(See also files Graph construction and Circuit notation.)
I was reading about Ekawahyu Susilo’s “SnapBloks” modular circuit design kit, each of which has an STM32 microcontroller inside, and I had an idea.
Stack machine instruction sequences are nice and flat, even as they express nested expression trees. Even three or four levels of stack are adequate for fairly complicated trees.
What about physical circuit building blocks you can plug together into a linear sequence? Things much more primitive than an entire microcontroller. Like resistors. Maybe you could have, say, nine wires, representing a stack of seven signals plus two power rails; simple passive wiring components would be adequate for DUP, SWAP, DROP, ROT, pushing Vcc and GND onto the stack, and shorting the two top stack-input lines together; two-terminal components like diodes and capacitors would be packaged to connect between the “input” and “output” on the top-of-stack line, running everything else straight through; logic gates and transistors and the like would fit into the scheme reasonably easily. Physical distances between components could be fairly short if each layer in the stack were only, say, 1 mm thick.
A Forth-style two-stack version with enough wires would be adequate for any series-parallel circuit, I think, as well as many that aren’t.
If you could change the orientation of processing modules in the stack, you might be able to get some extra expressiveness. Diodes, of course, could be turned around, but perhaps you could flip things around to select which of two stacks you were operating on.
A “vectorized” version in which each signal line was replaced by, say, a four-wire bus, would be no less expressive (you could always ignore the extra wires, though driving them would consume power) and more expressive for some uses. You’d want some extra “permuting” and “reducing” kinds of operations to interconnect the bitplanes.
If you had eight “stack items” of four wires each, plus power and ground, you’d have 34 lines. If the spacing was the standard 1.27 mm SOIC pin spacing with a 6×6 square matrix, the whole module size would be 6.35 mm square plus the width of a pin — say, 7 mm × 7 mm. This is a practical size to recognize by eye and manipulate by hand. An assembled circuit containing 50 elements and 50 passive “stack operations” might then be 7 mm × 7 mm × 100 mm (and cost about US$50 in parts, plus maybe another US$1000 in modules that were sitting around that you didn’t use). A huge variety of circuits can fit within these constraints, especially when the available components include things like programmable microcontrollers.
About orientations: a square pin array like that could be oriented in eight orientations (four in-plane rotations and two flips), while the slightly denser hexagonal packing would have twelve possible rotations. Getting these rotations to do something useful would be an interesting challenge, the alternative being to add a forcing function to reduce the possible number of rotations.
By way of size comparison, a AA battery is 14 mm × 14 mm × 50 mm. In that size, you could fit four separate such stacks of 50 items, totaling 200 modules and about 100 electrical component modules (i.e. not just passive wiring). So this seems like it might be a very reasonable alternative to breadboarding.
If the hypothetical 34 lines were distributed around the edges of the board at the same 1.27 mm spacing, you’d need 43.18 mm circumference, 13.74 mm diameter, the same as a AA battery. This could conceivably enable a larger number of possible rotations, but you’d have to figure out how to hook up the power rails, maybe with coaxial pins in the center of the board.
Is 1 mm a reasonable thickness? Common 0805 surface-mount resistors are 2 mm × 1.2 mm × 0.45 mm. A TQFP is nominally 1.0 mm, not counting the leads bending down below the body; an MLF is also nominally 1.0 mm. Standard PCB thicknesses (including 4-layer and 6-layer PCBs) are 0.031" and 0.062", apparently without regard to the number of copper layers, which work out to 0.79 mm and 1.57 mm. So 1 mm is maybe a bit low, but 3 mm should be doable. (Of course, not all the modules have to have the same thickness.)
I don’t know what kind of connectors the boards would have to use between them. I assume zebra strip would have unacceptably high resistivity for many uses.