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Strategy Mixture
⚡ Information Geometry
Shannon Entropy H(p):
0.000
KL Divergence from uniform:
0.000
Fisher-Rao distance to center:
0.000
Coordinate View:
Current State (Barycentric)
Strategy 1 (x):
0.250
Strategy 2 (y):
0.250
Strategy 3 (z):
0.250
Strategy 4 (w):
0.250
Avg Fitness:
0.0000
Active Dimension:
3
Information Geometry Features:
The simplex is equipped with the Fisher information metric g_ij = δ_ij/p_i - 1. Replicator dynamics can be viewed as gradient flow.Metric Visualizations:
Purple Grid Ellipses: Static grid showing overall metric structure across the simplex.Green Current Ellipse: DYNAMIC! Moves with the red point and grows/shrinks to show how the local metric changes. Watch it expand dramatically as the point approaches boundaries - this is the Fisher metric stretching space! At center it's small and uniform; near edges it grows large showing negative curvature.
Geodesics: The "straight lines" in this curved geometry, computed by interpolation in log-space.
Coordinate Systems:
Barycentric: Standard probabilities (x,y,z,w) summing to 1.Log-Ratio: Centered log coordinates log(p_i/g) where g is geometric mean. These reveal the natural linear structure of compositional data and are centered at 0 for uniform distribution. Note: CLR coordinates sum to 0!