## Contour Plots: Comparative Analysis of EFE1, EFER, and EFE2 ### Overview The image displays three side-by-side contour plots (heatmaps) labeled "EFE1", "EFER", and "EFE2". These plots visualize a scalar field over a two-dimensional domain defined by axes $X_1$ and $X_2$. Each plot features a distinct "swirl" or vortex-like pattern centered near the origin $(0,0)$ and a single white circular marker positioned at varying heights along the $X_2$ axis. ### Components/Axes * **X-Axis ($X_1$):** Horizontal axis ranging from approximately -1.5 to 1.5, with major ticks at -1, 0, and 1. * **Y-Axis ($X_2$):** Vertical axis ranging from -0.5 to 2.0, with major ticks at -0.5, 0.0, 0.5, 1.0, 1.5, and 2.0. * **Legends:** Each plot includes a vertical color bar on the right side, mapping colors to numerical values. * **EFE1:** Scale ranges from -10 (dark purple) to 15 (dark red). * **EFER:** Scale ranges from 5 (dark purple) to 30 (dark red). * **EFE2:** Scale ranges from 5 (dark purple) to 30 (dark red). * **Markers:** A white dot is present in each plot, positioned at $X_1 = 0$. * **EFE1:** $X_2 \approx 1.2$ * **EFER:** $X_2 \approx 1.3$ * **EFE2:** $X_2 \approx 1.7$ ### Detailed Analysis #### 1. EFE1 * **Trend:** The plot exhibits a large, low-value region (dark purple, $\approx -10$) occupying the upper portion of the domain. A high-value "swirl" (orange/red, $\approx 10-15$) originates from the left side ($X_1 < 0$) and spirals into a central point near $(0,0)$. * **Marker:** The white dot is located at $(0, 1.2)$, situated within the low-value dark purple region. #### 2. EFER * **Trend:** The color distribution is similar to EFE1 but shifted to a positive scale (5 to 30). A large dark purple region (value $\approx 5$) dominates the top half. A high-intensity vortex (dark red, $\approx 30$) is concentrated at the origin $(0,0)$. * **Marker:** The white dot is located at $(0, 1.3)$, slightly higher than in EFE1, still within the low-value region. #### 3. EFE2 * **Trend:** This plot is visually nearly identical to EFER. It features the same large dark purple region at the top and the same high-intensity vortex at the origin. * **Marker:** The white dot is located at $(0, 1.7)$, significantly higher than in the previous two plots, moving further away from the central vortex. ### Key Observations * **Vortex Feature:** All three plots share a common topological feature: a high-value vortex centered at $(0,0)$. This suggests a non-convex landscape or a potential field with a singularity at the origin. * **Marker Progression:** The white dot moves vertically upward across the three plots ($1.2 \rightarrow 1.3 \rightarrow 1.7$). This implies a sequential process, such as an optimization path, a parameter sweep, or a time-series evolution of a system state. * **Scale Discrepancy:** EFE1 uses a different color scale (including negative values) compared to EFER and EFE2, which use identical positive scales. This suggests EFE1 may represent a different function, a different phase of the system, or a normalized version of the data. ### Interpretation The data suggests these plots represent the evaluation of a cost function or a potential field in a 2D space. The "swirl" pattern is characteristic of optimization landscapes where a global or local optimum is surrounded by a "valley" or "ridge" that spirals toward the center. The progression of the white dot indicates that the system is moving away from the central vortex (the high-value region) as the index progresses from EFE1 to EFE2. Given the visual similarity between EFER and EFE2, they likely represent the same underlying model or state, whereas EFE1 represents a distinct state or a different mathematical formulation. The white dot likely represents the current "position" or "state" of an agent or algorithm being tracked across these different configurations.

