I'm guessing that, maybe twenty to fifty years from now, people will look at the current crop of 3D printers as rather quaint old macguffins that, oh, had their uses I suppose, but were superfluous to the greater vision of Processing. Let me get back to you on that.
3D printers, as they now are, can extrude more than one type of material, and thus already represent a level of sophistication way beyond the cute little x/y plotter with the extruded thermoplastic pooter. Were I to speculate, I would suggest that the end result will be some type of plasmonic surface or plenum that utilizes quantum teleportation to provide material information, building molecule by molecule, or atom by atom. No doubt it will be hooked up to, not only the internet of things, but a disintegrator that will supply a matter bank that supplies the printer with pure elemental materials. As such it really will grow what it is that you want. And it will range from laptop size to industrial strength, and in a utopian world, possibly be on street corners, and like a version of Mr. Fusion, will be fed garbage and squirt out consumer items.
In any event, I propose that the two ends of the thing be called "the maw" and "the spew". And that the whole be called a Sneetch Machine (after the Star-On and Star-Off machines that Sylvester McMonkey McBean made available to the Sneetches in Dr. Seuss's The Sneetches and Other Stories).
Processing, capitalized, will be what we humans, or post-humans, will be all about.
Remember the old canard about political affiliation, where if you go far enough right you go full circle and end up on the left? Well, that's not true, but I suspect it happens when it comes to increasing biological and civilizational complexity. Given the quasi-fractal aspects of nature, it seems there is a self-similarity of scale.
And so, when you move up the technological ladder, with increasing leverage and sophistication of control over the surrounding environs, it gets to a point where an advanced civilization looks a lot like a slime-mold, or a multi-cellular organism, and all it is doing is converting available matter and energy into more suitable habitat and more life. Where all you are doing is taking one order of matter, and Processing it into something more to your liking. The original matrix of organization is destroyed in favor of its new matrix.
Of course, with creative destruction, that Maw beckons to the Spew. Just hook up the two ends of the Sneetch Machine, and let her rip!