How frequently should I feed my sourdough starter?
My first impression is that the towel might not be porous enough to let the all-important yeast and bacteria in. Try cheesecloth.
If that doesn't do it, here's the long version:
Creating a Starter:
First and foremost, a week isn't necessarily enough time to get a starter going full steam ahead. It can take as little as a few days or as long as a month. You're relying on ambient yeast and bacteria that are floating around in the air, and the amount of yeast and bacteria available varies according to location,  climate conditions, and all sorts of other environmental factors.    The specific species and strains of yeast and bacteria also vary from place to place, which is why San Francisco is renowned for its ssourdough - they have the best ambient yeast and bacteria strains.  Give it time.

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Maintaining a Starter:
Feeding Schedule:
As a general rule:  Once your starter is healthy and active, bubbling, rising vigorously, and smelling sour, you have two options:

If you store the starter at room temperature, you need to feed it twice a day. Don't wait for the risen starter to collapse before the next feeding, because it messes with the ph levels and can make the yeast and bacteria less active. Every 12 hours, feed it.

If you store the starter in the fridge, you can go up to a week between feedings.  The cold won't kill the yeast and bacteria, it just slows them down. Just make sure the starter doesn't get shoved into a super cold spot and freeze.


The feeding process:
Stir the starter, remove all but 4 ounces of it (you can either discard the rest or use it to bake something). To the remaining 4 ounces, add 4 ounces flour and 4 ounces of purified or bottled water (chlorine in tap water is bad for the yeast and bacteria, and most filters remove chlorine taste, but not all the chlorine). Room temperature starter gets room temperature water; refrigerated starter gets lukewarm water.  Stir until no dry flour remains. Cover with a non-airtight lid.  Refrigerated starters need to stay at room temperature for several hours after feeding so the yeast and bacteria have a chance to wake up and eat.

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