In a fractai branching pattern the same rules govern branching at each subsequent level. The initial size (diameter) and the essential branching rules thus contain the information required to construct the whole pattern. If root branching patterns have fractal characteristics, measurement of the proximal root diameter at the stem base and the branching rules as observed anywhere in the root system, would be enough to predict total root length, root diameter distribution and root length per unit dry weight (specific root length).A 'pipe stem' model is used to derive algebraic relations between total root size and proximal root diameter for two classes of branching patterns, determinate and proportionate. To predict total root length from the proximal root diameter, at least information is needed on the minimum root diameter, the average length of internal and external links (segments) and the proportionality factor between total cross sectional areas before and after branching. For the length of the longest root or the specific root length further information on the branching rules is needed, as it is highest for determinate and proportionate branching rules, respectively. Abbreviations:CSA -cross sectional area.

If root systems have scale-independent branching rules, the total number of links in the root system can be predicted from the ratio of the largest and smallest root diameter. In Paper I we presented an algebraic model for a dicho-syntomous pattern (the simplest form of proportionate branching forming two equal branches at each node) and a herringbone branching model (the simplest form of determinate branching rules). Here, we present a recursive computer model and its results to analyze intermediate patterns, derived from allotomous proportionate branching (with unequal branches). The numerical and algebraic model gave the same results when applied to the same situation and parameter values.For practical applications of the relations found, a test is required on whether or not the underlying assumptions are met. To illustrate such a test, measurements of the branching pattern were made on Mondriaan's Red Tree painting. For patterns such as this tree a slight dependency of the proportionality factor on root diameter and random variability of several parameters may have to be included.

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KEY WORDS Root aeration Nitrate absorption Carbohydrate content Nitrogen contentBoth nitrate supply and aeration of the root environment affect plant growth. Enhanced nitrogen fertilization has often been shown to reduce the effect of insufficient aeration. It is an old and still open question, whether nitrate in the root environment can serve as an electron acceptor and alleviate the stress under anaerobic conditions. The present work attempts to gain more insight into these questions by following plant responses to interruptions of nitrate and/or oxygen supply to the roots. This has been done as follows: Pretreatment either + NO~ + A or -NO~-+ A. At time O, plants were transferred to: plus NO~ + A (aerated with normal air); plus NO 3 + N 2 (aerated with N2-gas); minus NO~ + A and minus NO~-+ N2.PREGROWN WITH NITRATE Omission of nitrate from the culture solution caused a decrease in shoot growth but not in root growth (Fig. 1A), leading to a decrease in shoot/root ratio [1]. Under nitrogen (+ A + N2), root growth was strongly inhibited in the presence and absence of nitrate; the inhibition of shoot growth was relatively weaker. Under nitrogen the nitrate content of the plants decreased, indicating that they were not capable of accumulating nitrate ( Fig. 2A, B). However nitrate reductase activity (NRA) stayed high (Fig. 2C, D). The nitrate concentration in the exudate was low and decreasing. In the root, the NRA seems to be stimulated under nitrogen [2,3]. Although there was no accumulation of nitrate in the roots of the -NO~ + A plants, root growth was not decreased. An increase in the accumulation of the total soluble carbohydrates (TSC) (Fig. 2E, F) with a decrease in the nitrate content, seems to be caused by a reduction in the usage of photosynthetic products. This is not in agreement with other experiences [2].