Mathematical Models of Trees by Fractal
Nana MAYUZUMI, Mayumi ISHIKAWA, Susumu OGAWA
Faculty of Geo-Environmental Science, Rissho University
1700 Magechi, Kumagaya, Saitama 360-0194,
Phone:(81)-48-539-1652 Facsimile:(81)-48-539-1632
JAPAN
Email: 031w00135@ris.ac.jp
ABSTRACT Vegetation and tree models are required for monitoring vegetation with remote
sensing in various fields. This research aimed at illustration of complicated tree growth process
with fractal models. Fractal tree and bifurcation-type tree models were constructed as a
mathematical model, and their fractal dimensions were compared natural trees. Consequently, a
branch-type tree model looked like real trees, while fractal trees performed like real tree growth.
Moreover, tree models showed similar fractal dimensions to real trees in photographs. These
trees expressed by simple models would be expected for monitoring vegetation in time series.
1. INTRODUCTION
In global environment, modeling of vegetation has become very important. Since the monitoring
error is large, the observation by remote sensing requires its improvement. Therefore,
construction of mathematical models for vegetation growth process was attempted: trees, a
paddy field, and an agricultural field as a model. Especially tree growth models were showed. In
order to draw trees by the mathematical model, two conflicting assumptions, "trees have no
self-similarity" and "trees have self-similarity", were introduced. Fractal tree and
bifurcation-type tree models were calculated and the forms of complicated trees were illustrated.
If a tree is expressed by fractal dimension, the improvement in accuracy is expected for growth
simulations for forest and the biomass estimate of environmental monitoring.
