Binomial Probability Distribution Tree

Math is my best friend.

I frequently work with binomial distributions, and as a visualization aid I created this tree of probability distributions for each of its states up to fourteen trials. Each node represents the beta distribution formed for a given number of successes and failures. At the top is the case with zero data and the probability is spread evenly, as expected. The distributions are shown in white, and the green cup is a positional reference. The red lines lead to the node that adds one additional success to the number of trials and the blue lines similarly lead to the node that adds one additional failure. As you'd expect, the more failures there are, the more the probability distribution crowds to the left and vice versa with increasing successes (notice they have mirror symmetry left to right). You can see the distribution becomes more concentrated as the number of data points increase (the effect is most easily observed straight down the center, where the number of successes equals the number of failures, so the mean stays constant).

Here are a couple more in a different style and varying scales. The last one has the distribution means shown in green.