There are different types of fractals in the field of mathematics and in nature too. Some of these are very easily created by using the concept of algebraic mathematical equations or by using complex numbers.

**There are some other fractals which are created by nature. These are listed below:****The Julia Sets:** These are those sets of fractals which are created by using the exact same formula as in case of the Mandelbrot set, except that the initial or the starting points are different every time. This implies, c is any constant with z1 as the initial or starting point on a plane. This definition implies that there can be infinite number of Julia Sets, having infinite number of values of c. In general, each and every point on a complex plane gives result to its corresponding Julia set. The following is an example of the fractals created by the Julia Set:

**The Mandelbrot Set:** This set is a subset of a complex plane which always consist of those variables or parameters from which any Julia set is joined with. In simpler words, Any Mandelbrot set is a set of those values for which the set has always one and only one finite upper bound.

The relationship between the Julia set and the Mandelbrot set is that the Mandelbrot set acts as an index set for the Julia sets. All the values of c, which are inside any Mandelbrot set, we will always be joined with the Julia sets, which will be connected. And conversely, the values of c that are outside the Mandelbrot set, we will always get unconnected sets.

**The Kleinian Group Fractals:**This group creates those types of fractals which depends on two pairs of Mobius transformations and facilitates to create quasifuchsian, Single and double Cusp, etc. The following is an example of the fractals created by the Kleinian Group Set:

**The Newton Method Fractals:**This method was discovered with Isaac Newton which was created by using the calculus applications, and gives us different kinds of interesting self similar patterns. The following is an example of the fractals created by the Newton Method Set:

**The Quaternion Fractals (3D):**The quaternion fractals which are in three dimensional are made by the exact principle, in which the old Julia set is created with the exception that this quaternion fractals uses a four dimensional complex number in spite of the use of two dimensional complex numbers. The following is an example of the fractals created by the Quaternion Fractals Set:

There are various other types of fractals which can be visualize by making a link between a 2 dimensional fractals in a three dimensional or more than 3 dimensions. As in case of the discovery of Mandelbulb, the following is an example of some hyper complex and the other three dimensional fractals:

The above are some of the most common fractals that are being used by various researchers for creating various design patterns.