## Heatmap and Subplot Analysis: Environmental Metric Evaluation ### Overview The image presents four environmental configurations (A-D: Corridor, Path, Maze, Room) with associated heatmaps and three subplots per configuration. Each configuration includes: 1. A heatmap visualization with grid-based spatial distribution 2. Three subplots showing metric evolution across λ values 3. Legend elements and fluctuation insets ### Components/Axes **Heatmap Elements:** - Grid-based spatial distribution with red/blue color coding - Central "obstacle" structure in each configuration - Labels A-D for configurations **Subplot 1 (Top):** - Y-axis: Metric value (0.6-1.4) - X-axis: λ (log scale, 10^-3 to 10^2) - Lines: - Red: Eλ(θ*) (mean metric value) - Blue: Hλ(θ*) (fluctuation metric) **Subplot 2 (Middle):** - Same axes as Subplot 1 - Inset: Fluctuation distribution (σ vs λ) - σ range: 0.00-0.05 **Subplot 3 (Bottom):** - Y-axis: MFPT/WHR (normalized, 0-1) - X-axis: λ (log scale, 10^-3 to 10^2) - Data points: - Black: MFPT (Mean First Passage Time) - Red: WHR (Wandering Home Ratio) - Shaded area: P_intuition (intuition probability) ### Detailed Analysis **Heatmap Patterns:** - A (Corridor): Central red cluster with blue periphery - B (Path): Concentrated red core with radial blue distribution - C (Maze): Fragmented red regions with complex blue network - D (Room): Compact red core with minimal blue extension **Subplot 1 Trends:** - All configurations show: - Red line (Eλ) increasing with λ, plateauing near 1.4 - Blue line (Hλ) following similar trend with higher variance - Notable σ peaks at λ≈10^-1 in all cases **Subplot 3 Patterns:** - MFPT (black): - Sharp decline at λ=10^-1 - Stabilizes near 0.2 for λ≥10^0 - WHR (red): - Gradual increase until λ=10^0 - Sharp rise to 1.0 for λ≥10^1 - P_intuition (cyan): - Peaks at λ=10^-1 across all configurations ### Key Observations 1. Environmental complexity correlates with: - Increased metric fluctuations (σ peaks at λ=10^-1) - More pronounced intuition probability peaks 2. WHR shows stronger λ dependence than MFPT 3. Maze configuration (C) exhibits most complex spatial distribution 4. Room configuration (D) demonstrates most stable metric behavior ### Interpretation The data suggests that: - λ=10^-1 represents a critical threshold where: - Metric fluctuations peak (σ) - Intuition probability maximizes (P_intuition) - WHR begins rapid increase - Maze environments create most spatially complex metric distributions - Room environments show most stable metric behavior across λ values - The relationship between spatial configuration and metric evolution indicates that: - Lower λ values (10^-3 to 10^-1) capture environmental sensitivity - Higher λ values (10^0 to 10^2) reflect stabilized behavioral patterns - The intuition probability (P_intuition) appears to predict significant behavioral transitions at λ=10^-1 *Note: All values are approximate due to image resolution constraints. σ values in fluctuation insets show consistent peak magnitude (~0.05) across configurations.*