FLATLAND: ASCENSION

A journey through the dimensions — a browser game inspired by Edwin A. Abbott's Flatland: A Romance of Many Dimensions (1884) and Flatland: The Movie.

▶ Play it online: https://rb14.github.io/flatland/

You play Arthur Square as he climbs the dimensional ladder: 0D → 1D → 2D → 3D → 4D. The unifying idea: in every chapter you see both the omniscient view and the native view of that dimension's inhabitants — so you feel why each world cannot conceive the one above it.

Chapters

#	World	What happens
0D	Pointland	A vignette: the Point that is its own universe.
1D	Lineland	Neighbours are forever — until you step sideways through the 2nd dimension (SPACE) and scandalize the King. Your "retina" is two points.
2D	Flatland	Free-roam the plane as A. Square. The bottom strip is a real-time 1D raycast of what a Flatlander actually sees (nearness = brightness: Abbott's "recognition by fog"). Meet Hex, then receive the Sphere — a circle that swells and fades as it passes through your plane.
3D	Spaceland	WebGL. Rise off the plane, see inside every house and citizen, then pass the Rite of the Sections: name solids from their 2D slices alone. Story rounds use Abbott's classic trio (sphere / cube-on-corner / cone); the Endless Rite afterwards draws from a library of eight bodies — cylinder, pyramid, tetrahedron, octahedron, and the torus (the only slice with a hole) — plus rounds where three randomly generated crystals tumble in a line-up and you pick which one (Ⓐ/Ⓑ/Ⓒ) is passing through the plane.
4D	Hyperland	A tesseract under genuine 4D rotation (XW/YW/ZW plane rotations), perspective-projected 4D→3D→screen. Toggle Slice Mode to see its morphing 3D cross-section, run the Ladder of Dimensions extrusion finale, and play the Hyper-Rite: a 4D body (tesseract, 16-cell, glome, hyperpyramid) turns as a wireframe shadow while you pick which of three candidate 3D solids is its slice at w = 0 — with Reveal (watch it pass through the hyperplane) and 3D Perspectives (picture-in-picture slices at w = −0.8 / 0 / +0.8).

Run

Any static file server works (ES modules require http, not file://):

./flatland.sh            # serves on http://localhost:8000
# or: python3 -m http.server 8000

Internet access is required on first load (Three.js + fonts come from CDN).

Controls

Desktop:

• W/S move · A/D turn · Q/E sidestep (Flatland) — A/D move (Lineland)
• SPACE / ENTER / click advance dialogue · SPACE hop dimension (Lineland)
• drag orbit · scroll zoom (3D/4D chapters)
• 1–5 jump straight to any chapter · ?ch=N URL param does the same
• 🔊 toggle in the top-right

Mobile / touch (controls appear automatically on coarse-pointer devices; ?touch=1/0 overrides):

• virtual joystick (bottom-left) — slide along the Line in 1D; in Flatland Arthur turns toward — and walks in — whatever direction you point (screen-up = north)
• HOP button (bottom-right) — step through the 2nd dimension in Lineland
• tap the dialogue box to advance · in 3D/4D the map-app scheme: one finger pans; two fingers pinch-zoom, drag to rotate/tilt, twist to spin — all in one gesture
• the dimension dots (top-right) jump between chapters

Tech

• Three.js (WebGL) via import map — no build step, plain ES modules
• Canvas2D 1D raycaster for the Flatlander retina (ray–segment casting + distance fog)
• One generic sliceEdges() powers both 3D solids sliced by a plane and the 4D bodies sliced by the w = 0 hyperplane (js/math/poly.js); random crystals are convex hulls of scattered points, sliced via the same path (extractEdges)
• NPCs are solid: Mrs. Point halts against you in Lineland (nobody passes anybody in 1D), and Flatland citizens steer around — and cannot walk through — Arthur
• Real 4D math: Givens plane rotations + 4D perspective projection (js/math/vec4.js)
• Procedural WebAudio ambience: one pad chord per dimension, typewriter blips, chimes
• The same 2D world geometry (js/world2d.js) is walked within in Chapter 2 and rendered from above in Chapter 3

Structure

index.html            shell + import map
css/style.css         HUD, dialogue, retina, title/end screens
js/main.js            scene manager, HUD, boot
js/dialogue.js        typewriter dialogue queue
js/audio.js           procedural sound
js/input.js           keyboard state
js/util.js            tween/until/lerp helpers
js/world2d.js         the shared 2D world (shapes, houses, wandering citizens)
js/three-setup.js     shared WebGL renderer
js/math/poly.js       raycasting, convex hull, generic edge-soup slicer
js/math/vec4.js       4D rotations, projection, n-cube generators
js/scenes/chapter0–4  one module per dimension