I see the other pattern - the forgiveness guy grows a rep as the guy who broke stuff, while the "ask permission" guy often finds out people say "yes". The end result is people are happier working with the ask permission guy.
Asking forgiveness entails taking a personal risk. If it works out, you're wonderful. If it doesn't work out, you have to answer for your bad judgment.
Asking permission is a way of hedging against your own judgment. In other words, it's a great thing to do when you're genuinely not sure. But if you are right, you don't get results as efficiently, since you have to let everyone bikeshed first. Maybe you don't even get results at all.
I find another pattern works well. You ask permission for ridiculous things, in order to focus other people on what you want to do and how they can help.
It's really simple. Don't open with what you want to do, open with what you'd like to get, and make sure that you're mentioning 2 or 3 things you're willing to give up. Don't say "I want to write a complex mobile app for the delivery department", say "I need a $200k to hire 2 programmers, buy 30 different phones, and 6 months of nothing on my plate, you got 15 minutes ?".
Obviously, you do this once every 6 months or so at most, preferably less, and follow through.
It's amazing, especially in America, how mentioning dollar amounts focuses people on solving problems and looking at opportunities instead of looking for excuses. Finding excuses is universal in organizations, especially big ones, and the higher ups have as much trouble with it at the cleaning lady. Plus, the fact that you even know how much to ask and have a plan for the negotiation means you have built a business case (don't go in without one).
Perhaps I'm an optimist.