1 chapter nonlinear complex systems and nonlinear thermodynamics
1. 1 self-organization phenomenon
1.2 Self-similarity
1.3 scale invariance
1.4 nonlinear nonequilibrium thermodynamics
The second chapter is the mathematical basis of fractal.
2. 1 non-Euclidean geometry
2.2 Hausdorf measures and dimensions
2.3 Other definitions of dimensions
2.4 Non-uniform linear transformation
2.5 renormalization group
Chapter 3 Classical Fractal and Mandelbrot Set
3. 1 cantor set
3.2 Koch curve
3.3 Sierpinski set
3.4 Julia Collection
3.5 Mandelbrot set
Chapter 4 Determination of Fractal Dimension
4. 1 Based on this method
4. 1. 1 Change the observation scale to find the dimension.
4. 1.2 Find the size according to the measurement relationship.
4. 1.3 Find the dimension according to the correlation function
4. 1.4 Find the dimension according to the distribution function
4. 1.5 Find the dimension according to the frequency spectrum.
4.2 Box dimensions
4.3 Size of Functional Diagram
4.4 Relationship between code scale and fractal dimension
The fifth chapter is the physical mechanism and growth model of fractal.
5. Physical mechanism of1fractal
5.2 Fractal and Chaos
5.3 Branching and Self-organization
5.4 limited diffusion condensation (di. A) model
5.5 Jet condensation (BA) model
5.6 reaction control coagulation (RI. A) model
5.7 Sticky finger stretching and leakage
Chapter VI Computer Simulation of Fractal Growth
6. Monte Carlo simulation of1DLA growth
6.2 DLCA growth simulation
6.3 anisotropic DLA condensation
6.4 Simulation of Diffusion Controlled Deposition
6.5 Simulation of complex biological forms
Chapter VII Gas-solid Phase Transition and Fractal
7. Fractal growth of1molybdenum oxide
7。 2 fractal growth of iodine
7.3 Fractal Growth of Tungsten Oxide
7.4 Nuclear Condensation (NA) Model
Chapter 8 Experimental Study on Fractal Growth
8 alloy film
8.2 electrolytic deposition
8.3 Sputtering solidification
8.4 crystallization of amorphous films
8.5 Sticky fingering
8.6 dielectric breakdown
8.7 aqueous solution crystallization
Chapter 9 Fractal Growth in Different Systems
9. 1 stannous oxide grows from crystal to fractal.
9. 1. 1 rapid cooling
9. 1.2 Slow cooling
9.2 Pig bile grows from crystallization to fractal growth
9.3 Fractal growth of human bile
9.4 Fractal growth of boric acid crystal
9.5 Fractal Growth of Amorphous Carbon in Vacuum
9.6 Fractal Growth Induced by Electron Irradiation in Polypropylene
Chapter 10 self-organized growth
10. 1 self-organized growth in nature
10. 1. 1 A circular figure composed of surface gravel in the North Pole.
10. 1.2 Ordered pattern of desert
10. 1.3 unpredictable clouds
10. 1.4 sequence diagram of human gene DNA
1. 1.5 shell
10. 1.6 ordered structure of coral surface
Self-organized growth of 10.2 cadmium oxide
Chapter 1 1 Application of Fractal Theory
1 1. 1 biology
1 1.2 Geophysics
1 1.3 physical chemistry
1 1.4 astronomy
1 1.5 materials science
1 1.6 computer graphics
1 1.7 Economics
1 1.8 Linguistics and Information Science
1 1.9 Music
12 development of fractal theory
12. 1 generalized dimension and extended dimension
12.2 multifractal
12.3 fractal and disordered systems
12.3. 1 vibration of fractal solid (introduction to fractal)
Experimental observation of 12.3.2 fractal
12.3.3 fractal sub-dynamic theory
12.3.4 fractal and spectral dimension
Application of 12.4 wavelet transform
12.5 fluctuations and orders
12.5. 1 fluctuation
Fluctuation and correlation
12.5.3 fluctuation magnification
12.6 research direction
Appendix computer simulation source program
refer to