The game idea. Every picture element is a working variable: the clipboard is a task list, the three bars are the keeper's state, the partner bar is a second state that reacts to food, tidiness and attention, and the hotbar tools are timed actions with cooldowns. All money is illustrative game credit, not a real wage.
Stamina (Energy). Activity burns energy as kcal = MET x mass x hours. MET values are typical numbers from physical-activity compendia (cooking about 2, washing dishes 1.8, laundry 2.3, vacuuming 3.3, mopping 3.5, bathing 1.5, walking 3); the resting MET of 1 is already paid by the body, so stamina falls by (MET - 1) x 60 kg x h / 800 kcal. The 800 kcal "daily active reserve" is an illustrative scale, not a medical value. Resting and a meal refill it; below 10 percent every chore runs 1.6 times slower.
Mess arrives randomly. Dirty plates, laundry, floor clutter, grime and dust arrive as independent Poisson events with rates scaled by the Mess slider. A chore with a fixed wash time behaves like a single-server queue: with arrival rate lambda and service rate mu the mean number waiting is rho/(1 - rho), rho = lambda / mu. Experiment 1 measures this by simulation and compares it with the formula. When rho exceeds 1 the pile grows without bound, which is the chaotic home of the title.
Tidiness. tidy = 1 - (0.30 D/8 + 0.25 L/6 + 0.25 F/10 + 0.10 grime + 0.10 dust) with D plates, L kg of laundry and F clutter items. The weights are chosen for play, not measured.
Moods relax. Both moods follow first-order relaxation, dM/dt = (M* - M)/tau, updated with the exact exponential so the result does not depend on the time step. The targets M* add up tidiness, the partner's mood, stamina and the decor "cosiness". The partner's fullness decays exponentially with a half-life you can set; a meal resets it.
Hot water and the bill. Heating m kg of water by dT needs Q = m c dT with c = 4186 J/(kg K). A 110 L bath from 12 to 38 degrees C needs about 3.3 kWh. A washing cycle heats 40 L plus about 0.25 kWh of motor and electronics; each washed plate uses 2.5 L. Energy is multiplied by the electricity price (default $0.28/kWh; electric heating assumed 100 percent efficient). Hotter water makes dishes slightly faster (+0.4 percent per degree, an illustrative factor) but costs more.
Independent checks on the page. (1) RK4 heating of a tank with heat loss against the exact solution; (2) Newton cooling of bath water against its exponential; (3) Q = m c dT against a full simulated washing cycle's bill; (4) the MET energy formula against the simulated stamina drain; (5) the Poisson arrival mean against lambda t; (6) the M/M/1 queue against rho/(1 - rho).
Honest simplifications. Two people and a dog, one room layout, no cleaning chemistry, no wear on objects, constant electricity price, instantaneous hot water, rigid-part character animation (limbs swing, nothing is skinned). Characters are generic stylised figures. Every constant that is not a physical value is a game-balance number.