Madison (Grace) is the official mascot of A Fork In Time and Alexis' dog.
A sometimes contributor as the background barking that can be heard on some episodes, Madison is a mixed-breed rescue that joined the family on July 4, 2015, and takes her name from American history in the form of homage to First Lady, Dolly Madison.
Her middle name of Grace was chosen simply because all of us need a middle name to be used on us when we get in trouble and in recognization of a connection to her beloved and missed predecessor, Faith.
We are always curious but will never know of the alternative timelines that run through her head. One can only imagine.