SCS — Module 02 - Sunset, Local Structure, and Color Budget

A connected module: what you see in the sunset is explained by local chromatic budgets.

01

Sunset, Local Structure, and Color Budget

This version connects the scene and the theory directly. The sunset is compared in HSL and SCS, then two local regions — sky and sun — are sampled and read through the exact chromatic budget of SCS.

Controls

50%
50%
The same two sliders are sent to both systems. In HSL, lightness and saturation act in cylindrical coordinates. In SCS, luminance ℓ and chromatic structure are treated separately, which makes the difference easier to read on a high-contrast scene.
The two colored markers on the scene identify the local regions read below as exact SCS budgets.

HSL

In HSL, increasing L mixes pixels toward white. Local chromatic relations collapse progressively.
Control applied
L = 50%, S = 50%

SCS

In this scene proxy, each region keeps its chromatic simplex direction π fixed while only luminance ℓ changes.
Control applied
ℓ = 50%, S = 50%
Sky sample Sun sample

Sky sample — exact local budget

S
0.000
L
0.000
S+L
1.099
π
θ

Sun sample — exact local budget

S
0.000
L
0.000
S+L
1.099
π
θ

How to read the module

The scene is the intuition: HSL and SCS do not handle a bright, saturated sunset in the same way. The two local budget cards are the explanation: in SCS, each local color keeps a coherent chromatic structure π while luminance varies.

Exact law

S(π) = DKL(π || u),   L(π) = H(π),   u = (1/3, 1/3, 1/3),   S + L = log 3
The scene part is a qualitative proxy. The two local readouts are the exact simplex quantities.
Theory

SCS separates two different things.

ℓ ∈ [0,1] is the luminance term: it measures brightness relative to white.

π = (π₃, π₅, π₇) ∈ Δ² is the chromatic structure: a probability distribution on the three active channels.

On the simplex, saturation is S(π)=DKL(π||u) and chromatic entropy is L(π)=H(π). These obey an information-theoretic sum rule: S+L=log 3. The identity is generic for any probability distribution on three outcomes; what is color-specific here is the choice of three active channels and the physical reading of S and L.

In this module, the sunset scene is not the proof of the sum rule. It is the visual intuition. The two local samples — sky and sun — are what connect the scene back to the exact SCS quantities.