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Shannon entropy of every three-outcome distribution, drawn over the probability simplex p1 + p2 + p3 = 1. Drag to orbit, scroll or pinch to zoom, and hover or tap the surface to read off a distribution.
The simplex is an equilateral triangle with the pure distributions at its corners. Height is H in bits. Each edge is a two-outcome distribution, so the surface meets the walls along the binary entropy curve and rises to log23 ≈ 1.585 bits at the uniform distribution.
The mesh is a triangular grid in barycentric coordinates, so the boundary is exact rather than clipped from a square grid. Colour, contours and shading are computed per pixel from the exact formula, including the gradient, which becomes vertical at the edges.
Contours are lines of equal entropy, with every fifth one heavier. The floor repeats them as a flat ternary diagram. Faint lines mark pi in steps of 0.1.