Are there any mythologic Gods, creatures or equipment that have "exponential" characteristics? The hydra is classically described as growing two heads back for every one cut down. Mjolnir, theoretically, became exponentially heavier to the unworthy. What other Gods, creatures or equipment have powers that are tied to doubling or exponential characteristics?

Not associated with any "gods" as such; there are a large number of folktales containing items with exponential growth.

The Aarne-Thompson classification system groups many of these stories into category, AT 565. One of the best-known of these is **_Why the Sea is Salt_** , where an out-of-control salt mill grinds out an endless amount of salt.

The goings-on in **_The Sorceror's Apprentice_** certainly smack of the Lernaean Hydra, but that one is more literary than folkloric.

And of course there is the matter of how darn fast that beanstalk grew...