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2 Discrete Modeling (L-Systems)


1 Introduction to Simulation and Modeling
2 Discrete Medeling (L-Systems)
L-Systems
Fractals and Fractal Dimension
3 Population Dynamics
4 Number Representation and Error Propagation
5 Modeling with Random Numbers
6 Heat Transfer in a Rod (Connection Mathematica and C: MathLink)
7 Special Topics in Stochastic Finance
8 Appendix: Introduction to Mathematica
9 Population Dynamics in Vensim®PLE
     
 

2.1 L-Systems

2.2 Fractals and Fractal Dimension

Acknowledgements

Parts of the material in this section was taken from a number of sources, which are listed below

Mathematica 4.0, S. Wolfram.
Mathematica User's Guide to the X Front End, Wolfram Research.
The Algorithmic Beauty of Plants, Przemyslaw Prusinkiewicz and Aristid Lindenmayer, Springer Verlag 1990.
Brian H. Marston http://www.fatdays.com/
D. Stauffer and H.E. Stanley, From Newton to MandelBrot, Springer 1995
For the Koch-curve: AMS Vol.39 #7 Sept 92, page 709
S.Douady and Y.Couder, Phyllotaxis as a Physical self-Organized Growth Process Phys Rev Lett 68(13) 1992.

Introduction

This notebook will introduce some concepts of discrete modelling and simulation. Emphasis is on examples taken from nature. The focus of this notebook is on Lindenmayer systems, Fibonacci numbers and fractals, which are used to build model of plants and growth.

Important  instructions  for  all students:
Each notebook  contains several questions that must be handed in. Theses questions are labeled accordingly:

Required: These questions must be done by all students.

Advanced:  These questions are considered to be more difficult and may be assigned by the instructor.

Optional:   These questions are optional  to all students  and will be counted towards   extra  marks.


 
     
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