A few googologisms involve time. The idea of a "dynamic googologism", one that grows through the passage of time, was pioneered by the invention of numbers lynz and clarkkkkson. Other time-related googologisms include those originating in physics, such as Promaxima and the Poincare recurrence time (the former is just using time in its definition), and any googologism using the radius of the observable universe in its definition.
A dynamic function is the iota function.