refractive computation
multiple logical operations simultaneously at different frequencies
Time
0.00s
Grains
0
Contacts
0
Energy
0.0
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.
Input Grains: Green grains represent logical inputs, with brightness indicating the input state (bright = 1, dim = 0).
Force Chains: Green lines show force transmission paths that carry computational information through the material.
Output Grain: The rightmost grain shows the computational result (green = correct logic output, red = incorrect).
Understanding Polycomputation
How It Works
Vibrations at different frequencies propagate through the granular material differently, creating frequency-dependent force networks. By evolving the grain arrangement and properties:
- • Frequency 1: Creates force chains implementing one NAND gate
- • Frequency 2: Creates different force chains for another NAND gate
- • Output Grain: Reports different logical results at each frequency
- • Nonlinearity: Contact mechanics provide necessary logical nonlinearity
NAND Gate Universality
NAND gates are functionally complete - any logical circuit can be built using only NAND gates:
| A | B | NAND(A,B) |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Material Evolution
The granular assembly is evolved using genetic algorithms to discover configurations that perform desired computations:
- Initialize random grain configurations
- Apply vibrations at multiple frequencies with input signals
- Measure output grain responses
- Select configurations closest to target logic functions
- Mutate and crossover to create next generation
- Repeat until convergence
Applications & Implications
- • Harsh Environments: Mechanical computers for extreme conditions
- • Soft Robotics: Computation embedded in compliant materials
- • Energy Harvesting: Computing powered by environmental vibrations
- • Parallel Processing: Many computations in single material
- • Fault Tolerance: Distributed computation provides robustness
References
- • Parsa et al. - "Universal Mechanical Polycomputation in Granular Matter"
- • Bongard & Levin - "Living Things Are Not (20th Century) Machines"
- • Wright & Flecker - "Mechanical Computing: The Computational Complexity of Physical Devices"