Metabolic cost — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Also named here as optimisation — the same set of essays touches all of them, so they are one junction rather than several.
The cube law
A branching network built to move fluid for the least work obeys one relation at every junction — the cube of the parent radius equals the sum of the cubes of the daughters. It is a minimisation result, it is checkable on a real tree, and it is the rare biological rule with a derivation.
Which junctions say anything
Da Vinci's rule and Murray's law differ by 12% at an even fork and by a tenth of a per cent at a twig. So one even fork settles which is right, and two thousand twigs do not — a factor of two thousand across a tree, decided entirely by the shape of the junction and not by how carefully it is measured.
Named alongside it
The objects these essays reach for when they reach for this one.
Murray's lawOptimisationAllometryBranchBranching exponentBranching networkDa Vinci's ruleExponent fittingFittingMeasurementPoiseuille flowSampling