Hyperbolic World — an H²×ℝ block walker

examples/physics/hyperbolic_world.ling is a tiny game world inspired by Hypermine. Hypermine is set in H³ (fully 3-D hyperbolic space); this demo uses the simplest playable cousin, H²×ℝ: you walk on the hyperbolic plane (the Poincaré disk) with ordinary vertical gravity.

ling run examples/physics/hyperbolic_world.ling

Controls

What makes it hyperbolic

• Exponential crowding. Blocks are placed on a lattice of growing rings; because the plane is hyperbolic, ever more cells pile up toward the horizon (the disk boundary = infinity) and shrink via the Poincaré conformal factor 1 − |z|².
• Möbius locomotion. You stay at the disk centre and the whole world slides under you by a Möbius translation z ↦ (z + a)/(1 + ā z). Turning is a rotation about the centre.
• Holonomy. Walk a closed loop and you come back rotated — the signature effect of moving through negatively-curved space. (Try strafing in a square.)
• Gravity acts on the ordinary vertical axis (the ℝ factor), so jumping and falling feel completely normal even though the ground is hyperbolic.

Procedural block “textures”

Each cell hashes its lattice id (fract(sin(...))) into a block type (grass / stone / dirt / crystal) and a height, so the world is generated without any texture assets — the colour is the procedural texture, shaded with the holographic cel renderer.

Notes & ideas

• The blocks are drawn with the cube primitive; swap in prism, cylinder, or icosahedron for different tilings.
• Increase the ring count or cells = 6 * ring for a denser world.
• This is H²×ℝ, not full H³ — a true Hypermine-style H³ voxel engine would track an {p,q,r} honeycomb and node graph, which is a much larger build.