For someone so seemingly unpretentious, Bill Murray accepts the role of paternal antihero with devastating ease. Remember when he was alienated by Tokyo’s techno-haze in “Lost in Translation”? Or when he served as the axis of tragedy in Wes Anderson’s trilogy of quirk? He’s the pock-marked face that’s launched a thousand dorm posters.

His most recent film is the wonderfully resigned “Broken Flowers,” which revolves around a better Homeric construct than my own. In the film, which is masterfully directed by Jim Jarmusch, Murray’s Don Johnston (“Wait, like Don Johnson?” says nearly every character in the film) is a deflated Don Juan who embarks on an ambitious odyssey to search for his illegitimate son. Wrought with color and verisimilitude, his journey through our country’s anonymous landscapes is deeply funny (in a kind of searing Alexander Payne way).

After a symmetrically-shot sequence showing the bombshell “you have a child” letter being processed through the postal service, the film cuts to its core: gray-skied Americana. Jarmusch takes the camera for a stroll down Don’s leafy suburban street. Past a home of giggling children, it arrives at Johnston’s sterile ice palace. Landscaped with geometric hedges and furnished with a cruel Euro-trash aesthetic, the house craves a bottle of Valium.

Wrapped in a black tracksuit, Don waits while girlfriend Sherry (an underused Julie Delpy) rolls a suitcase of her belongings into the foyer. The film’s use of color is very deliberate — the art direction and set design are truly superb — and Delpy’s lavender ensemble pops against the rot of Murray’s shadowy home.

“I’m like your mistress,” she sighs. “But you’re not even married.” (It is a typical Jarmusch break-up: His 1986 masterpiece “Down By Law” begins with Tom Waits’ girlfriend throwing his belongings out to the street, where Waits protests half-heartedly.)

After those few breathy words, Murray dons his empty gaze and slips into “Lost in Translation” mode. But it’s not a bad thing: His characterization is much sharper this time around.

But before leaving, Murray guts that small pink envelop tattooed with red ink, and he reads the typewritten latter it carries. Per the letter, of course, he has a son. But unfortunately for Don Johnston, the letter is completely anonymous, endowing him with a leviathan mystery to ponder. Luckily for him, his precocious Rastafarian neighbor Winston is quite the detective. They fruitlessly pour over the letter amidst the home’s earthy beads and confused fabrics, but nothing comes of it. So Don lackadaisically heads out on a cross-country tour of his sexual history and search for his lost son.

There’s a strong emphasis on the anonymity and sameness of travel in the film. Perhaps this could be some commentary on the banality of modern American life, or a rather convenient foil for the heavily staged environments of the (crazy) exes Don casually visits (“Always, always, bring flowers. Pink flowers,” advises Winston). The film is at its height during these wonderfully bizarre yet somehow crushingly normal encounters.

Don’s first stop is at the awful white-trash rambler belonging to Laura Daniels (the talented Sharon Stone). While Laura’s away, her scandalously-clad daughter Lolita answers the door and admits Don into the living room, festering with bad wallpaper and NASCAR flatware. Soon enough, Laura’s roaring Camaro pulls into the driveway, and the family sits down to dinner. Laura, a professional closet designer, inevitably beds Don, who manages to escape the estrogen-laced home unscathed (despite the nude siren song of Lolita).

What follows is the frigid suburban prison of his former flame, turned realtor, Dora (Frances Conroy of “Six Feat Under”). The tract home’s oppressive white walls and worse conversation are reminiscent of the dystopic “American Beauty.” Yet the film quickly changes tone, planting itself in a bourgeois animal communication clinic belonging to Carmen (Jessica Lange), a vignette that is impeccably designed and thoroughly well acted.

The aesthetic engendered by the film’s elaborate and painstakingly realistic sets is ceaselessly curious. While the bevy of supremely talented actors portray their characters with sincerity, they are dwarfed by the infinite scope of their surroundings. The film argues that these varied personas, while mirrored in their furnishings, are somehow less interesting than the worlds around them. Ultimately, “Broken Flowers” shows cluttered commodities as the cornerstone of its characters’ pathetic lives — that is, everyone exists in a disconnected material medium.

And while this notion eventually takes a backseat to the lost son plot, it remains pressing throughout. Even after his odyssey has ended, Murray remains rootless and alone is his sleek abode. Reaching the profundity of “Translation” without any neon glamour, this film unearths issues of modernity’s isolation in our own faceless neighborhoods, streets and airports. And Murray — l’Etranger as always — idly watches with cold detachment.

You know you want the poster.