diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4930ac1..6e5a5ed 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -4,6 +4,7 @@
 
 ### Bug Fixes
 
+- `LONVisualizer.compute_lon_colors()` and `compute_cmlon_colors()`, and therefore all plots, now classify global optima using the network's `eq_atol`, like the network metrics, instead of exact equality. `CMLON.get_local_sinks()` now returns exactly the sinks that are not global sinks, so a sink within `eq_atol` of the best fitness is no longer both a global and a local sink. Previously, such sinks counted towards `n_global_funnels` but were drawn as local sinks. Plots of networks with rounded fitness (`fitness_precision`) and the default `eq_atol` are unchanged.
 - Raised the minimum Plotly version to 6.1.1 and Kaleido to 1.0.0 to exclude incompatible image-export dependencies. Documented the Chrome/Chromium requirement and added real PNG and rotation GIF export tests, with Chrome installation in CI. `plot_3d()` now passes image dimensions explicitly to the exporter so the minimum supported versions preserve the requested size.
 - `LONVisualizer.get_layout()` with a `seed`, and therefore `plot_2d()`, `plot_3d()`, `create_rotation_gif()` and `visualize_all()`, no longer reseeds the global NumPy RNG or leaves a seeded RNG installed in igraph. The seed now applies only to the layout, and igraph's default RNG is restored afterwards. Seeded layouts are unchanged (#53).
 - Continuous sampling now handles failed local searches explicitly. A local search fails when `minimize` raises `ValueError` or returns a non-finite fitness. A failed initial local search fails its run, and a failed search after a perturbation is rejected and counts as a non-improving iteration. Previously, runs starting at a `nan` minimum silently vanished, and an `inf` minimum made `LON.from_trace_data()` fail after all sampling had finished. Results with `success=False` and a finite fitness are still used as local optima. Each failed local search emits a warning with its context and reason (#44).
diff --git a/src/lonkit/lon.py b/src/lonkit/lon.py
index 2d6a14a..71ecfe5 100644
--- a/src/lonkit/lon.py
+++ b/src/lonkit/lon.py
@@ -542,20 +542,17 @@ def get_sinks(self) -> list[int]:
         return [i for i, d in enumerate(out_degrees) if d == 0]
 
     def get_global_sinks(self) -> list[int]:
-        """Get indices of global sinks (sinks at best fitness)."""
+        """Get indices of global sinks (sinks at best fitness within `eq_atol`)."""
         sinks = self.get_sinks()
         fits = self.vertex_fitness
         return [s for s in sinks if self._allclose(fits[s], self.best_fitness)]
 
     def get_local_sinks(self) -> list[int]:
-        """Get indices of local sinks (sinks not at best fitness)."""
-        sinks = self.get_sinks()
-        fits = self.vertex_fitness
+        """Get indices of local sinks (sinks not at best fitness within `eq_atol`)."""
         if self.best_fitness is None:
             return []
-        if self.minimize:
-            return [s for s in sinks if fits[s] > self.best_fitness]
-        return [s for s in sinks if fits[s] < self.best_fitness]
+        global_sinks = set(self.get_global_sinks())
+        return [s for s in self.get_sinks() if s not in global_sinks]
 
     def compute_network_metrics(self, known_best: float | None = None) -> dict[str, Any]:
         """
diff --git a/src/lonkit/visualization.py b/src/lonkit/visualization.py
index 1583d12..46fd918 100644
--- a/src/lonkit/visualization.py
+++ b/src/lonkit/visualization.py
@@ -103,13 +103,16 @@ def compute_node_sizes(self, graph) -> list[float]:
         return sizes
 
     def compute_lon_colors(self, lon: LON) -> list[str]:
-        """Compute node colors for LON visualization."""
+        """Compute node colors for LON visualization.
+
+        Nodes within `lon.eq_atol` of the best fitness are colored as global optima.
+        """
         colors = []
         fits = lon.vertex_fitness
         best = lon.best_fitness
 
