This book is devoted to a phenomenon of
fractal sets, or simply fractals. Topics covered includes: Sierpinski gasket,
Harmonic functions on Sierpinski gasket, Applications of generalized numerical
systems, Apollonian Gasket, Arithmetic properties of Apollonian gaskets,
Geometric and group-theoretic approach.
Goal of this course
note is primarily to develop the foundations of geometric measure theory, and
covers in detail a variety of classical subjects. A secondary goal is to
demonstrate some applications and interactions with dynamics and metric number
This note covers the
following topics: Basic Properties and Examples, Iterated Function Schemes,
Computing dimension, Some Number Theory and algorithms, Measures and Dimension,
Classic results: Projections, Slices and translations, Tranversality and
Iterated function schemes with overlaps.