"Put pen to paper" is often used as a synonym for writing. However, there are plenty of other similar phrases to express the same idea. One such phrase is "jotting down," which means to quickly write something down on paper. Another popular phrase is "scribbling away," which implies writing quickly and enthusiastically. "Putting ink to paper" is another great option, which evokes the idea of a writer using a pen to write something down. Lastly, "penning a piece" is a more formal way to express the act of writing and could be used in an academic or professional context. Regardless of the phrase used, all carry the same meaning of putting thoughts down in writing.