physarum

Physarum polycephalum (slime mould) on the CPU, loadable through kernels, two ways: an agent model that grows the organic transport networks the organism forms, and a flow solver that finds shortest paths and builds networks by the Tero adaptive-conductivity model. The reference baselines are breadth-first search, Dijkstra, and the terminals' minimum spanning tree, matched exactly on length.

Slime mould solves routing problems by growing: it thickens the tubes that carry flux and abandons the rest, and the surviving network is a shortest path or an efficient multi-terminal network. This kernel runs both formulations fast enough to be interactive on a Raspberry Pi, so the biological algorithm becomes a usable network-design tool, including one thing the classical algorithms do not give: a network that survives any single edge cut.

1200x1200 field, 680k agents, on a Raspberry Pi 4.

Usage

import torch
from kernels import get_kernel

physarum = get_kernel("phanerozoic/physarum", version=1, trust_remote_code=True)

open_mask = physarum.maze(127, 127, seed=5)      # 1 = open, 0 = wall
solver = physarum.PhysarumFlow(open_mask)
solver.solve([(2, 2), (124, 124)], [1, -1])      # a source and a sink
path = solver.path((2, 2), (124, 124))           # [(x, y), ...], the route

sim = physarum.Physarum(width=1024, height=1024, agents=200_000, seed=0)
for _ in range(400):
    sim.step()
img = sim.image()            # [H, W, 3] uint8, inferno colormap

version selects the release branch; trust_remote_code is required by kernels for publishers without the trusted-publisher mark.

API

Method

The flow solver follows Tero et al. (2010): current flows between terminals on a masked grid, each step reinforces high-flux edges and lets the rest decay, so the conductivities converge onto the shortest path (one source and sink) or an efficient network (several terminals). The inner step is a weighted-graph-Laplacian solve exposed as flow_cg, Jacobi-preconditioned conjugate gradients over a NEON 5-point mat-vec.

The agent model follows Jones (2010): each agent samples the field at three sensors (ahead, and +/- sense_ang at sense_dist px), rotates by turn toward the strongest, moves speed px, and deposits deposit; the field is then convolved with a separable 3-tap [1 2 1]/4 kernel and multiplied by decay. The agent update runs across cores via at::get_num_threads(), and agents are counting-sorted into 32px tiles every eight steps so consecutive and same-core agents sense a hot window rather than scattering three gathers across the field. The step is deterministic for any thread count.

Measured

Flow solver, single-core solve time (200 adaptation steps, flow_cg):

CG is sequential and the grids are modest, so the solve is vectorised but not threaded; the mat-vec is a 5-point weighted stencil in gather form.

Agent model, 1024x1024 field, 200k agents (NEON, tile-sorted):

Comparison with classical algorithms

benchmark.py compares the solver to breadth-first search, Dijkstra, and the terminals' minimum spanning tree on a 4-connected grid, averaged over random configurations:

The flow model converges to the shortest path for a single source and sink, reproducing Dijkstra's length exactly (Dijkstra is faster in time). solve connects several terminals with a network of spanning-tree length; solve_robust reinforces the flux over every terminal pair to build a network that survives any single edge cut.

Requirements and limits

• float32, CPU. NEON on aarch64; portable scalar elsewhere.
• Flow solver: 4-connected grid, one node grounded for the gauge; deterministic.
• Agent model: threaded update (torch.set_num_threads), serial deposit and diffusion, deterministic for any thread count.
• Behavioural and phenomenological models of Physarum, not biophysical ones.
• get_kernel loads a prebuilt aarch64 or x86_64 variant for torch 2.11-2.13; for other torch versions, load_local.load() JIT-compiles the same source.

References

Tero et al., "Rules for biologically inspired adaptive network design" (Science, 2010); Jones, "Characteristics of pattern formation and evolution in approximations of Physarum transport networks" (2010).

License

Apache-2.0.