Forma 形 — Game Series

Design Philosophy

Inspired by 3Blue1Brown: some math problems become easy when you lift them into a higher dimension, and some become clearer when you project them down. People tend to look at a problem in the most direct way — but switch dimensions, and the answer is often right in front of you.

Forma is a collection of games where you only see the answer after changing dimensions.

形 (Forma) means shape, structure, mathematical form. Each game wraps one mathematical insight: while you struggle in the current dimension, a change of perspective makes the problem dissolve.

Core Principle: The Dimension Shift Is the Solution, Not the Action

"Rotate an object until its shadow matches" has been done before (Shadowmatic, Fez's 2D/3D switching). If we only do "rotate and match", players will feel they've seen it.

• Ordinary version: here's a 3D object, rotate it until the shadow looks like a cat — the player is just searching for an angle.
• Forma version: present a problem that is hard or even unsolvable in 2D, let the player get stuck; once they discover "lift it up and look", the answer becomes obvious.

The 3B1B feeling comes from "oh, that's why", not "I matched it". Every level follows: stuck → shift dimension → insight → a few-second animation explaining why.

Level design test: is the reason the player gets stuck here exactly the thing that a dimension shift resolves? If the level can be solved without shifting, it doesn't belong in Forma.

One Game = One Insight + One Core Verb

Recommended first title: Lattice or Shadow — the most intuitive, no math background needed for the insight, and the easiest to bring to App Store quality.

Series Identity

A shared UI style with a different color per game is still just "several games by the same developer". The series feeling comes from layering:

1. The 形 motif (most important)

Each game's logo and final level spell 形 using that game's mechanic:

• Shadow: a seemingly random 3D sculpture casts 形 from one specific angle.
• Lattice: rhombi tile into 形; switch to 3D and it becomes a pile of cubes.
• Knot: a single string writes 形 under one projection.

When players finish a game they remember the previous one ended the same way — that is the series signature. For non-Chinese players, the opening explains it in one shot: a structure rotates, projects into 形, and Forma — form fades in beside it.

2. The dimension map (world)

The series is a map from 0D → 1D → 2D → 3D → 4D; each game occupies one "jump". The protagonist can simply be a wordless "point" travelling between dimensions, like Flatland. No story needed — just consistent opening and closing images.

3. Cross-game collection: Theorem Cards

Every insight unlocks a Theorem Card: a short animation plus one sentence. All games share one collection, and cards from other games appear greyed out.

Technically feasible: apps from the same developer (same Team ID) can read and write shared data via an App Group or a shared iCloud container. Install Shadow after Lattice and the map lights up.

4. A shared interaction grammar

The same gesture means "shift dimension" in every game (e.g. tilting the phone). Returning players already know the first move in a new game.

5. Sound

Each game gets its own instrument or scale, but the moment of insight always uses the same sound signature.

Forma: Lattice — Detailed Design

Don't make it "rotate the tiles". The interesting part is that these rhombi are cubes; the gameplay is built around that double identity.

Core move: flip a small hexagon

Every way of tiling a hexagon with rhombi in three orientations is exactly the top view of cubes stacked in a corner. The three orientations are the top, left and right faces of a cube.

The basic move is not "rotate one tile" but flipping a small hexagon (three rhombi forming a small hexagon):

• Seen in 2D: a strange local rearrangement; hard to predict what several flips in a row will produce.
• Seen in 3D: simply adding or removing one cube.

Hard in 2D, obvious in 3D — exactly the gap Forma wants.

Layers that keep it from being dry

1. Make the insight a gesture

Early levels only use flat colors; the three rhombi are three unrelated colors. At a certain level, tilt the phone: the rhombi light up into three shades and the picture "pops" into 3D. This moment should feel ceremonial. From then on, tilting is the series-wide "shift dimension" gesture.

2. Something that needs to walk

The series protagonist, the "point", walks on the surface. In 2D its path looks like an impossible staircase; in 3D they're just steps. The goal shifts from "match the pattern" to "build it a path": which cube to remove, which to add, so it can reach the exit. Every path is real geometry.

3. Stacking rules

Cubes can only be stacked into the corner and need support underneath (the monotonicity condition of plane partitions). In 2D this appears as "some flips can't be done sometimes" — mysterious; in 3D it's just gravity. This enables ordering puzzles: to reach a shape, which cube must go first?

4. The "This is impossible" button

The number of rhombi of each orientation is fixed (equal to the areas of the box's three face pairs), so some targets can't be tiled at all. Give the player a "declare impossible" button: if right, they clear the level and unlock a Theorem Card. Mathematical proof becomes a game mechanic — the first time players feel "I proved something".

5. Painting with light

With lighting, the three orientations are three shades, so tiling becomes pixel art. Later goals are silhouettes; the final level is 形 — the series signature.

Chapter pacing (draft)

Risk

After the insight, 2D difficulty collapses instantly. That's intended, but the second half needs challenges that remain hard in 3D (paths, ordering, move limits, impossibility proofs), or players will feel "got it, done" after Chapter II. The prototype's key question: are the 20 levels after the insight still fun?

Naming & Market

• Primary language: English; aim for a mostly wordless game so localization (JP, zh-Hant, KR, DE, FR, ES) is cheap.
• Series name: Forma, with 形 as the brand mark. "Forma" alone is crowded on the App Store (Formas ×2, forma.8 GO) — use a distinctive store name such as Forma 形 · Lattice and check trademarks.
• Mainland China App Store requires a game license (版号); plan to exclude that storefront and ship to HK/MO/TW and international.
• Closest existing game: kubic (Escher-inspired isometric cube illusions, assemble pieces into a target). Lattice must differentiate through the flip = add/remove cube mechanic, the 2D → 3D reveal, and invariant/impossibility puzzles.

Reaching App Store Quality

• Ship one game first. The series only exists after the first game ships and gets feedback. Reference: Euclidea and Pythagorea — same developer, same design language, one at a time.
• Prototype for a week to validate the insight. A Three.js prototype of the core mechanic takes days. Test with 5 people without hints: can they discover the dimension shift themselves? If not, it's a guidance problem; if they do but feel nothing, the puzzle choice is wrong.
• Scope: one core mechanic, 40–60 levels, 2–4 hours, premium (paid upfront).
• Tech stack: prototype in Three.js; for native feel in production, SwiftUI + RealityKit/SceneKit, or Godot/Unity. A web wrapper can ship, but gestures and rendering must be polished until it doesn't feel like a web page.
• Level design matters more than the engine.