Exploring macro scale fluidic logic systems in LGA
Aaron N. Parks - CSE599D/EE590A Autumn 2013, University of Washington

What’s it all about?

It has been shown that logic functions can be implemented given knowledge and control of the micro-state of the lattice gas automata (LGA). However, the deterministic behavior of the LGA at the micro scale does not well represent the far more stochastic behavior of moving particles in the real physical world, and therefore it's possible that use of micro scale LGA logic is limited to the realm of academic curiosity.

Figure 1. An example of micro scale LGA logic.

In this project, I propose to use the macro scale behavior of the LGA (which is known to be similar to that of real fluids) to implement approximate or exact logic systems with macro scale inputs and outputs. Two classes of macro logic systems were attempted: Impulse gates, in which the transient response of the density of particles at specified locations has a logical dependence on initial particle distribution, and flow gates, in which the gate inputs and outputs are defined in terms of particle flow rates through well-defined thresholds.

Because macro scale behavior of an actual fluidic system is easily observable, these systems have more potential to be applied in actual use, while still potentially preserving the interesting and much-studied computational energy properties of micro-scale LGA logic.

Impulse gates

The first stage of this project involved building a series of novel gates whose inputs are defined as an initial particle distribution (the initial density of particles at each of several “input” chambers), and whose outputs are defined as the transient characteristics of the density in one or more predefined “output” areas. The first such gate devised is shown in Figure 2, and attempts to implement a NAND function.

Figure 2. A NAND Impulse gate. Initial particle densities in the “A” and “B” chambers represent the two inputs, and the transient behavior of the density in the “OUT” chamber should be dependent on those inputs.

The NAND impulse gate leverages the 3-particle collision rule for the FHP-I LGA, in which three particles which collide will all reverse trajectory. The A and B inputs are reflected by angled mirrors towards the always-present flow of particles from the center chamber, and when both A and B are initialized with a high particle density, the number of 3-particle collisions which occurs prevent the center chamber particles from reaching the output and thereby reduce the peak density in the output chamber.

Figure 3. Impulse NAND simulation showing transient dependence of particle distribution on inputs. Region 4 is the output. In the top experiment, one input is low (zero intial density). In the bottom experiment, both inputs are high.

After verification that the simple NAND gate worked, a generalized gate was produced which can perform both NAND and an inversion operation. It is shown in Figure 4, and NAND results were similar to those in Figure 3.

Figure 4. Generalized version of the macro impulse gate which leverages 3-particle collision rules. A NAND function can be implementing by setting C=1 and using A and B as inputs, while a NCOPY (inverting copy gate) can be produced by setting A=B=1 and using C as the input.

The transient behavior of the particle density in the output chamber clearly has some dependence on the logic function implemented, and so the hypothesis was confirmed in this case.

One caveat of impulse gates is that the particle distribution at equilibrium is always the same (evenly distributed) and therefore no logical dependence will be seen once the system achieves equilibrium. Also, the initial attempts shown here at producing an impulse gate did not result in any amplification. In other words, the quantity of inputs particles required to modulate an output stream was always larger than the resulting output fluctuation. These two factors are likely to limit the usefulness of these gates.

Flow gates, and fluidic devices

Taking a step back and examining the problem from a system perspective, it appears that the best way to define “input” and “output” values for a fluid based logic system is as flow rates (quantity of particles passing across a given threshold per unit time). In examining implementation possibilities for such flow based devices, I uncovered some fluidic devices from ancient history (the 60’s and 70’s) which were able to achieve logic using flow based fluidic devices. Figure 5 shows a Popular Science article from June 1967 which describes some of these fludic devices and their operating principles.

Figure 5. In June 1967, popular science reports on the then-cutting-edge science of fluidic logic devices, and on how they will change our future forever.

At the time of their invention, these devices were seen as having huge potential for use in logic systems of the future, to replace fragile and expensive vacuum tubes. Since the advent of inexpensive transistorized and integrated circuits, these fluidic devices have largely fallen out of interest. However, two recent examples (1, 2) of fluidic devices indicate a potentially renewed interest in the devices, though not exactly in computational logic applications.

Two effects from fluid dynamics are at work in these fluidic devices:

1. Momentum transfer, simply the transfer of kinetic energy from one particle to another through particle-particle collisions.

2. The Coanda effect, the tendency of fluid streams to gravitate towards and follow nearby surfaces

Figure 6 illustrates a bistable fluidic device which makes use of both momentum transfer and the Coanda effect for its operation. The device can latch into one of two stable states, and in either state the stability is achieved by the tendency of the fluid stream to stick to the closest wall.

Figure 6. A bistable fluidic device, making use of the Coanda effect for latching and momentum transfer for perturbing the system state.

The latter portion of this project involved attempting to implement the fluidic device in Figure 6 in both the LGA simulator and in the real physical world. To develop a physical prototype, 3D modeling software and a 3D printer was used.

Examining fluidic devices in LGA

The Coanda effect is essential to most fluidic devices, and therefore it became the focal point of this study of LGA properties. Two models were constructed in the LGA simulator to determine whether the LGA exhibited the Coanda effect. The left-to-right flow in the first of these models, shown in Figure 7, should tend to stick to the curved wall and therefore should be diverted mostly downward in its travel, if the Coanda effect occurs in the LGA.

Figure 7. Structure used to determine existence of Coanda effect. All walls are reversing boundaries, not specular reflecting walls.

Unfortunately, the expected diversion of flow along the curved surface was not observed in simulation, and this is evidence towards a conclusion that the Coanda effect does not occur in an FHP-I LGA. Figure 8 shows the simulated particle flow for the structure in Figure 7.

Figure 8. Simulation results for the structure in Figure 7, with a particle source place at the leftmost point in the structure. No diversion of flow is observed, so I have concluded that the Coanda effect is not exhibited in this test.

In hopes that momentum transfer might still be adequately modeled by the LGA, I then simulated a structure (Figure 9) which should provide some flow diversion based on the state of the two control inputs. This is a simple model of a fluidic transistor. The smaller tubes running vertically through the midpoint of the structure are control inputs, and the larger tubes running horizontally are control inputs. Two outputs are used in this structure, and, if momentum transfer behaves as we expect, the differential flow between them should be modulated by the control input flow.

Figure 9. Structure used to determine existence of momentum transfer. All walls are reversing boundaries, not specular reflecting walls.

Yet again, the LGA fails to exhibit the expected effect of momentum transfer. This may be due to the specifics of the collision rules in the LGA; only head-on collisions or 3-particle collisions cause a change in velocity, and the orientation of the control inputs with respect to the main flow does not primarily result in these types of collisions. Figure 10 illustrates the failure of the output flow to be affected in the case where the bottom control input is “high” (high flow rate).

Figure 10. Simulation results for the structure in Figure 9, with a particle source placed at the leftmost point in the power feed and another source place at the bottom most point in the lower control input. If momentum transfer occurred, we would expect to see most of the flow diverted to the upper output.

3D-Printed fluidic devices

Although the LGA failed to reproduce the effects necessary for implementation of fluidic logic devices, the devices themselves were still an interesting example of physical logic/computing. I decided to attempt to build a real-life model of the bistable fluidic transistor simulated above, and find out if the device could work in the real physical world.

I made use of OpenSCAD, a solid modeling language, to develop a parameterized model of the bistable latch device with two finger-switched control inputs. An image depicting this device is included in Figure 11.

Figure 11. A rendering of a parameterized model of a bistable fluidic circuit. This circuit makes use of the Coanda effect for latching, and momentum transfer for perturbing the latch state.

I selected some “best guess” values for each of the parameters of the circuit, for instance, for the pipe diameters and the radius of curvature of the diverging output pipes. I then made use of a 3D printer to fabricate two versions of the device, each at a different scaling factor, to try and maximize the odds of a working gate.

The video below shows some testing done on the 3D printed gates. Both air and water were tested on both printed devices. The two small holes on the top face of the device are intended to allow manual diversion of flow into each of the control inputs. If the device exhibits the required fluidic properties, we hope to see the output flow diverted opposite to the active control input.

Unfortunately, even the real physical model failed to exhibit the expected fluidic device properties. This result calls into question the preliminary conclusions drawn from the LGA simulation results, as the same designs were used in the LGA; it’s possible that the structure fails to exhibit the Coanda effect or momentum transfer effect simply because the design is flawed, rather than indicating the absence of these effects in the LGA.

Conclusion

While the impulse gates simulated in the LGA did exhibit some logical dependence, they made use of somewhat unrealistic 3-particle collision rules which are unlikely to be exhibited by real physical systems and are therefore unlikely to work in the real world.

Flow based gates deserve more study, and in my opinion it’s not yet clear whether or not the Coanda effect or momentum transfer effect, two effects seen in real fluid dynamics which are necessary for fluidic device operation, are actually exhibited by the LGA.

The failure of the 3D printed model to behave as a fluidic logic device is likely due to the enormous size of the design space for this device, multiplied by my unfamiliarity with that design space. Since prior work has shown that these devices can be made to operate as intended, I will not draw any particular conclusion about real fluidic devices in general other than to say that they are not trivial to design.

3D printing enables rapid and inexpensive prototyping of fluidic devices, and this is an exciting collision of a very old and very new technology. It will be interesting to see what future fluidics research will bring us in the age of 3D printers.

Source code

Source for the LGA simulations and the parameterized design files for the bistable fluidic latch are available here