Function Platformer

A puzzle platformer where the platforms are your function. Type f(x), and the curve becomes a road; a rider follows it, building the momentum needed to clear the gaps and reach the finish line.

Play it live: https://function-platformer-xdvj.vercel.app/

Or open index.html in a browser — no build step and no dependencies, so the file works straight from disk.

Mechanics

• The curve is the road. Polynomials, trig, roots, exponentials — anything the built-in parser accepts (+ - * / ^, implicit products like 2x or 3sin(x), sin cos tan sqrt abs exp ln log10 floor ceil min max, constants pi e tau).
• The level is a grid of fixed-pixel cells (16×9 cells of 60 px), of three kinds:
  • Path cells — where the function should be traced; the curve is rideable here.
  • Gap cells — places on the grid that are not on the optimal path: the curve is cut inside them (it cannot be used as road), but the kart may fly through. Jumps happen here, carried by momentum.
  • Filler cells — fill all remaining space; they cut the curve and crash the kart on contact.
• Momentum jumps. Launching off a rising lip throws the kart upward; it detaches from crests on its own when fast enough (curvature vs. gravity).
• Runner levels. Level 1's rider is a person under full player control: nothing moves without input. Run with ← / → (or A / D), jump with Space / ↑ / click, with a little mid-air steering. The intended solution is floor(x) + 1: the floor function draws discrete platforms that climb to a finish line on higher ground than the start, and the runner must jump up each successive platform. Walls and ceilings bonk the runner instead of crashing them.
• Fillers constrain the solution to one or a few shapes: level 1 wants a step function aligned to its staircase (wrong offsets and zooms fail, and no climbing straight line wins — verified by search); level 2 falls to a plain downhill line; level 3 needs a launch ramp (no line works); level 4 needs a tilted wave (no line, pure sine, or parabola works); level 5 is an open sandbox. Maps were generated from verified winning runs (gen.js, historical) and re-verified.
• Zoom via canvas limits. The plot window is 0 ≤ x ≤ x max, 0 ≤ y ≤ y max (y = 0 at the bottom). Changing the limits rescales the curve only — the cell grid and the kart keep their pixel size, so the same formula gets steeper (and faster) as you shrink y max.

Files

• index.html — UI, rendering, game loop.
• engine.js — expression parser, terrain sampling, kart physics, level definitions. Shared between the browser and Node.
• test.js — headless checks: parser behavior, every level's hinted solution wins, and the filler constraints actually exclude the trivial function families. Run with node test.js; node test.js search grid-searches solution families (used to tune the levels).