Complex Dynamics and Fractals

Code: MA545 | L-T-P-C: 3-0-0-6

Classical Fractals, Cantor set, Sierpinski triangle, Von Koch curve, Hilbert and Peano curves, Weierstrass function. Self-similarity, Scaling, Similarity dimension, Box-counting dimension, Information dimension, Capacity dimension. Foundations of iterated function systems (IFS), Classical fractals generated by IFS, Contractions mapping principle, Collage theorems, Fractal image compression, Image encoding and decoding by IFS. Iteration of quadratic polynomials, Julia sets, Fatou sets, Mandelbrot set, Characterization of Julia sets, Dynamics of functions ez , sin z and cos z, Bifurcation and chaotic burst.

Software Support: MATLAB, MATHEMATICA, GNUPLOT

Texts / References:

1. M. F. Barnsley, Fractals Everywhere , 2nd edition, Academic Press, 1995.
2. Ning Lu, Fractal Imaging, Academic Press, 1997.
3. M. J. Turner et. al, Fractal Geometry in Digital Imaging, Academic Press, 1998.
4. A. F. Beardon, Iteration of Rational Functions, Springer Verlag, 1991.
5. L. Carleson and T.W. Gamelin, Complex Dynamics, Springer Verlag, 1993.