“As soon as you see them juxtaposed in such a way, you realize that strangeness,” Mr. Neiss said.

About 3,500 miles away in London, James O’Malley, a freelance journalist and currently the interim editor of Gizmodo UK, felt a similar call to action. His theory was that the best way to understand the workings of Mr. Trump’s inner circle is to follow the Trump family’s actions on Twitter.

Image The account @TrumpsAlert keeps track of the Twitter activities of President Trump, his wife, three of his children and his adviser Kellyanne Conway.

“It reminds me more of like a royal court from European history,” Mr. O’Malley said. “It’s about proximity to power and working out who’s in and who’s out with the king.”

A self-proclaimed coding amateur, Mr. O’Malley, 30, spent a few weeks creating a Twitter bot called @TrumpsAlert. It tracks the Twitter habits of Mr. Trump, his wife, his three eldest children and one of his advisers, Kellyanne Conway.

Mr. Trump follows a carefully curated list of 45 Twitter accounts. And tracking how he interacts with members of that list can be important in understanding the president. On Sept. 22, for instance, Mr. Trump appeared to unfollow or block his former chief of staff, Reince Priebus. An hour and a half later, he appeared to follow Mr. Priebus again. And in August, @TrumpsAlert said Donald Trump Jr., Eric Trump and Ivanka Trump had all unfollowed the actress Marlee Matlin after she condemned their father’s response to the white supremacist demonstration in Charlottesville, Va.

“When the president speaks, that’s really important — that changes the world,” Mr. O’Malley said. “He can tank the stock market or start wars with his words. So having a greater understanding of what’s going on inside the West Wing is surely a really useful thing.”

And, Mr. O’Malley said, studying the Twitter activity of the Trump children can help provide a peek into their thinking.