With a single burst of tweets, US President Donald Trump can fire and hire a chief of staff, bar transgender soldiers from the military and undercut negotiations with foreign nations.

It's "diplomacy by tweeting", said Russel Neiss, a software engineer for an educational technology nonprofit.

In June, Mr Neiss saw a tweet from Pat Cunnane, a former member of President Barack Obama's White House staff, in which Mr Cunnane formatted one of Mr Trump's Twitter posts to look like an official statement from the office of the White House press secretary.

"For context — because he's President — all of Trump's Tweets should be mocked up in the correct Presidential statement format," Mr Cunnane wrote. "It's telling."

That inspired Mr Neiss to give every tweet from the president the same treatment.

A few days later, while his two children were napping, Mr Neiss spent 48 minutes in his St Louis home writing about 50 lines of code for a Twitter bot he calls @RealPressSecBot. The account scans anything tweeted by @realDonaldTrump and automatically formats the tweets so that they look like official statements from the White House.

"For me, I just want to give the president's tweets the honour they deserve," Mr Neiss, 34, said.

Within a few hours, the account had about 80,000 followers. It now has more than 120,000. It has been "the definition of viral", Mr Neiss said. "It spoke to people."

He suggested that @RealPressSecBot resonated because it visually intersected Mr Trump's often bellicose words with the reality of the impact they can have.

"As soon as you see them juxtaposed in such a way, you realise that strangeness," Mr Neiss said.

About 5600 kilometres 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.

"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 September 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, Virginia.

"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.

"It's sort of fascinating to see Don Jr and Eric's media diets," he said. "Don Jr goes and he'll like tweets from all sorts of interesting people and organisations, and I think that shows you the sort of worldview and the world they exist in."

The accuracy of @TrumpsAlert, which has about 42,300 followers, can be dicey. If Twitter suspends an account or if someone blocks Mr Trump, his wife, his children or Ms Conway, the bot reads it as an unfollow. Mr O'Malley explained in a series of tweets: "The way unfollow detection works is by downloading the current following list, and comparing it to the previously downloaded list. This means that if a followed account is suddenly missing from the new list, it is labelled unfollowed."

But this hasn't stopped numerous political journalists from following the account. Mr O'Malley is hopeful that one day something big will come out of his bot.

"I guess the dream is that one day you'd see Donald Trump has unfollowed @VladimirPutin or something," he said. "And we'd go: 'Aha! We've got him!'"

New York Times