What a cool Lego machine! There's an issue of the definition of 'coding' here. Your CAD design of the machine would clearly not contain a design of the paper plane, but there would be a direct causative relationship between it and the plane that allows the plane to be predicted on the basis of the machine's design. I agree on that.
Of course, most metabolic pathways involve several components, not just one protein and one substrate, so things get a bit more complicated: the end result cannot be predicted from one design (gene). Potentially though (with considerable extra effort) it could be predicted by looking at all the genes involved. I'm not claiming this not to be the case.
But now imagine the following. You have not one but 10,000 Lego machine designs in a book. You throw this book into a bath tub containing a 3d printer and a heap of raw materials (sheets of paper, bits of wood,...) that the machines described in the book could work on. You're not there to intervene and tell the printer which pages to read, and what we want is not a simple paper plane, but a complex contraption built of hundreds of these little machines. Is the book of CAD designs going to be sufficient to get this done?
It doesn't stop there. Now imagine that we've got millions of these bathtubs, each with the same instruction book and more or less the same raw materials. We want them to make not just one but hundreds of different kinds of contraption, composed of different collections of machines. And then we want the millions of contraptions built to join together in an orderly fashion into one huge entity in which each of them is in just the right place to play its part.
Is the book of CAD designs really going to be sufficient to get this done?
"imagine that we've got millions of these bathtubs, each with the same instruction book...want them to make not just one but hundreds of different kinds of contraption...Is the book of CAD designs really going to be sufficient to get this done?"
When the scale is small enough that Brownian motion and van der waals interactions become major players, yes. Particularly since the "book" is itself a macheine of sorts, and all the contraptions are set up to only connect properly in a single fashion though the BM an VDWF.
There's a very interesting wording you use here "each of them is in just the right place to play its part" as if it matters terribly where things end up. Do Identical Twins have the same moles? Do you think each scutoid is defined in placement? That's just silly. Cells are packed in and shift around constantly. DNA is a set of overall bootstrapping blueprints, and variations will occur because of the way the data unpacks itself.
Much the same way you'll see the exact same house built 50 to 100 times in infill housing, but walls will vary by an inch here or there, none of the nails will be in the same place, and the drywall in some will be vertical standard while others use cross lapped horizontal. Couple might have a dog-flap in the door while others are secure.Of course a body is not a stretch of infill housing, but the analogy is there even with the workers building that infill township: drywallers drywall even if some of them do sloppy corners, electricians hook up the fixtures even if one guy puts the wires along a different joist than the next guy, and plumbers send stuff downhill even if the stack placement moves around between different houses because the city boys were a little off on their sight lines. Same deal goes with vascular/osteoblast/nervous systems; no 2 people's are the same even with a shared master design.