I recently watched a YouTube video by “GreatScott!” demonstrating a bistable magnetic electromechanical 7-segment display; each segment is a slot through which a moving part is visible, one part of which is white, while another part is black. There are 7 electromagnets on the back of the display; by passing a pulse of current through them in one direction or the other, a permanent magnet attached to this moving part is given a kick big enough to swivel the part and change the color of the segment. The permanent magnet has two stable positions in which it is attracted to a ferromagnetic core, so the display remains stable without applied power.
The display is multiplexed with a per-digit common ground, so that, for example, an 8-digit display with 56 segments requires only 15 wires — but 7 of them need to be bipolarity.
It occurred to me that in some sense this was excessive; 7 bipolarity signals (with distinct +, -, and 0 states) can encode 3⁷ = 2187 commands rather than the 14 needed to switch 7 segments or even the 112 needed to switch 56 segments. 7 unipolarity signals are enough to encode 128 commands, enough to switch 64 segments on or off. Moreover it should be feasible to route the magnetic flux in such a way that the decoding is done passively, by the magnets.
The crucial tricks are:
You can route magnetic flux to an area by providing a low-reluctance path from a coil to that area; for example, a sheet of electrical steel, or more prosaically, a mild steel wire. (At kHz and higher frequencies, ferrites might be useful.)
You can sum flux from different coils by terminating low-reluctance paths in the same area, but with enough of an air gap between them that there isn’t a low-reluctance path between the different coils. It’s sufficient that the flux they produce impinge on a magnet or magnets attached to the same movable part.
You can route magnetic flux from either end of a coil, so you can get both subtraction and addition.
By including fixed permanent magnets in the mix, you can include a constant term in these sums.
This allows you to set the flux in a given area to an arbitrary affine function of the currents in the different coils. Consider an area you want a movable permanent magnet to be attracted to only when the code 0001101 is present on the coil control wires. You route the positive ends of coils 0, 2, and 3 to that area, and the negative ends of coils 1, 4, 5, and 6, and include a fixed permanent magnet powerful enough to counteract the flux from just over 2 coils, but not more.
In this area, if coils 0 and 2 only are energized, they are not sufficient to overcome the fixed permanent magnet, and the movable magnet continues to be repelled from the area. If coil 1 is additionally energized, it partially cancels the flux from coils 0 and 2, repelling the movable magnet even more strongly. Now if coil 3 is energized, we have 0, 2, and 3 fighting against 1 and the permanent magnet, not quite enough to overcome it; but if coil 1 is then de-energized, the balance flips, and the area becomes attractive rather than repulsive.
In practice this probably means that one such “balance point” is needed for each pixel — a position which can be made a stable equilibrium with the right combination of energized coils, but becomes an unstable equilibrium when power is removed — and once the movable part has been brought to this balance point, one of two additional coils is energized to tip the equilibrium in one direction or the other, while the other coils are de-energized.
(Slightly tweaking this, instead of using two additional coils, you could use one additional coil and a permanent magnet; this means that the balance point is not quite an unstable equilibrium when power is removed.)
So, simply by choosing the polarities with which each coil is coupled to each pixel, we can make a unique combination of coil activations the strongest for that pixel, then provide a permanent magnet strong enough to cancel any combination other than that one. In essence this is an electromechanical McCulloch–Pitts neuron.
Stable, high-coercivity rare-earth or even ferrite permanent magnets will work much better for this than unstable alnico magnets, because one of the magnets needs to have a strength that stably discriminates between the case where, say, 6 coils are activated in concert, and the case where 7 are.
A trick not needed: by using different thicknesses of ferromagnetic material, you can get different amounts of flux from the same amount of electrical current. This allows you to compute weighted sums and differences. However, though this trick is not needed, it is an alternative to using varying strengths of fixed permanent magnets in the different cells; it would allow them all to be the same strength.
A hard disk drive’s head is positioned with a voice-coil actuator by running a precisely controlled current through a “voice coil”, producing a precisely controlled magnetic field which moves the head to a precisely controlled position within a few milliseconds. Dynamic speakers work on the same principle, moving the speaker cone to what is in principle a precisely controlled position by producing a precisely controlled magnetic field with a precisely controlled ac voltage. Class-D audio amplifiers generate that voltage by, essentially, reactively low-pass filtering a PWM signal.
A very simple way of decoding PWM would put a floating magnetic compass globe, like those people used to have on their car dashboards in the 1980s, in an enclosure with a small transparent window through which a single digit could be seen, out of ten printed on the globe in different positions; a permanent magnet would align the globe to display “0” in its equilibrium position, and a coil producing a field at perhaps 120° from that of the permanent magnet could swivel the globe to any desired position 1–9 by applying an appropriate strength of field. A second coil producing a vertical magnetic field could provide a magnetic dip to counteract the globe’s tendency to return to a default horizontal position; this could be used, for example, to select from a larger repertoire of characters, or to engage mechanical interlocks that kept the globe from turning when power was removed.
(For some reason, the traditional way of doing this, the galvanometer, uses a mechanical hairspring rather than a permanent magnet to return the needle to its zero position when power is removed.)
If you have some array of magnetically-responsive pixels — for example, Dapper-Dan-style magnetic whiskers in tiny mostly-transparent plastic boxes, parts of which are opaque white — you can use a similar approach to scan a needle in a four-bar linkage involving two galvanometers back and forth over this array of pixels, activating a magnetic field at its tip to change the color of a pixel when appropriate. I think we can expect this to be slow and scale down poorly, but it would work.
