Canvas Scatter Chaos

Canvas Scatter Chaos is a puzzle about finding the coordinate system that makes chaos disappear. Twelve glowing gems are scattered across a dark canvas. They look completely random — no pattern, no structure, no visible organisation. Two luminous arrows extend from the centre: a teal e₁ pointing right, a violet e₂ pointing up. Between them, a faint parallelogram grid covers the canvas. The player grabs an arrow and drags. The entire grid rotates with it. The gems don't move. But three of them just turned orange. The player adjusts the second arrow, stretching it slightly and angling it. Six gems glow warm. Eight. The grid is no longer square — it has become a tilted, stretched parallelogram lattice. Eleven gems on intersections. One stubborn gem floats between lines. The player nudges e₁ by a fraction. The gem slides toward an intersection. Touches it. Every gem simultaneously blazes white. Gold rings expand outward from each position across the grid. The lattice itself brightens, holding for two seconds before fading. Resonance achieved. The mathematics running beneath this is basis change — one of the foundational concepts in linear algebra. Every point in the plane has coordinates in any basis. In the wrong basis, the gems look random. In the correct basis, they are all sitting exactly on integer positions of a perfect lattice. The player finds the correct basis not by computing matrix inverses but by physical exploration: drag, watch, adjust. The lock condition updates every frame, giving continuous feedback as each gem transitions from cold blue through warm orange to locked gold. Five levels. The first two show ghost arrows — translucent guides indicating where e₁ and e₂ need to go — teaching the relationship between basis vectors and the resulting lattice. The third level removes the ghosts: eight gems, no hints, pure exploration. The fourth introduces a hexagonal lattice whose basis is not perpendicular — the correct e₂ is angled relative to e₁, and finding it requires noticing that the correct configuration is not a square grid at any rotation. The fifth level has twelve gems, an oblique basis, and no assistance of any kind. The game teaches without stating: that the same set of points looks random in one coordinate system and perfectly periodic in another. That two vectors fully determine a two-dimensional coordinate system. That shearing and rotating a grid are the same kind of operation — a change of basis. That there is no universal correct coordinate system, only convenient ones.