rate-distortion-theory #

Visualizes the variational definition of the rate–distortion function. The animation sweeps a distortion target D, updates an R(D) curve (minimal bits per symbol), and shows a discrete test-channel p(x̂|x) that becomes sharper at low distortion (more informative, higher mutual information) and flatter at high distortion (less informative, lower mutual information).

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practical uses #

01.Tuning video/audio/image codecs by selecting a bitrate–quality operating point
02.Designing quantizers and reconstruction rules under an average distortion constraint
03.Understanding ML compression and bottlenecks (information constraints vs. fidelity)

technical notes #

Pure Canvas2D, green-on-black, grid-snapped geometry. D cycles smoothly (ease(tri)). R(D) is a stylized convex decreasing curve; p(x̂|x) is a 3x3 softmax over negative squared-error distortion with temperature tied to D; mutual information I(X;X̂) is computed from the discrete distributions and displayed alongside the variational equation.

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