What do you like about their writing? A good (constant) exercise is to edit what people write, e.g. take an Altucher post and try rewriting it to make it better in some regard.

Hunter S Thompson supposedly typed the works of Hemingway until he finally could copy the pacing and rhythm. Maybe scan the headlines and find something that Altucher hasn't written about yet and write about it in his style.

Like a football game told as Altucher would. lol.