The third in the Harry Palmer series is still deriving material out of its difference from Bond. The map of London on the wall of Palmer's dingy office contrasts with the world maps on walls in early scenes of Bond films. Now a private detective, Palmer's sphere of activity is local, not global.
When Palmer does travel, he faces the un-Bondlike challenge of finding on a map an address in a phone book.
Ou maps pull back from this exactly pinpointed address in Helsinki to a more general view of the Baltic region, and even when - in Ed Begley's centre of operations - we have the familiar world map that signifies megalomania, the Baltic region is marked by a concentration of lights.
In a further contrast with the Bond corpus, Syd Cain's operations rooms in Billion Dollar Brain are deliberately modest affairs compared with, for instance, the spaces created by Ken Adam for that year's Bond film (even if that is clearly the same map on the wall, above and below - both scenes were shot at Pinewood) :
For its climax Billion Dollar Brain shows opposing forces plotting the final confrontation, each on their own maps:
These last two map scenes both show humans attempting to arrange the world my arranging things on maps. This is the complement of the film's nature motif (as in the Alexander Nevsky-like climax on the ice). Human endeavour vs untamable nature is an opposition neatly foregrounded in this dissolve from the penultimate to the last sequence: