Darkwaar27

Pigment

Rotation, Color Algebra & Deterministic Puzzles

One die. Six faces. Twenty-five cells.

darkwoodcom.itch.io/darkwaar27

One die, one rule

Movement determines
the pigment.

Tip onto a neighbor. Rotate 90°. The down face stains the cell.

Tip East — yellow lands.

The six faces

Orientation is the resource.

Initial orientation. Tip any direction.

Null ↔ Black Red ↔ Blue Yellow ↔ White

Opposites stay fixed. Every tip is a permutation of six slots.

Rotation is a permutation

No physics. Just a table.

East → D ← E · U ← W · E ← U · W ← D

North and South unchanged.

"E":
    return {"D": e, "U": w, "N": n, "S": s, "E": u, "W": d}

The next state is computed, then drawn.

Color algebra

next_stain = mix(existing, face)

Yellow + Blue → Green

G

Orange Purple Green

The state transition

Accept, or spend nothing.

Input→ Validate→ Roll→ Mix→ Update→ Victory?

if not _floor(current, to):
    return {state, events: {accepted: false}}
# roll → mix → spent += 1 → phase

Off-board tips are refused without consuming a turn.

More than pathfinding

Same position ≠ same state.

State = Position × Orientation × Pigments × Moves

Path A · E S W N E

Path B · E S E N W

Two greens. Different leftovers. Different die facing.

Level 2 · Return

Solving Green

Start (0,0). Mark Green at (1,0). Limit 5.

E → S → W → N → E

0 | 5 · Start at (0,0).

Yellow + Blue = Green

Levels 2 → 3

A solution is the whole board.

E S W N E · wins L3

Green at (1,0) · Yellow at (0,0)

E S E N W · fails L3

Green yes · start not yellow

Both green level 2. Only one preserves the start.

Five levels, five constraints

Same machine. Steeper asks.

1 · First Face

Paint

2 · Return

Mix

3 · Leave

Preserve

4 · Other Pair

Combine

5 · White

Clear

Purple lives in the mix table — unused by these five boards.

Small Godot architecture

Rules first. Scene second.

rules.gd

Deterministic transitions: roll, mix, apply, levels, replay checks.

main.gd

Input, drawing, tween, undo history. Projects state — never invents faces.

main.tscn

One Control. No ECS, no physics bodies, no large framework.

Small games benefit from small architectures.

Rendering the rules

Feedback is comprehension.

Pseudo-3D die Face glyphs Pigment tween Target rings Roll arc Orientation compass

If facing is unreadable, the mix feels arbitrary. Animation that names a rule is interface, not decoration.

Determinism & undo

S₀ → S₁ → S₂
then S₂ → S₁

Snapshot before accept. Deterministic transition. Known-solution replay.

S₀ · tip East, then Undo.

Deterministic — not purely functional.

Engineering lessons

What the model implies

Orientation is a resource.
Movement modifies future actions.
Small transition tables create complex decisions.
Deterministic systems replay and debug cleanly.
Animation should expose rules.
Small games benefit from small architectures.

Play Pigment

One die.
Six faces.
Twenty-five cells.

Tip carefully. Leave the board you meant.

https://darkwoodcom.itch.io/darkwaar27