The producers of children’s television know the key to holding a distractible audience’s attention: interactivity.

Dora the Explorer asks kids to repeat after her (“Swiper, no swiping!”). Mister Rogers broke the fourth wall to welcome them to his neighborhood. The hosts of “Romper Room” pretended to see them through a “magic mirror,” and read their names on the air.

It turns out you can apply the same formula to morning news. “Fox & Friends,” the three-hour wake-up program on Fox News, is an interactive magic mirror for Donald J. Trump.

President Trump is the show’s subject, its programmer, its publicist and its virtual fourth host. The stars offer him flattery, encouragement and advice. When he tweets, his words and image appear on a giant video wall. It’s the illusion of children’s TV — that your favorite show is as aware of you as you are of it — except that for Mr. Trump, it’s real.