Unit-I

Classical Fractals, Self-similarity, Metric Spaces, Equivalent Spaces.

Unit-II

The Space of Fractals, Transformation on Metric Spaces.

Unit-III

Contraction Mapping and Construction of fractals from IFS.

Unit-IV

Fractal Dimension, Hausdorff measure and dimension, fractal Interpolation Functions.

Unit-V

Hidden Variable FIF, Fractal Splines, Fractal Surfaces, Measures on Fractals.

Course Outcomes

CO1: Understand the basic concepts and structure of fractals .
CO2: Understand the space of fractals and transformation on metric spaces.
CO3: Understand the iterated function system with contraction mapping theorem.
CO4: Apply fractal concepts to compute fractal dimension of sets and construct fractal interpolation functions.
CO5: Understand the hidden variable fractal interpolation function, fractal splines and fractal surfaces.

1. M.F. Barnsley, Fractals Everywhere, Academic Press, 1993.
2. P.R. Massopust, Interpolation and Approximation with Splines and Fractals, Oxford University Press, 2009.
3. K. Falconer, Fractal Geometry (Mathematical Foundations and Applications), John Wiley & Sons, 2003.
4. P.R. Massopust, Fractal Functions, Fractal Surfaces and Wavelets, Academic Press, 1994.
5. Richard M. Crownover, Introduction to Chaos and Fractals, Jones and Bartlett Publishers, 1995.