World of Fractals - Introduction

Self Similarity in the Koch Curve.
Geometrical Fractal.

Introduction

My interest in fractals has continually grown over the past few years. I find fractals to be one of the most interesting and beautiful objects in Mathematics, and nature alike.

My knowledge on fractals is very limited, but, I have outlined what I know about fractals below. Please feel free to leave comments correcting my work, or adding to what I have to say.

Self similarity in the Mandelbrot Set.
Geometrical Fractal.

Self Similarity
Fractals are objects that are self similar at all
scales. Look at the images of Koch Curve and Mandelbrot Set, the jaggedness of these objects look the same regardless of how much we zoom in.

Categories
I think all fractals can be characterized in two main categories, Statistical and Geometric Fractals. The Koch Curve and Mandelbrot Set on the right are both Geometrical Fractals. They have some definite shape, something that is not random. Statistical Fractals, on the other hand, do not have a definite shape. They are produced using random numbers and a particular algorithm. Their shape changes every time it is produced. One thing that is the same for both, is that they are all self similar at all scales. 

I have provided several examples of different fractals that I have created myself or found it online throughout this blog post.