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