refractive computation
Granular Polycomputation
This visualization shows how granular materials can perform multiple logical operations simultaneously at different frequencies. The system demonstrates frequency-multiplexed computation where the same physical medium processes different logic gates based on vibration frequency.
How it works
Vibrations at different frequencies propagate through the granular material differently, creating frequency-dependent force networks. By evolving the grain arrangement and stiffnesses, frequency 1 builds force chains that implement one NAND gate, frequency 2 builds different chains for a second NAND gate, and the output grain reports a separate logical result on each channel. The nonlinearity needed for logic comes from the contact mechanics: force is transmitted only when grains actually overlap.
The refraction metaphor
One medium, many frequency channels, computed at once.
A prism bends red and blue light by different angles because the refractive index depends on frequency. An evolved grain bends incoming vibration energy differently at different frequencies in the same way, so one physical element can play distinct roles in two computations at the same time. That shared structure, one passive body routing many channels, is why this mechanical system is framed as refractive computation.
NAND completeness
NAND is functionally complete; every Boolean circuit can be built from NAND gates alone, so a material that robustly computes NAND is in principle a universal logic substrate.
| A | B | NAND(A,B) |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Material evolution
A gate-performing packing is discovered offline by a genetic algorithm, not in real time. The live canvas animates one fixed packing and its frequency response; the evolution controls describe how such a packing would be found, by initialising random configurations, applying vibrations with input signals, measuring the output grain, selecting the configurations closest to the target logic, and mutating across generations until convergence.
Where it could go
Mechanical logic embedded in materials suggests computers for harsh environments, computation inside compliant soft robots, processing powered by ambient vibration, many gates multiplexed in one body, and fault tolerance from distributed force chains. The open obstacle is cascadability: whether the noisy output of one mechanical gate can drive the next without degrading the signal.
Implementation
Calibration
Assumptions
Model changelog
- logic module: contactNormalForce (F = sqrt(overlap)*k), frequencyFactor (1 + 0.5 sin(2 pi f t)), NAND and nandBit, readChannelBit threshold readout, outputCorrect multiplex check, and grainRadius / packedGrainCapacity geometry.
- two vibration channels multiplex two NAND gates through one fixed packing; the output grain reports each gate by thresholding its displacement along one axis.
- calibration: six deterministic checks (contact force at a known overlap, zero force without contact, the NAND low row, all-four-rows NAND match, packing-geometry round trip, and a correct multiplexed output), every predicted value recomputed from the logic module.
- framing kept honest: the live canvas animates one fixed packing, the genetic-algorithm controls describe an offline search rather than the on-screen dynamics, and the contact-law exponent is flagged as a softened approximation to the Hertz 3/2 power law.
References
- Parsa et al., "Universal Mechanical Polycomputation in Granular Matter"
- Bongard and Levin, "Living Things Are Not (20th Century) Machines"
- Sheffer (1913), the NAND as a sole sufficient operator for Boolean algebra