They nodes on the side are for connecting other functions to :)
they are used for creating complex functions, you can use a fractal to give random output to drive say, another fractal's inputs, or many other things.

i'ts best seen by trying for yourself, say, start with a cube, Rest its material
give it a bump using a fractal or noise node
then start driving the main function's input nodes with other functions.

this is how folks create really complex procedural functions that give, say, a cratered moon surface, complex terrain heights, or bizarre tehnological machinery looks
:)

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