From left, Bryan Cranston as “Chief,” Bob Balaban as “King,” Koyu Rankin as “Atari Kobayashi,” Bill Murray as “Boss,” Edward Norton as “Rex” and Jeff Goldblum as “Duke” in “Isle of Dogs.” (Fox Searchlight Pictures)

It was 1999 when I first interviewed Wes Anderson, in the back of a yellow tour bus that had been rented by the studio behind “Rushmore,” his sophomore film. The un­or­tho­dox setting, as the then-29-year old filmmaker explained, was a concession to his fear of flying. When I caught up with him earlier this month by phone, Anderson was traveling by train through his home state of Texas, where he had just flown in from Germany for a screening of his latest (and ninth) movie, the stop-motion animation “Isle of Dogs.”

Obviously, much has changed for the 48 -year-old director, two of whose films (“Fantastic Mr. Fox” and “The Grand Budapest Hotel”) have since been nominated for Oscars, and who regularly hops between Paris and New York, where he and his partner, the writer and designer Juman Malouf, divide their time.

In that 19-year interval, Anderson says, the biggest change is how much easier it has become to make movies, given that he has developed what might be called a working company of actors who regularly jump at the chance to appear in his films. (Several of them are in “Dogs,” including Bill Murray, Jeff Goldblum, Edward Norton, Frances McDormand and Tilda Swinton.) More important, Anderson says, is the “whole gang of people” who regularly work behind the scenes — a gang that includes his frequent producer Jeremy Dawson, who has worked with him on five films.

It’s a comfortable sort of family that, along with Anderson’s highly idiosyncratic and easily parody-able style of storytelling — what he calls his “handwriting” — has helped make his films immediately recognizable.

Director Wes Anderson: “For this movie, to me, these dogs — they’re people.” (Fox Searchlight Pictures)

Recognizable to everyone but Anderson, it seems. I mentioned to the director that there are numerous websites devoted to analyzing his peculiar style, including one that has used a ­machine-learning program to identify such Wes Andersonian visual quirks as the use of on— screen titles, TV screens, shelves and people on walkways (each of which, by the way, is a prominent motif in “Dogs”). Anderson insists it’s not intentional.

“Every time I start a movie,” he says, “all I’m trying to do is make something completely different from what I’ve made before, and to try to go in a new direction. Yet every time I do that, by the time the thing is done, people tell me, ‘Well, I knew in about three seconds who had made this movie.’ I never repeat anything deliberately. I want to make each movie as different from the other one as possible.”

In making “Dogs,” Anderson’s second stop-motion feature after “Fantastic Mr. Fox” (based on a Roald Dahl book), the director says he and his co-writers, Jason Schwartzman, Roman Coppola and Kunichi Nomura, drew inspiration not from children’s literature or movies, but from Japanese director Akira Kurosawa. The faces of several characters in the new movie, which is set in the fictional Japanese city of Megasaki, are modeled after such regular Kurosawa actors as Toshiro Mifune, Tatsuka Nakadai and Takashi Shimura.

But one scene features a subtler nod to the great Japanese director. According to Anderson, “It’s a very common thing, in a certain kind of Kurosawa movie, where there’s a group of men in a room together, whether it’s an Edo-period piece — one room with sliding screen doors — or a 20th-century city conference room. They do something that we don’t really commonly accept in movies nowadays, which is, they tell each other who they are, what their history is with each other and what their relationships are. ‘You were my friend, and now we have become rivals. . . . ’ They’ve basically just given you all the exposition. I have a scene exactly like that.”

It’s not surprising that Anderson would seek inspiration from the past, and not the present. His films have a quality of being out of time — not quite nostalgic, yet not quite contemporary either. Anderson has described his body of work as “five degrees removed from reality,” and has said that “Dogs” grew out an early idea of what people in the 1960s imagined the year 2007 would be like, but for dogs.

The past — and how parts of it are constantly being saved within, changed and/or erased by the present — is, he says, something of an obsession. “I think looking back, seeing old pictures, old photographs of a place you know well today but that is different, it’s always fascinating.”

The plot of “Dogs,” which concerns anti-dog hysteria that has led to the banishment of canines to a trash-filled island by a cat-loving mayor, evokes, among other things, the U.S. internment of Japanese Americans during World War II. Ironically, Anderson says he was not consciously trying to evoke instances of bigotry from the past, but rather, from the present.

Bill Murray, left, as “Boss” in “Isle of Dogs.” (Fox Searchlight Pictures)

“In starting with this idea, we knew that the dogs had to represent a small part of a society that’s been ostracized by a larger group, which has turned against them, for its own purposes,” he says. “Once you have that, there are so many examples from history, because it’s a cyclical thing. We started by looking at the known, 20th-century historical events like Japanese internment. And yet, it became, more and more, that the inspiration had moved from the history books to the front page of today’s newspaper, in so many different places. I feel like that theme only started to come in, more urgently to us, while we were making the movie.”

But if this is Anderson’s most timely film, why use animated dogs, not actors, to make his point?

Anderson says there was something hard to explain about the germ of the idea — a society of outcast and abandoned dogs living on a trash-strewn island — that fired up his imagination. “When Roman and Jason and I were first discussing this story, they said, ‘What do you see here? What is it that you are so interested in?’ I don’t know why, but I just had this idea that there’s a movie in that world and about this group of dogs. What are they going through? Why are they there? And the next thing you ask is, ‘What happens?’ The story just came out of our subconsciousness as much as anything else.”

Although one of the film’s themes is the power of love to soften the heart of an angry dog, Anderson insists he is not particularly softhearted when it comes to pooches.

“You know, Jason Schwartzman is a definite dog person,” he says. “He’s lived with the same dog for 11 years. Roman Coppola is a definite cat person. He has a cat, and before that he had another cat, and so on. I mean, I grew up with dogs, so if I had to be one or the other, it would be a dog person. But I don’t really feel one or the other. For this movie, to me, these dogs — they’re people.”

Isle of Dogs (PG-13, 94 minutes). At area theaters.