Research method
Growth-Pattern Taxonomy
A working taxonomy for multi-ink plots: classify a system by mechanism and inputs before assigning it a biological metaphor.
Use
These categories are not all slime-mould models. They gather different procedures that can produce growth-like paths, networks, fronts, or fields. For a separable multi-ink plot, one layer should have a distinct structural role—not simply be a recoloured duplicate.
Mechanisms, inputs, character, and ink roles
- Physarum-inspired agent/trail models. Agents sense, steer, deposit, diffuse, and decay; inputs are attractor/repellent maps and agent parameters; character: tendrils, aggregation, adaptive trails; layers: fresh deposit, persistent trail, and attractor/constraint field. Example: Jones’s particle model.
- Graph optimisation and transport reinforcement. Edge flow strengthens or decays network capacity; inputs are terminals, edge costs, and source/sink conditions; character: economical routes with optional redundancy; layers: reinforced backbone, alternate connections, and terminals. Example: Physarum shortest-path model.
- Diffusion, reaction, and chemotaxis fields. Coupled concentrations diffuse, react, or follow gradients; inputs are initial concentrations, masks, sources, and rates; character: fronts, spots, waves, labyrinths; layers: isolines, threshold bands, and gradient trajectories. See Gray–Scott reaction–diffusion study.
- Branching, space colonisation, and L-systems. Tips extend toward attractors or rewrite symbolic rules; inputs are attractor clouds, branching angles, grammar, and pruning rules; character: trees, veins, dendrites; layers: trunk order, branch order, and attraction points. Example: space-colonisation algorithm.
- Cellular automata and excitable media. Local states update from neighbours; inputs are seed states, neighbourhood, thresholds, and rule table; character: discrete growth, pulses, wavefronts; layers: activation front, stable trace, and boundary cells. Example: excitable-media maze research.
- Flow, particles, and field-driven growth. Particles integrate a vector field or follow a potential; inputs are vector/scalar fields, seed distribution, and lifetime; character: streamlines, accumulation, directional drifts; layers: source field, long trajectories, and short local marks. Example: Perlin’s coherent-noise reference.
- Data-constrained growth and contours. Growth is limited or directed by sampled measurements, masks, topology, or elevation; inputs are data, thresholds, and sampling rule; character: legible correspondence between data and path; layers: contours, gradient traces, and flagged extrema.
Multi-ink implications
Give each ink a non-overlapping job: structure versus event, persistent network versus exploratory trace, low-frequency organisation versus high-frequency correction, or source data versus derived path. Separate layers must remain meaningful alone, register to the same coordinate system, and avoid using colour to conceal indistinguishable geometry. Test each layer as a one-pen plot before combining it.
Scope note
Interpretation, not equivalence. A branching line can resemble an organism without being a biological model. Record the actual rule set, input data, seed, and update process; use terms such as “Physarum-inspired,” “reaction–diffusion,” or “field-driven” only when they describe the mechanism.