There’s a certain creative rhythm to capturing the perfect frame. The photographer moves around the subject, surveying it as a sculptor might study a formless lump of granite in anticipation of a masterpiece. An angle will appeal, a crack in the subject’s deportment will open, and, click.

Check the card afterwards and you’ll find the visual diary of all the indecisive moments before (and sometimes after) that decisive moment. The B-roll of failures that weren’t failures at all, just imperfect stepping stones to a destination you never knew existed, but anticipated would be there, somewhere.

Magnum Contact Sheets, published by Thames & Hudson,  is a catalogue of these visual diaries from some of the finest photographers to ever stumble towards their destination. There’s glib satisfaction that comes from inspecting them, that their bad shots are just as bad as my bad shots. And also that those images that could shatter stereotypes, define eras, bring down governments, were the result of the very same dedication to a creative process that every photographer quietly steps through every time they slip a camera out of a bag.

In May 1968, two photographers walked into a shop in Paris to buy crash helmets. One was Henri Cartier-Bresson—the man who coined the phrase ‘the decisive moment’—and the other, fellow Magnum photographer Bruno Barbey. Then they wandered out into the streets to capture the protests and rioting that threatened to bring down the government.

Using his contact sheet as storyboard, you can watch as Barbey lines up behind the police in their riot gear, then moves down a side street so that the menacing line of helmets and batons are now half a block away.

He’s with the students now, wearing anoraks and toting sticks. He’s shooting as a group coalesces, and four move forward, one bending down to pick up a rock, another at full stretch, hurling a cobblestone into the air—that was the picture that would define this conflict, and Barbey seemed to know it. He pirouettes back to the police line as they march forward, and finds a group of officers carrying a wounded colleague from the scene—they’re back-lit, an avenue of trees disappearing into a point of perspective at centre-frame. Two frames, then a shot in portrait orientiation—no, landscape was working better, he switches back—and as the officer crumbles to the ground, shoots frame 16. It’s perfect. He doesn’t waste time improving on it, and instead seeks a higher vantage point. Two frames then he returns to the fray—back to the student army, and this time a protagonist. He focuses now on one individual, standing on a park bench that forms part of a street barricade. The image has good values—a defiant student, a barricade, a strident stance—and he expends the rest of the roll at this one spot, most of it on that singular figure, changing the angle until he’s satisfied he got the picture. Three historic pictures on one flimsy length of celluloid.

Martin Parr visited a New Brighton ice cream shop in Thatcher-era Britain for his epic feature, ‘Last Resort’. Children and adults press against a counter where a young woman scoops ice cream from plastic tubs and dumps it into cones. Shooting sparingly on medium format he captures three with her back turned, but the keeper arrives when she spins around and eyeballs the camera, hand on hip.

Thomas Hoepker is in the gym with Muhammad Ali, a new roll of film in the camera. Frame 4A is his first, perhaps to check the shutter is working—it’s a dud. 5A is opportunistic; an attempt to capture Ali in a mirror and in the foreground—fails. 6A, some tripod legs. 7A, nothing. Ali walks up to Hoepker, who he hasn’t seen for a couple of days, and offers his trademark left-right-left to the lens. 8A captures the left fist, body square to the camera. 9A, the broad, unstoppable right paw, and that most recognisable face of the 1960s sports world in soft focus. He only tried one more, 10A, and it failed to improve on the previous, and it was under-exposed. Evidently Hoepker knew he had it in the can, and the rest of the shoot was some interesting pick-up shots. This, one of the most recognisable frames in sport, with just two advances of the film.

David Hurn visited Abbey Road Studios as The Beatles were examining the script of the film A Hard Day’s Night. He tried just two frames at the sound desk before settling on an angle in which the four were arranged geometrically in the foreground, the scripts laid out on the glossy lid of a grand piano. He shot 26 exposures without altering his perspective, until they lined up, just so. His last frame was his best, and he knew it, as so many photographers often do.