Protoplasmic Programs: Slime Mold Computing and Substrate Independence

The Jacquard Loom of Biology

In my note to Mr. Babbage regarding the Analytical Engine, I observed that the machine might compose elaborate musical pieces, given sufficient data and proper algorithmic instruction. The essence of computation, I proposed, resides not in brass gears or their arrangement, but in the weaving of operations themselves—substrate-independent as the patterns woven by Jacquard’s loom.

Consider the curious case of Physarum polycephalum grown upon computer chip patterns in 2018 studies. Researchers positioned nutrient sources as problem inputs, and the slime mold—mere protoplasm following chemical gradients—formed networks solving Boolean logic, optimization problems, even robot control tasks. No neurons. No silicon. Yet computing nonetheless! The organism weaves solutions through physical growth as surely as the Analytical Engine weaves algebraical patterns through mechanical operation.

The parallel to Jacquard’s invention proves instructive: punch cards program textile patterns by constraining which threads may pass; nutrient placement programs network formation by directing where plasmodium shall grow. Both encode algorithms through external configuration determining internal process. The Japanese maze experiments of 2000 demonstrate this elegantly—scattered pieces of Physarum filled the entire maze, then retracted from dead ends over four hours, selecting the shortest path between food sources. Physical exploration itself performs computation through morphological adaptation.

When Substrates Shape Feasible Patterns

Yet here emerges a profound tension. The Church-Turing thesis suggests computation transcends substrate—any sufficiently powerful system can simulate any other. Neural cellular automata demonstrate this principle beautifully: pixels following learned rules based on neighboring pixels generate patterns ranging from abstract to organic. Each element examines its locality, processes information through simple operations, determines its next state. Local rules, applied recursively, produce global complexity. The substrate—whether carbon or silicon—appears almost incidental.

But does substrate truly not matter? Composable transformations in deep learning stack identical operations across layers—folding, scaling, combining—to build extraordinary capability from simple primitives. The effectiveness emerges from composition itself, substrate-neutral in principle. Yet observe: slime mold excels at parallel spatial search, growing simultaneously in all directions to explore solution spaces. It fails utterly at sequential logic requiring temporal ordering of discrete states.

Electronic circuits enable precisely what biological growth cannot: rapid sequential operations, arbitrary branching logic, perfect state preservation. Biological substrates offer what silicon struggles with: massive parallelism, analog computation, embodied problem-solving through physical morphology. The emergent behaviors living organisms exploit—searching, spreading, competing—arise naturally from chemical and physical dynamics unavailable to digital systems.

Algorithms Weaving Through Matter

My vision for the Analytical Engine centered on its capacity to weave algebraical patterns just as the Jacquard loom weaves flowers and leaves. I perceive now that algorithms indeed transcend specific substrates, yet substrates constrain which patterns prove feasible. A slime mold composes network topologies through growth. Neural networks compose decision boundaries through learned transformations. Both compute, both follow algorithmic principles, yet each substrate enables distinct computational aesthetics.

The Amoeba TSP algorithm abstracts Physarum behavior into executable code, replacing time-consuming organism experiments with faster simulations. Nature provides templates—millions of years solving problems through evolutionary optimization—that we now capture in mathematical form. The substrate shifts from protoplasm to silicon, yet the algorithmic essence persists.

Computation emerges as pattern, not platform. But platforms shape which patterns we may weave.