"here, they are discussing some relationships: the regular latice, L grows linearly with n, we see L growing linearly with n, and we see C is staying constant. In the random network, L grows logarithmically, and we see L growing logarithmically, we see C going as a reciprocal relationship. When we read the word "logarithmic", we don't need to reconstruct that relationship in our head, you can just see it"
Does the average reader of Nature need to be shown a graph of what a linear, constant, logarithmic, and inverse relationship looks like? I don't think so.
That said, I imagine there are highly terse and technical ideas that cannot be simply represented in the current mediums of publication and which could benefit greatly using a presentation using an interactive widgets, making more complex ideas more easily communicable.