#Analysis Limitations And Extensions

#Evidence Boundary

The Wildfire and Epidemic results are descriptive experiments on one $512\times512$ toroidal grid, using one version of each preset, one $12$-cell seeding protocol, a fixed ruleset random seed ($42$), and $30$ runs per density. They locate strong finite-grid crossovers but do not estimate universal critical points.

The main sources of uncertainty are:

• Finite sample size: $30$ runs per density reveal the large transition effects, but they give limited precision for rare outcomes such as Epidemic resurgence.
• One grid size: no finite-size scaling was performed, so transition location and width may shift with grid dimensions.
• One topology: toroidal wrapping removes outer boundaries and can reconnect fronts that would meet an edge in a bounded world.
• One seed geometry: seed count is fixed at $12$, but location, shape, and boundary placement were not varied systematically.
• One preset parameterization: vegetation thresholds and Epidemic transition probabilities were not swept.
• Common ruleset seed: every archive records seed $42$. Different randomized brush layouts produce distinct runs, but the probability field itself was not re-seeded across replicates.

No confidence intervals, hypothesis tests, changepoint model, or finite-size scaling fit has been applied. The boxplots, IQR curves, medians, and quartiles should therefore be read as empirical summaries of the collected runs.

#Data And Metric Limitations

The analysis scripts use aggregate metrics.csv rows, downloaded from the engine built-in export. They do not use the spatial pattern inside every recorded generation.

Consequences include:

• Wildfire burn fraction does not identify connected fuel components, front perimeter, crossing probability, or unburned-island geometry.
• Epidemic episodes reconstruct the total number of S → I events but do not identify how those events are distributed among cells.
• Aggregate prevalence cannot distinguish $1$ coherent wave from several simultaneous local outbreaks.
• Final-state summaries do not measure spatial clustering, correlation length, or front velocity.

#Resurgence Sensitivity

The resurgence definition uses an $11$-generation centered smoother, $0.15\%$ start threshold, $0.05\%$ end threshold held for $25$ generations, $8\times$ trough-to-peak rebound, and $10$-generation persistence requirement. These are explicit, arbitrary analysis choices rather than preset, derived, or standard parameters.

The current conclusions do not show whether the $31$ runs with at least $1$ resurgence remain the same under nearby settings. The centered mean also uses future values, making it appropriate for retrospective analysis but unsuitable as an online detector.

#Possible Analysis Extensions

#Replication And Uncertainty

• Increase repetitions near $89\text{–}91\%$ Wildfire and $40\text{–}42\%$ Epidemic density.
• Report bootstrap confidence intervals for medians, IQRs, fadeout probability, and any-resurgence probability.
• Predefine endpoints and analysis thresholds in a machine-readable experiment specification.

#Finite-Size And Geometry Tests

• Repeat on several square grid sizes and estimate how crossover location and width change.
• Compare toroidal and bounded topology.
• Vary active seed count, compactness, position, and number of simultaneous foci.
• For a matched NetLogo comparison, add left-edge ignition and a common boundary-crossing endpoint.

#Parameter Sensitivity

• Wildfire: vary vegetation mix, ignition thresholds, fire-state duration, regrowth, and directional effects.
• Epidemic: vary infection, recovery, mortality, and immunity-loss probabilities independently.
• Replace the saturating infection rule with neighbor-count-dependent exposure and compare the transition.
• Perform a sensitivity grid around the resurgence thresholds and smoothing window.

#Spatial Analysis

• Measure connected components, spanning clusters, front speed, perimeter, anisotropy, and correlation length for Wildfire.
• Measure infection-cluster count, wavefront geometry, spatial autocorrelation, and source locations for Epidemic.
• Track each fixed cell's state history to obtain the distribution of reinfections, not only aggregate episodes per initial population.

These extensions would turn the current exploratory result into a more formal computational experiment without changing the conclusions already supported by the archived data.