I am looking for a book to self-study fractals with a certain criteria. I have checked out Getting Aquainted with Fractals. Note that Getting Aquainted with Fractals does not include exercises/problems. I would like to find a book that has exercises/problems, geometrical interpretations and more explanations (I do not like textbooks that are full of fluff, but I also do not think I am ready to fill in every blank either). To clarify about the last criteria, I do like books that are in the definition, theorem, proof format, however I would like a book that presents easier to read proofs that contain more detail. Also, I would like some discussions that prelude definitions which give their motivation and possibly give rise to geometric intuition.
I would also like a supplementary text covering the material in Mathematical Analysis as a lot of vocabulary, concepts and ideas come from analysis.
I know the basic concepts and properties: Self-Similarity, Recursively defined, and the Box Counting Dimension. I know about the classic fractals: Koch Curve, Sierpinski triangle and their variations. However, I do not know anything about fractals defined in the complex plane such as Mandelbrot set and Julia set. I also do not know much about the link between fractal geometry and chaotic theory.
Thanks for all the help!