BOX 1 Figure.

The gradient is assumed to be linear. As the organ grows, the maximum and minimum limits are conserved while recently divided cells take up intermediate scalar values from their neighbours (some evidence for this can be found in REF. 34). The steepness of the gradient at each point, measured perhaps as a differential across each cell, correlates with the dimension of the organ. A measure that, in principle, could be delivered locally to each cell. During normal growth and development, the identity of cells changes, so that the “target steepness” will vary from stage to stage. This process could be responsible for the observed and precise logarithmic increase in the length of organs, such as limbs, from instar to instar in hemimetabolic insects¹⁰.