Background
Both Shannon and Boltzmann used a common mathematical formula to define a new quantity known as entropy. The formula is:
$$ {\large\displaystyle \mathrm {H} (X)=-\sum _{i=1}^{n}{\mathrm {P} (x_{i})\log _{b}\mathrm {P} (x_{i})}} $$
I am a visual learner. The interpretation of the information $\log _{b}\mathrm {P} (x_{i})$ is nice and simple: it is the height in a tree of shape b. Non integers results are a sort of mental extension of it ( cant think of a representation ).
Question
Is there any visual or intuitive way to look at $\large\mathrm{H(x)}$?