Cellular automata: implementation evidence
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A cellular automaton updates many local cells under a common rule. Universality of a rule is not an implementation claim; the matrix asks whether the local-update machine has been built and used.
| Stage | Mark | Summary |
|---|---|---|
| Reference | ● | Executable rules and universal variants |
| Physical | ● | FPGA, CMOS, and memristive realizations |
| Integrated | ● | State and local transition logic combined |
| Scaled | ◐ | Arrays demonstrated, but not general systems |
| Access | ◐ | Research implementations rather than a public appliance |
| Operational | ◐ | Specialized repeated computation only |
Reference — demonstrated
- Claim
- The matrix credits cellular automata at the Reference stage: executable rules and universal variants.
- Evidence
- Cellular-automaton rules are directly executable, and universal constructions are established. The reference mark concerns the semantics of local state transition, not the practicality of compiling ordinary software into those rules.
- Criticism
- Executable semantics do not establish purpose-built hardware, integration, scale, external access, recurring use, or comparative advantage.
- Sources
- Cellular automata embedded in memristor-based recirculated logic
Physical — demonstrated
- Claim
- The matrix credits cellular automata at the Physical stage: FPGA, CMOS, and memristive realizations.
- Evidence
- Purpose-built FPGA and CMOS implementations exist. The cited memristive work physically embeds a cellular-automaton update in recirculated in-memory logic, coupling stored state to local computation.
- Criticism
- A physical realization does not by itself establish system integration, efficient scaling, external access, recurring use, or comparative advantage.
- Sources
- Cellular automata embedded in memristor-based recirculated logic
Integrated — demonstrated
- Claim
- The matrix credits cellular automata at the Integrated stage: state and local transition logic combined.
- Evidence
- The memristive demonstration combines memory, local Boolean operations, and repeated state update in one array. This is enough for a coherent device-level implementation, though external control and readout remain conventional.
- Criticism
- A coherent system does not by itself establish efficient scaling, external access, recurring use, or comparative advantage.
- Sources
- Cellular automata embedded in memristor-based recirculated logic
Scaled — limited
- Claim
- The matrix credits cellular automata only partially at the Scaled stage: arrays demonstrated, but not general systems.
- Evidence
- Arrays contain many cells and update them in parallel, but the evidence does not establish a general machine whose useful programs preserve locality as the array grows. Global communication can erase the architectural advantage.
- Criticism
- The mark is limited on the current public record: arrays demonstrated, but not general systems. Composition at the reported scale does not establish useful scaling across workloads, favorable economics, or comparative advantage.
- Sources
- Cellular automata embedded in memristor-based recirculated logic
Access — limited
- Claim
- The matrix credits cellular automata only partially at the Access stage: research implementations rather than a public appliance.
- Evidence
- Rules, papers, and some research implementations are available to outsiders. The purpose-built devices themselves are not exposed as generally programmable public systems.
- Criticism
- The mark is limited on the current public record: research implementations rather than a public appliance. Access does not establish broad availability, recurring use, workload generality, or comparative advantage.
- Sources
- Cellular automata embedded in memristor-based recirculated logic
Operational — limited
- Claim
- The matrix credits cellular automata only partially at the Operational stage: specialized repeated computation only.
- Evidence
- The hardware can perform repeated local updates and specialized in-memory logic. This is narrower than recurring deployment on externally chosen applications, so the cell is partial rather than full.
- Criticism
- The mark is limited on the current public record: specialized repeated computation only. Recurring work does not establish workload generality, independent reproduction, favorable economics, or comparative advantage.
- Sources
- Cellular automata embedded in memristor-based recirculated logic