Welcome to Columbia... is it someone new?
Not his very first interaction, but in order to enter the city of Columbia, Booker must submit himself to be baptized. As he enters the circle of religious devotees, the preacher begins his baptismal offering with a familiar question: "Is it someone new? Someone from the Sodom below?"
Jack has mysterious tattoos that we never were given a full understanding of. Most likely they represent that he is, essentially, a slave who obeys, whereas Andrew Ryan is a man who chooses.
Booker has branding too, and it's this branding that gives him away to Comstock's people. This was a self-inflicted brand, though--one he gave himself as a way to repent for his mistakes.
Fill your cravings at the Circus of Value!
Peppered throughout Rapture, the Circus of Value vending machines provided much-needed health and ammo restocking as well as a wholly obnoxious voice that will forever be burned into our brain. Of course, when youre running short on cash, that godforsaken clown was always sure to point it out: Come back when youve got some money, buddy!
Dollar Bill. Who needs competition when you have quality?
Just like the Circus of Value, Columbias Dollar Bill machines keep Booker stocked, locked, and loaded. But more than their contents, you probably recognized a familiar phrase, albeit slightly more antiquated: Return when you have some currency, fella!
The power of plasmids
With the worlds greatest scientists gathered together in Rapture (and the help of a DNA re-writing sea slug), medical, technological, and scientific advancements abounded in Rapture, chief among them: plasmids. This memorable shot shows Jack getting accustomed to his first fistful of lightning.
Vigors--power from another world
Columbias version of Plasmids, Vigors provide similar extraordinary powers to the user, such as lightning, fire, or control of animals. The obvious similarities between vigors and plasmids are explained by a voxophone recording in which Jeremiah Fink mentions observing a brilliant biologist, possibly Brigid Tenenbaum, through a tear, implying that he likely drew inspiration from Raptures plasmids themselves when developing Columbias vigors.
Messages from the past--Audio Diaries
One of the most compelling bits of storytelling in the original BioShock was the usage of recorded Audio Diaries to give context to the catastrophic state of Rapture.
Voxophone--personal, portable audio
Infinite uses the exact same technique, though its position earlier on the timeline meant that recordings were made on the relatively newly invented voxophone, a sort of miniature, personal phonograph recorder.
Raptures lumbering guardians
Adorning the box art, the Big Daddys hulking man-machine hybrid form is an image of mechanical and biological advancement we are not soon to forget.