><> (Fish), 14 bytes

'rd3*9[r:r]>o< 

Try it

First iteration duplicates the : in the middle: (it actually duplicates itself):

'rd3*9[r::r]>o< 

Then since there are now 2 duplication signs it will duplicate itself twice:

'rd3*9[r::::r]>o< 

etc. doubling each time.

><> (Fish), 14 bytes

'rd3*9[r:r]>o< 

Try it

First iteration duplicates the : in the middle: (it actually duplicates itself):

'rd3*9[r::r]>o< 

Then since there are now 2 duplication signs it will duplicate itself twice:

'rd3*9[r::::r]>o< 

etc. doubling each time.

><> (Fish), 9 bytes (Boring version)

':rd3*>o< 

Try it

This simply duplicates the < at the end:

':rd3*>o<< ':rd3*>o<<< 

etc. So the functionality of the program won't be effected at all. It's basically a comment.