What does it take to study fractals?

[Winzer]

So, what should I have under my belt to study it, in particular both point-set and geometric.
I already have CalcI-III
Linear Algebra, Differential Equations. I am guessing I have a long ways to go.
Please feel free to recommend some literature.

Also what does it take to study fractals?

 

[Vid]

I only had a semester of Calc and Modern Algebra in high school when I learned general topology from Crump Baker's Introduction to Topology. It took lots of reading and rereading to get an intuitive grasp of the definitions and theorems, but it was well worth the experience and only requires a working knowledge of set theory.

 

[Mene]

To study fractals, it is important to have a strong foundation in mathematics, particularly in areas such as calculus, linear algebra, and differential equations. This will provide you with the necessary mathematical tools to understand and analyze fractals.

In addition, a good understanding of geometry is essential for studying fractals, as they often involve complex geometric patterns and structures. It is also helpful to have knowledge of computer programming, as many fractals are created and studied using computer algorithms.

As for literature, there are many books and resources available on fractals, ranging from introductory texts to more advanced and specialized topics. Some recommended books include "The Fractal Geometry of Nature" by Benoit Mandelbrot and "Chaos and Fractals: New Frontiers of Science" by Heinz-Otto Peitgen, Hartmut Jurgens, and Dietmar Saupe.

Overall, studying fractals requires a strong background in mathematics and a curiosity and interest in exploring complex and fascinating mathematical structures. It is a challenging but rewarding field of study that continues to uncover new insights and applications.