Looking at Signatures on a parliament.uk Petition
You can browse the signature data for Petition 171928. Note that the graphs are interactive, so you are able to zoom and pan the data. The most interesting part of the data is at the beginning of the set. There is an obvious sogging of of signatures in the night time, and some peaks which I presume to be caused when another well followed twitter user tweeted about the petition.
A section of the rate data can been seen here: