Not information from nowhere, no. But information from outside the genome. To use cats again, colorpoint cats such as Siamese are subject to a temperature-sensitive mutation in the genes which code for fur pigment, so the fur at the coolest parts of their body (face, ears, paws, tail) is the darkest. The colorpoint pattern is not coded for in DNA. It needs input from the environment in order to be expressed.

It's not really compression. It's more like, you can write a much shorter Lisp program to do the same task as a C program, but you need the entire Lisp runtime to get it that short.