Oh yes! I love bread baking period, and when I moved into my farmhouse I started up a sourdough culture by doing exactly what you say, mixing flour and water and leaving it partially covered on the countertop, and feeding it each day by discarding half and adding water then flour to the culture.
Here is some advice. First off, it is way more easier when you feed your starter to dilute it with water and then add in the flour. The alternative I’ve seen recommended is to mix the new water and flour into a dough and mix that in to the liquid starter, and that is just a pain and a half to do. I have seen no differences in the culture’s health when I mix water in first, and the time you save is simply amazing.
For the first week or even up to the second week, the culture is getting started, so its yeasty potential will not be as big. If you are like me, I really didn’t like the idea of discarding the daily half, so I used it to make up breads and pancakes. For the first while though I supplemented it with regular active dry yeast, the bread had a very small tanginess and the dough wasn’t simply discarded so I enjoyed it, but it was certainly not a sourdough bread.
Sometimes when you go to feed your culture, it will have some liquid floating on top which smells of alcohol. Well it basically is alcohol-ish, as it is a byproduct of the feasting yeasts. I simply mix it back in before halving and feeding.
After two weeks of daily feeding, you will probably have a potent-enough culture to create some bread without needing any yeast. I often never use a recipe, instead I water down the portion of starter (or sometimes add in some milk), add in a bit of salt, a bit more sugar, and enough flour to make a good consistency dough (which often involves adding a bit more flour when I take it out of the mixing bowl to knead on the countertop – remember you can always add flour but it’s really a pain to wetten a firm dough). After four weeks though you will certainly have a tangy sourdough culture! Nowadays my breads are mighty tangy.
Once you reach the tanginess level you enjoy, you can choose to suspend the culture by storing it in the fridge. Simply take it out and let it warm up to room temperature over a few hours on the day you intend to feed it, divide and feed as normal and put it right back into the fridge. This way you only have to feed your culture once every 3 days as the fridge slows down the action of the yeast.
Sometimes, despite the best of efforts, you will inadvertently encourage the wrong type of yeast/bacteria to grow. I’m not sure if they can pose any harm to you, but they might not make the bread rise or may impart a different flavour. Simply discard and start again if this happens. To avoid situations like this it can be handy to have a backup starter – after a week of successful development, when you feed your starter don’t discard or use the discard portion, put it into another container and cultivate both of them. Worst situation is you end up with two successful starters, one could be given as a gift or simply baked into bread.
Oh, and a tip for the bread baking itself, we were met with a lot of success when we took our culture portion and mixed it with a portion of water and flour, and left this to ferment all night. We then completed the bread-mixing and baking in the morning and were left with a really really poofy and airy sourdough loaf which required very little effort to knead. It is fun to experiment with things like this, as well as things like different shaping and bread scoring, as making the dough is only one part of the bread-baking experience!