I've now detangled the core convergent assembly decisions in Chris Phoenix's
"Design of a Primitive Nanofactory" document.
I've separated it from other IMO less important decisions about geometric and other things.
Here are the relevant crop-outs:
quote: Chris (CHRISPHOENIX)
4. Nanofactory Architecture
... The current design, ... uses only one block from each fabricator per product cycle. This implies that each stage will receive all its blocks in parallel. In general, then, each stage must have either eight (non-redundant) or nine or ten (redundant) inputs. (The first gathering stage has only four inputs, to compensate for the eighteen inputs of the final stage in the production module; see below.) ... A square of nine fabricators (one redundant) forms a stage. ... Likewise, a square of nine of these stages forms the next stage. This continues through several levels; in the current design, four levels is chosen ... unlike Merkle's design, each input port delivers only one block per product cycle instead of two. ...
4.3. Gathering stages
... product assembly requires 14 further assembly stages where each stage assembles 64 sub-blocks to produce eight product blocks. ... A final stage, ... assembles eight ... sub-blocks (per product cycle) to produce the final product. Note that the first stage in the Figure is not an assembly stage, but serves only to gather 8 sub-blocks for delivery to the next stage, since each production module makes only two blocks per product cycle. Each assembly stage gathers 64 sub-blocks from substages, assembles them within the assembly/delivery tube, and delivers the 8 assembled blocks to the superstage.
Since its a bit tricky to read out the specifics about the "welding" between the lower stages and upper stages with the frame of reference shifting around I'll reformulate it.
I hope I can make it more obvious that there is no discontinuity or convergent-assembly-character-change.
The four 4 lower stages (including the fabricators at the bottom) make up a production module which has 8(+1*) outputs
Now 2 production modules
with each 8(+1*)subblocks = 1fullblock of outputs
make 16(+2*)subblocks = 2fullblocks of output together.
This is a production module pair.
The first(isn't it the only one) gathering stage takes four production module pairs as inputs and thus gets 16*4=64subblocks which equates to 2*4=8fullblocks.
Those do not get assembled here yet. This does not change the character of the convergent assembly though. It makes just a small local delay.
Stages further up take 8*8=64fullblocks and assemble them to 8biggerfullblocks
(Did I get that right?)
As far as I can see all the these stages with identical convergent assembly characteristic can simply be added up. This makes all in all 4+14=16Stages.
Assuming a throughput capacity (not throughput!) of 1kg per second at the topmost stage (gross underestimation) calculating downwards toward the stage just before the fabricators leads to a throughput capacity of 2^16kg~=64000kg/second - wow. The fabricators at the bottom though won't come even close to 1kg per second of throughput. I see a major mismatch everywhere. I hope this formulation makes more clear what I'm trying to get at than the abstract formulation that I've given above.
I think it would be great to have a clean separation of convergent assembly parameters and geometric design.
This way one could just dial in the parameters (and step-sizes) and out comes an auto-generated 3D model.
Practical designs will probably only be viewable in their entirety (over wide scales) with visualization methods similar to the one I've outlined above.
quote: Lukas (LSUESS)
What also bothers me is that although this is supposed to be a practical design it adheres rather closely to the very small side-length doubling steps which I've tried to argue against above.
Ooops I've missed that line:
quote: Chris (CHRISPHOENIX)
The design can be compacted somewhat if multiple convergent assembly stages can be combined; such optimization is beyond the scope of this paper.