are no functional dependencies from the outset. Constraints on these independent variables arise by demanding that each listed variable in the diagram take exactly one value. Then if a variable is determined by two functional equations, the independent variables in those two equations must be chosen compatibly. Notice that there are some values that are completely dependent ($dx/dt$, $dy/dt$, and $dz/dt$), in that they have no arrows going out of them, while there are also intermediate variables ($x$, $y$, and $z$), that have arrows going in and out.

The diagram in the left frame of Figure \[fig:lorenz2\] is that of a partially ordered set. The partial order ranks the variables appearing in according to their “independence” of one another. The independent variables are the minimal elements of the partial order, while the completely dependent ones are the maximal elements. Therefore, the arrows in the diagram in the Figure point from lower variables to higher ones in the partial order.

The diagram on the right frame of Figure \[fig:lorenz2\] has the same structure as the partial order, but is labeled a bit differently. This kind of diagram is that of a *sheaf*, which is a mathematical way to represent local consistency 