Recipe(tried): making buttermilk from scratch

I have heard that buttermilk is created by shaking heavy cream so much that butter separates out and the liquid that is left is the buttermilk. This is actually a procedure that my children performed when they were preschoolers and it was fun for them to see where butter came from. Yes, it is a lot of shaking but yes, you do get butter. And buttermilk. I myself have not made butter this way.
But I have made buttermilk by taking some of the buttermilk created in the above procedure, mixing it with some skim milk (buttermilk: skim milk is 1:3) and mixing well in a plastic jug, leaving the lid on and letting the liquid sit at room temperature for several days. The result was that the mixture in the jug became all buttermilk and was delicious. The 'starter' is carried along. That is, save a little and do it all over again to make another jug full. I learned this from a contributor to 'The Confidential Chat' in the Boston Globe. It works wonderfully.