Tiny permanent magnets behind white paper, or better still boundaries between magnetic poles behind white paper, could potentially make the pixels bistable in the absence of friction — the black filings would remain stably stuck to them in the absence of any applied magnetic field, even in the face of slight vibrations, but could be persuaded to leap to a different attractive spot by a temporary cancellation of the magnetic field with the needle tip.
An advantage of using magnetic-pole boundaries is that the field projected from the magnetic tip wouldn’t have to be perfectly calibrated — any amplitude large enough to temporarily more than cancel one of the poles would cause all the pole boundaries around that pole to temporarily disappear, encouraging the filings to migrate to a different still-existing boundary between poles. By alternating the field a number of times, filings in the area could perhaps be vibrated loose from any frictional moorings that prevent them from vacating the area.
Even without any PWM signals, scanning one or more needle tips over a two-dimensional area could be effected by purely mechanical means, for example in a VCR-like helical pattern, or a Spirograph-like family of circles of the same radius rotated around a center, or a Lissajous pattern created by two elastic resonant modes of different frequencies. Then, a persistent image could be produced simply from a time-varying magnetic field at the needle tip.
Suppose that instead of magnetic fields we use electric fields, and instead of permanent magnets we use electrets, which have the potential advantage of being monopole-capable. (As far as we know, magnetism is not monopole-capable, but all the electrical particles we know of are electrical “monopoles”, and so too are chunks of charged electret.) As described in Paper/foil relays, this should scale down rather well. This is more or less how e-ink displays work, but without the in-display decoding.
To be concrete about one possible realization, suppose we have some negatively-charged black electret particles suspended in oil in a tiny linear capsule; one end of the capsule is transparent, while the other end is opaque. We have some more negatively-charged electret embedded in the wall of the capsule near its center, slightly toward the opaque end, so the particles tend to drift toward the ends of the capsule when no voltage is applied, and in particular if they start out precisely in the center, they will tend to drift toward the transparent end, making the capsule look black. Lines 0, 2, and 3 are connected through capacitors to electrodes wrapped around places near the center of the capsule, but not overlapping, so that their mutual capacitance is low. Lines 1, 4, and 5 are connected through somewhat larger capacitors to electrodes at each end of the capsule, and line 6 is connected through a capacitor to an electrode on the opaque end of the capsule.
If +5V is applied to all of lines 0, 2, and 3, this pushes a certain amount of charge through the capacitors onto the electrodes around the center of the capsule, calibrated to be sufficient to shift the equilibrium such that the suspended electret particles will tend to drift from the ends to the center of the capsule. If only two of these lines are energized, this will not push enough charge onto those electrodes to cancel the wall-embedded electret. If all three of them are energized, but also one or more of lines 1, 4, and 5, there will be a net positive charge in the center of the capsule, but a larger net positive charge at the ends, so electret particles will remain at whichever end they are. But if none of these inhibitory lines are energized, the particles will move to the center, or rather, into a cloud near the center but slightly toward the transparent end.
If lines 0, 2, and 3 are then grounded, the wall-embedded electret will repel the cloud back to the transparent end. But if first line 6 is brought high, it will move the cloud past the wall-embedded electret, and then when lines 0, 2, and 3 are grounded, the cloud will migrate to the opaque end instead.
Of course, the same seven lines can control 63 such capsule pixels in this way, with lines 0–5 varying between inhibitory and activatory roles on different pixels, and line 6 always controlling which way the equilibrium falls when the decoding lines are released. Different capsules may require different amounts of wall-embedded electret to cancel their varying numbers of activatory lines, or perhaps the series capacitances that set the charge could instead be varied.
This is substantially more complex than the current schemes of e-ink displays, and it requires fairly high precision of manufacture to precisely calibrate the varying amounts of electret in each capsule, as well as precision of design to distribute the electrical fields properly.
We can easily go rather far afield with these ideas.
A scanning needle tip (whether raster, Spirograph, Lissajous, or otherwise controlled) of course can be activated in other ways. For example, mechanical actuation — in machining this is called a dot-peening machine and is used for alphanumeric part marking of malleable surfaces, and I’ve used a handheld “Vibro-Graver” version of the same process to mark my hand tools. In an electrolyte, voltage on a scanning needle tip can produce an image on a surface by selective electroplating or electrochemical machining (depending on polarity), and in air it can produce a corona discharge, which can selectively functionalize passivated surfaces (see Cold plasma oxidation) or produce light. If scanned over the same surface in an electrolyte for a long period of time, it can be used to 3-D print by electrodeposition or to cut an almost arbitrary cavity by electrochemical machining. On a few metals, like silver, such electrolytic processes can be used to induce a reversible, localized, dramatic color change; as mentioned in Electrolytic anodizing, with a small movable electrode, anodizing of titanium can produce quite brilliant colors through iridescence, and this can be done selectively to produce color images.
Some of the summing-and-differencing approaches discussed above might be usable to select individual “pixels” in such processes as an alternative to moving a needle around; for example, anodic dissolution of a metal workpiece will happen only in areas where there’s a net current of positively-charged cations from the workpiece to the tool pixels, while it’s possible to prevent anodic dissolution of tool pixels by making them out of carbon, and electroplating of the tool pixels with a suitable electrolyte. So if all but one of the tool pixels have a positive current flowing from them to the workpiece because of summing negative and positive currents, it should be possible to do selective electrochemical machining at the one pixel that is sucking up cations instead.
Most of the above methods can be adapted to activate electrical switches rather than optical pixels.