Blakely's Red Gum

title

Abstract

In this paper we built 2 models to answer the questions. In model 1, we built a BP-neural network to describe and classify leaves. In model 2, based on fractal and L-system, we built a tentative model to simulate the growth of Blakely's red gum, and then we build a further model to meet reality. Finally we discuss the sensitivity of our second model.

The major assumption is that the Blakely's red gum is isolated, still and in good conditions.

At first, we explain that why leaves have many shapes and why leaves of the trees shade the others too much. Then we find that there are relationships between the shapes of trees and their profiles i.e. trees with wide leaves extend to the air , looking huge and bloat ; trees with narrow leaves tight up , looking tall and straight.

  In the next section, we build a BP-neural network; we get the data(leaf length, width, length-width ratio, angle between venations) of 30 kinds of trees, and classify them into 3 types according to the shapes. We use 15 data to train the BP-neural network, and the rest of the data is used to test the model. The result is famous.

     To solve the problem of estimating leaves weight, and according to fractal and L-system, we built a model to simulate the tree growth. The number of iterations is introduced into this model. In this way, the number of leaves is found if we know the number of iterations. Then we find the relationship between the number of iterations and tree height.The relationship between tree height and the number of leaves is found. We get the weight per leaf and after calculation we get the weight of the leaves in a tree. To a 21m tall Blakely's red gum, the leaves weight 54.9kg.Some researchers give an equation of tree height, canopy diameter and total leaf area of a tree. Through this equation and per area of a leaf we checkout our model, and find that we the error of our model is 26%.

But in reality, variation exists among biont, so we develop our model using Stochastic L-system, get a new equation of leaves weight and tree height.To a 21m tall Blakely's red gum, the leaves weight 67.08kg. Then we checkout the result: the error decrease to 9.7%.

Then we analysis the sensitivity of our model.

In further modeling, we explain the feasibility of applying our model to other kinds of trees, just after some simple adjustment.

Dear editor:

I am honored to present you a letter to tell you our research findings.

Every day we see leaves, leaves of grass or trees. Sometimes we will come up with some crazy’ ideas: Why do leaves have so many shapes? Is there any relationship between leaf shape and the profile of the tree？How much do the leaves in a tree weight? These questions are very creative and pregnant, for they are interesting and important to some tree, e.g. some leaves can extract some useful medicine.

In our paper we abbreviated answer why leaves have many shapes; it is the influence of natural environment and gene. What’s more we can classify and describe leaves through a BP-neural network model we build. We also find a relationship between the shapes of leaves and the profiles of trees, i.e., The branches of trees with wide leaves extend to the air , looking huge and bloat ; the branches of trees with narrow leaves compact , looking tall and straight. To the last question, we use L-system and fractal to simulate the growth of Blakely's red gum, then though a series of calculate , we finally find the relationship between tree height and leaves weight and then estimate the weight of leaves in a Blakely's red gum .

These findings are believable and easy to use for normal readers and can be applied widely. So we expect that these findings to be published. We are looking forward to your circumspect consideration.

Yours

Sincerely

1. Introduction

Leaves, the sources of energy, are the sites of photosynthesis, producing nutrient for other parts of the plant. Besides leaves take in a vast variety of shapes, and therefore this feature provokes the exploration of many scientists. Merely by naked eye, based on the morphological characteristics of leaves, we can classify leaves into different categories, e.g. ovoid leaves, needle-pointed leaves, pinnate leaves, etc. However, as a matter of fact by visual measurement, we might not tell the difference between some kinds of leaves. As a result, it is necessary to work out an accurate method of description or classification. Scientists in this field have adopted the concept of LAI (leaf area index) to describe leaves, and in the recent decades with the aid of computer science the access to LAI is greatly developed. Though LAI is important, it is not suitable enough for classification of leaves. Based on the length width and their ratio, with some direct-viewing information on leaf veins, we found a fast method to describe and classify leaves.

Among the different kinds of leaves, the category of tree leaves stands out owing to their special usages and effects. For example: the aromatic leaves from Eucalyptus that yields oil; mulberry leaves can be utilized for feeding live stock. Thus, to estimate the mass of leaves within a tree is practically helpful, and especially a simple but effective method is in need, namely by sampling a small number of parameters that are easy to come by. Biologists have long been working on the relation between biomass and the apparent information on canopies or trunks. However, this approach may not tell the interactive connection from the leaf to the tree. To solve the problem, we built a model based on L-system with some easily accessible information of the height of a tree to estimate the leaf mass.

In the next section, after a statement of the basic problem, methods that involves in classifying and weighing tree leaves are demonstrated.

To classify leaves, we consider that

• The parameters of the length and width and their ratio (length-width-ratio) of a leaf are needed to describe a leaf, and
• The angle of main leaf vein is needed to describe a leaf, and besides it helps to explain the shape, and
• Neural network is used to classify leaves.

To weigh the leaves, we consider that

• Fractal is the key to illustrate the relation between the leaf and the entire tree, and
• L-system is used to simulate real trees making it possible to estimate the size characteristics of the trees

2. Analysis of the Problems

2.1 Why do leaves have different shapes?

To find out the answer to the question, we should observe the appearances of different leaves. We find out that

• Most of the leaves are symmetrical,
• The size of leaves has a large variation range,
• The geometrical characteristics of leaves from different species may varies, and
• The leaf veins, known as the passages of conveying nutrient, the distribution of which observes proper rules, may guide the growth of a leaf.

It is inferred that the way in which leaf veins stretch through the leaf is a decisive factor in the shape of a leaf. Different kinds of trees interact with the environment differently, so the distribution of energy and the recycling of substances are correspondingly different.