In 1926 the physiologist Cecil D. Murray asked what vessel bore a body should build. A wide vessel is cheap to pump through — resistance falls as the fourth power of the radius — but it holds a costly volume of living blood that must be fed and defended every second. The body pays both bills at once.
Minimize that combined cost and a clean law appears: the optimal radius cubed is proportional to the flow it carries. Because flow is conserved where a vessel forks, the parent's cube must equal the sum of the daughters' cubes — r₀³ = r₁³ + r₂³. It is engineering, written into anatomy.
The same economy fixes the fork's angle. Balancing the junction cost gives about 74.9° between equal twin daughters — and you can read that angle emerge on the bench as you tune the bores. Murray's law holds remarkably well in arteries, in plant xylem, and in the breathing tubes of insects.
The simulation stopped unexpectedly — the lesson continues without it. You can move on; nothing you did was wrong.