Modeling full-scale leaf venation networks
Fig 5
Murray’s law for loopy networks.
(a) Subsection of a leaf image, with model output edge widths (red lines) and fluxes (blue arrows) indicated. The arrow sizes indicate the relative average time the flow moves in the respective directions given by the arrows. (b) vs.
for all nodes in a sample of S. albus, for the optimal
and
. The points closely follow the line of equality. (Inset) The same data with both axes logarithmic. (c-d) Loss values for individual leaf samples (thin lines), with the mean value for each species (thick lines). The dashed vertical line is located at
. (c)
. The optimal value of
is predicted for all samples. (d) Best-fit values of
[Fig 4a–4b]. The optimal values have been shifted in the positive direction. (e–h): Residual plots with Gaussian weighted means and standard deviations (SD). (e–f)
. The residuals are (e) biased negatively, and (f) subsequently corrected by a term proportional to the associated sink area. (g–h)
. The residuals are (g) biased positively, have a larger SD compared to the case of no sink fluctuation, and are (h) corrected by a term proportional to the associated sink area.