Author | Edition, Pilot. author |
---|---|
Title | Fractals in Science [electronic resource] : An Introductory Course / by Pilot Edition |
Imprint | New York, NY : Springer New York, 1994 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-7012-7 |
Descript | 320 p. online resource |
1. From Coin Flipping to Motion of Molecules -- 1.1 Introduction -- 1.2. Randomness: Making Predictions Even When No One Knows What Will Happen Next -- 1.3. How Often Something Happens (Probability Distributions) -- 1.4 Random Movement (Random Walks) -- 1.5 Pascalโs Triangle -- 1.6 Average Displacement and Average Squared Displacement -- 1.7 Diffusion -- 1.8 Periodic Precipitation: Liesegang Rings -- 1.9 Postlude: The Meaning of Models -- Appendix A Demonstration that Average Squared Displacement Is Equal to Number of Steps Taken -- Appendix B. Preparation for Liesegang Ring Experiment -- 2. Fractals in Nature. Growing and Measuring Random Fractals -- 2.1 Introduction -- 2.2. Coastline -- 2.3. The Meaning of Dimension -- 2.4. Growing Random Patterns -- 2.5. Computer Measurement of Fractal Dimension -- 2.6. Modeling the Growth of a Fractal Pattern -- 2.7. The Hele-Shaw Experiment -- 2.8 Branching Patterns Formed by Bacterial Colonies -- 2.9 Termite Nesting and Foraging in Two Dimensions -- 2.10 Fractal Root Systems -- 2.11. Research! -- Appendix A. Dimensions and Logarithms -- Appendix B. Construction of ECD and Hele-Shaw Cells -- Appendix C. Using Video Frame Grabbing -- Appendix D. Using the Scanner for Imaging -- Appendix E. Preparing the Carrageenan Solutions -- Appendix F. Using the Vernier pH Meter -- Appendix G. Preparation of Bacterial Growth Experiment -- Appendix H. Constructing the Cell for a Termite Colony -- Appendix I. Constructing Rhizotron for Root Systems -- 3. Growth Patterns in Nature: Percolation -- 3.1 Growing a Forest -- 3.2 Burning a Forest -- 4 DNA and Literature -- 4.1 DNA Sequences -- 4.2 Storing Information in DNA -- 4.3 Word Occurences and Zipfโs Law -- 4.4 Landscapes of Literature and DNA -- 4.5 Discover coding regions in DNA -- A Answers to problems. -- B Log-Log-paper -- C This and That -- 5 Spin Glasses and Neural Networks -- 5.1 Introduction -- 5.2 Magnetic Order -- 5.3 Ising Model -- 5.4 Magnetic Disorder -- 5.5 Spin Glasses -- 5.6 Hopfield Model -- 5.7 Bibliography -- 6 Lightning and Soap Films -- 6.1 Introduction -- 6.2 Electric Field -- 6.3 Electrostatics -- 6.4 Laplace Equation -- 6.5 Numerical Approach to our Main Task -- 6.6 Fractal Growth -- 6.7 Bibliography -- 7 Analyzing Rough Surfaces Digitally -- 7.1 Introduction -- 7.2 Defining the Self-Affine Surface -- 7.3 Activity: The Paper Tear Experiment -- 7.4 The Paper Tear: Understanding Experiments with Models -- 7.5 Testing the Minimal Energy Model -- 7.6 Conclusion