Golden Fondue

// Golden Fondue: a heat-softened, conservative lattice material.
// Temperature, mass and time use illustrative lattice units, not calibrated cheese physics.
// Only the heater input supplies heat; the pan is a passive platform. No latent-heat,
// elastic-string, surface-tension or momentum solver; molten material creeps by local flux.
property FondueHeat { temperature: Float<0.05> [0.0 1.0]; }
property FondueMatter {
	mass: Float<0.0> [0.0 1.0];
	down: Float<0.0> [0.0 1.0];
	left: Float<0.0> [0.0 1.0];
	right: Float<0.0> [0.0 1.0];
	front: Float<0.0> [0.0 1.0];
	back: Float<0.0> [0.0 1.0];
}
// A static surface shade; the platform has neither heat nor cheese fields.
property FondueHardware { shade: Float<0.16> [0.0 1.0]; }
model Cheese : FondueHeat, FondueMatter { mass<1.0>; };
model FonduePan : FondueHardware;
model FondueSpace : FondueHeat, FondueMatter;
// Heater power: 0 switches off heating, 1 is full heat; intermediate values warm more gently.
in heater: Float<1.0> [0.0 1.0];
world { dimensions 3; cell Cube; neighborhood VonNeumann; }

// The input warms the material directly. Neighbor diffusion redistributes heat;
// a missing thermal neighbor (including the pan) is insulating.
behavior WarmCheese for FondueHeat
needs inputs(heater: Float [0.0 1.0])
{
	update {
		let exchange = sum n in neighbors[FondueHeat using VonNeumann] { n.temperature - self.temperature };
		set self.temperature = clamp(self.temperature + 0.1 * exchange + 0.018 * (0.05 + 0.80 * heater - self.temperature), 0.0, 1.0);
	}
}
// Cold cheese has a yield threshold. Above it, mobility increases continuously.
// The downward flux cannot exceed either donor mass or receiver capacity.
behavior PlanCheeseFall for FondueMatter + FondueHeat {
	update {
		let mobility = clamp((self.temperature - 0.25) / 0.4, 0.0, 1.0);
		let below = (neighbors[FondueMatter using VonNeumann, -Z].mass else 1.0);
		set self.down = min(self.mass, 1.0 - below) * mobility * 0.85;
	}
}
behavior MoveCheeseDown for FondueMatter {
	update {
		let incoming = (neighbors[FondueMatter using VonNeumann, +Z].down else 0.0);
		set self.mass = clamp(self.mass - self.down + incoming, 0.0, 1.0);
	}
}
// Four horizontal fluxes share at most 80% of available mass/capacity. A supported
// layer spreads slowly; material in mid-air falls first instead of diffusing sideways.
behavior PlanCheeseSpread for FondueMatter + FondueHeat {
	update {
		let below = (neighbors[FondueMatter using VonNeumann, -Z].mass else 1.0);
		let support = clamp((below - 0.6) / 0.4, 0.0, 1.0);
		let mobility = clamp((self.temperature - 0.25) / 0.4, 0.0, 1.0) * support * 0.2;
		set self.left = max(self.mass - (neighbors[FondueMatter using VonNeumann, -X].mass else self.mass), 0.0) * mobility;
		set self.right = max(self.mass - (neighbors[FondueMatter using VonNeumann, +X].mass else self.mass), 0.0) * mobility;
		set self.front = max(self.mass - (neighbors[FondueMatter using VonNeumann, -Y].mass else self.mass), 0.0) * mobility;
		set self.back = max(self.mass - (neighbors[FondueMatter using VonNeumann, +Y].mass else self.mass), 0.0) * mobility;
	}
}
behavior SpreadCheese for FondueMatter {
	update {
		let incoming = (neighbors[FondueMatter using VonNeumann, +X].left else 0.0)
			+ (neighbors[FondueMatter using VonNeumann, -X].right else 0.0)
			+ (neighbors[FondueMatter using VonNeumann, +Y].front else 0.0)
			+ (neighbors[FondueMatter using VonNeumann, -Y].back else 0.0);
		set self.mass = clamp(self.mass - self.left - self.right - self.front - self.back + incoming, 0.0, 1.0);
	}
}
// Each plan is read from one completed phase, so every edge's loss has one equal gain.
phase heating { run WarmCheese on Cheese; run WarmCheese on FondueSpace; }
phase gravity_plan { run PlanCheeseFall on Cheese; run PlanCheeseFall on FondueSpace; }
phase gravity_move { run MoveCheeseDown on Cheese; run MoveCheeseDown on FondueSpace; }
phase spreading_plan { run PlanCheeseSpread on Cheese; run PlanCheeseSpread on FondueSpace; }
phase spreading_move { run SpreadCheese on Cheese; run SpreadCheese on FondueSpace; }

visual GoldenCheese for FondueMatter + FondueHeat {
	color {
		let soft = clamp((self.temperature - 0.25) / 0.4, 0.0, 1.0);
		rgba(1.0, 0.78 - soft * 0.15, 0.16 - soft * 0.10, clamp(self.mass * 3.0, 0.0, 1.0))
	}
}
visual PanSurface for FondueHardware {
	color { rgba(self.shade, self.shade + 0.03, self.shade + 0.07, 1.0) }
}
visualize Cheese with GoldenCheese;
visualize FondueSpace with GoldenCheese;
visualize FonduePan with PanSurface;