That is what Guardiola has brought to the team."

"The modern team have much more possession and control of games, and a lot more detailed pre-match preparation is done," says Albert Ferrer, the former Barcelona and Chelsea right-back. "The current team are more solid, which you have to be in the modern game. There was more of a fantasy element with the old Dream Team, more improvisation. We might score five goals one day, but also let in three."

The new educational philosophy was summarised in Sid Lowe's seminal interview with Xavi, who said: "Think quickly, look for spaces. That's what I do: look for spaces. All day. I'm always looking. All day, all day. Here? No. There? No. People who haven't played don't always realise how hard that is. Space, space, space. It's like being on the PlayStation. I think shit, the defender's here, play it there. I see the space and pass. That's what I do.

"Some youth academies worry about winning, we worry about education. You see a kid who lifts his head up, who plays the pass first time, pum, and you think: 'Yep, he'll do.' Bring him in, coach him. Our model was imposed by Cruyff; it's an Ajax model. It's all about rondos [piggy in the middle]. Rondo, rondo, rondo. Every. Single. Day. It's the best exercise there is. You learn responsibility and not to lose the ball. If you lose the ball, you go in the middle. Pum-pum-pum-pum, always one touch."

He makes it sound quite knockabout and easy to replicate. But when the ball is lost for the other 30% of the match "pum" becomes pummel. To create their own joy they must kill the opposition's. There is a kind of smothering cruelty in their art.