The concentration $U$ of one of the morphogens concerned at the point $x=(\rho\theta,z)$ is to be given by the formula
$U=\sum_{\eta} e^{i(\eta,x)} G(\eta^2) W(x)$ (I)
where the summation is to be over the lattice (A B \\ C D) reciprocal to (a b \\ c d). The function $G(\eta^2)$ is to have a maximum near the square of the shortest vector of the lattice (A B \\ C D). A suitable form for $G(\eta^2$$ and the suitable range for the shortest vectors of the reciprocal lattice (A B\\ C D) is given in Fig .
(Fig)
The function $W(x)$ should depend only on $z$ and typically may be of the form $e^{-z^2/2\sigma2)$. The ratio of the standard deviation $\sigma$ to the shortest vectors of the lattice (a b \\ c d) is probably between two and five. The inclusion of this factor $W(x)$ of course results in the pattern not having the symmetry of the lattice (a b \\ c d) or of any other lattice. But it is nevertheless possible to use the lattice (a b \\ cd ) applying the formula (I) to describe the pattern instead of the symmetry lattice. It remains only then to describe what in the lattice is to be used for each value of the diameter of the petiole.
JS 23/9/98