## Heatmap Visualization: EFE1, EFER, EFE2 ### Overview The image contains three side-by-side heatmaps labeled **EFE1**, **EFER**, and **EFE2**, each depicting a 2D spatial distribution of values across axes **X1** (horizontal, -1 to 1) and **X2** (vertical, -0.5 to 2.0). All heatmaps share a consistent coordinate system but differ in color intensity ranges and spatial patterns. A white dot is consistently positioned at **(X1=0, X2=1)** across all plots. --- ### Components/Axes - **Axes**: - **X1**: Horizontal axis, labeled with values **-1, 0, 1**. - **X2**: Vertical axis, labeled with values **-0.5, 0, 0.5, 1, 1.5, 2.0**. - **Color Scales**: - **EFE1**: Ranges from **-10 (dark blue)** to **15 (dark red)**. - **EFER**: Ranges from **-10 (dark blue)** to **30 (dark red)**. - **EFE2**: Ranges from **5 (light blue)** to **30 (dark red)**. - **Legend**: Positioned on the right of each heatmap, with a vertical gradient from dark blue (low values) to dark red (high values). No explicit legend labels beyond the colorbar. - **White Dot**: Located at **(X1=0, X2=1)** in all heatmaps, likely a reference point. --- ### Detailed Analysis #### EFE1 - **Color Distribution**: - Dominant **dark purple/blue** in the upper-left quadrant (X1 < 0, X2 > 0.5), indicating values near **-10**. - A **gradient from red to blue** in the lower-left quadrant (X1 < 0, X2 < 0.5), transitioning from **15 to -10**. - A **small white dot** at **(0,1)** stands out against the dark background. - **Key Features**: - A **circular red region** centered at **(X1=0, X2=1)** with a radius of ~0.5 units. - A **funnel-like gradient** in the lower-left corner, transitioning from red (high values) to blue (low values). #### EFER - **Color Distribution**: - Similar **dark purple/blue** upper-left quadrant as EFE1. - A **larger red region** in the lower-left quadrant (X1 < 0, X2 < 0.5), extending to **X1=-0.5**, with values up to **30**. - The white dot at **(0,1)** is surrounded by a **darker red halo** compared to EFE1. - **Key Features**: - The red region in the lower-left is **more extensive** than in EFE1, suggesting higher values in this area. - The gradient near **(X1=0, X2=0.5)** transitions sharply from red to blue. #### EFE2 - **Color Distribution**: - **Dark purple/blue** upper-left quadrant, but with a **smaller red region** near **(X1=0, X2=1)** compared to EFER. - A **broad red-to-blue gradient** in the lower-left quadrant, with values peaking at **30** near **(X1=-0.5, X2=0)**. - The white dot at **(0,1)** is surrounded by a **moderate red halo**. - **Key Features**: - The red region in the lower-left is **less concentrated** than in EFER but covers a wider area. - A **distinct gradient** from red (high values) to blue (low values) along the X1=0 axis. --- ### Key Observations 1. **Consistent Reference Point**: The white dot at **(0,1)** is present in all heatmaps, possibly indicating a critical threshold or anomaly. 2. **Color Scale Variability**: - EFE1 has the **narrowest range** (-10 to 15), while EFER and EFE2 extend to **30**. - EFE2’s scale starts at **5**, excluding negative values. 3. **Spatial Patterns**: - All heatmaps show a **concentration of high values (red)** near **(X1=0, X2=1)**. - EFER exhibits the **strongest gradient** in the lower-left quadrant, while EFE2 has a **wider but less intense red region**. 4. **Anomalies**: - The white dot’s position remains unexplained by the color gradients, suggesting it may represent an outlier or predefined value. --- ### Interpretation - **EFE1** likely represents a baseline scenario with moderate value ranges, where the white dot’s significance is unclear. - **EFER** shows amplified values in the lower-left quadrant, possibly indicating a localized phenomenon (e.g., a shockwave or energy concentration). - **EFE2** suggests a broader distribution of high values, with the white dot acting as a focal point for moderate-intensity effects. - The **white dot’s consistent placement** across all heatmaps implies it is a **fixed reference** (e.g., a sensor location or theoretical origin point). Its lack of alignment with the red regions in EFE2 may indicate a decoupling between the reference and high-value zones in this scenario. The heatmaps collectively demonstrate how spatial distributions of values (possibly energy, pressure, or error metrics) evolve across different conditions or parameters, with the white dot serving as a critical anchor for analysis.