swallowtail and butterfly functions

Speaking of things I do not understand,
look at these beautiful graphs which I stumbled upon in my search for integrals.
What a world we live in that some people work these things out!
And yet the lines look so beautiful, and the descriptors are even better.

And in case you are wondering, it sounds like she is trying to explain catastrophe theory based on her observations of the evaporations of water droplets.
Note my hesitation in the 'sounds like' part: this is utter Greek to me.

"I find this relatable to the evolution I am seeing from the evaporating water droplets. When the elliptic umbilic and fold merge into a parabolic singularity, they essentially annihilate at the critical points. Hence, the reversal process can be explained by the idea that once this higher singularity is met a “catastrophe” happens and the lower order catastrophe shapes re-appear."

via {samantha scibelli}