         for f in fits:
-            if f == best:
+            if lon._allclose(f, best):
                 colors.append(COLORS["lon_global"])
             else:
                 colors.append(COLORS["lon_local"])
@@ -117,11 +120,14 @@ def compute_lon_colors(self, lon: LON) -> list[str]:
         return colors
 
     def compute_cmlon_colors(self, cmlon: CMLON) -> list[str]:
-        """Compute node colors for CMLON visualization."""
+        """Compute node colors for CMLON visualization.
+
+        Nodes within `cmlon.eq_atol` of the best fitness are colored as global optima,
+        consistently with `get_global_sinks()` and the network metrics.
+        """
         n_vertices = cmlon.n_vertices
         colors = [COLORS["local_basin"]] * n_vertices
 
-        sinks = cmlon.get_sinks()
         global_sinks = cmlon.get_global_sinks()
         fits = cmlon.vertex_fitness
         best = cmlon.best_fitness
@@ -133,13 +139,12 @@ def compute_cmlon_colors(self, cmlon: CMLON) -> list[str]:
                 colors[v] = COLORS["global_basin"]
 
         # Color suboptimal sinks
-        for s in sinks:
-            if fits[s] != best:
-                colors[s] = COLORS["local_sink"]
+        for s in cmlon.get_local_sinks():
+            colors[s] = COLORS["local_sink"]
 
         # Color global optima (overrides basin color)
         for i, f in enumerate(fits):
-            if f == best:
+            if cmlon._allclose(f, best):
                 colors[i] = COLORS["global_optimum"]
 
         return colors
diff --git a/tests/test_visualization.py b/tests/test_visualization.py
index 8c3fedf..974a457 100644
--- a/tests/test_visualization.py
+++ b/tests/test_visualization.py
@@ -4,10 +4,12 @@
 import igraph as ig
 import matplotlib.pyplot as plt
 import numpy as np
+import pandas as pd
 import pytest
 from PIL import Image
 
-from lonkit import LON, LONVisualizer
+from lonkit import LON, LONConfig, LONVisualizer
+from lonkit.visualization import COLORS
 from tests.conftest import SEED
 
 
@@ -114,3 +116,37 @@ def test_plot_2d_saves_to_file(
 
         assert output_path.exists()
         assert output_path.stat().st_size > 0
+
+
+class TestColorsRespectTolerance:
+    """Colors classify global optima with `eq_atol`, consistently with the metrics."""
+
+    @staticmethod
+    def _two_sink_lon() -> LON:
+        trace = pd.DataFrame(
+            {
+                "run": [1, 2],
+                "fit1": [5.0, 5.0],
+                "node1": ["x", "y"],
+                "fit2": [0.0, 0.05],
+                "node2": ["a", "b"],
+            }
+        )
+        return LON.from_trace_data(trace, LONConfig(eq_atol=0.1))
+
+    def test_cmlon_sinks_within_tolerance_are_global(self, visualizer: LONVisualizer) -> None:
+        cmlon = self._two_sink_lon().to_cmlon()
+        sinks = cmlon.get_sinks()
+        colors = visualizer.compute_cmlon_colors(cmlon)
+
+        assert sorted(cmlon.get_global_sinks()) == sorted(sinks)
+        assert cmlon.get_local_sinks() == []
+        assert [colors[s] for s in sinks] == [COLORS["global_optimum"]] * len(sinks)
+        assert cmlon.compute_network_metrics()["n_global_funnels"] == len(sinks)
+
+    def test_lon_nodes_within_tolerance_are_global(self, visualizer: LONVisualizer) -> None:
+        lon = self._two_sink_lon()
+        colors = dict(zip(lon.vertex_names, visualizer.compute_lon_colors(lon)))
+
+        assert colors["a"] == colors["b"] == COLORS["lon_global"]
+        assert colors["x"] == colors["y"] == COLORS["lon_local"]