Types of Fractals   

Quaternions

Complex numbers, in the form a + bi are essential in creating fractals like Julia Sets, which use the complex number formula z = z² + c. There are, however, equivalents of complex numbers which contain 4 instead of 2 terms and can be expressed as a + bi + cj + dk. They are called quaternions and were introduced by Hamilton in 1847. There is a completely separate algebra of quaternions, which is very important in math and physics. Quaternions can also be used to create fractals equivalent to Julia Sets by being used in the formula z = z² + c instead of complex numbers. Since quaternions have 4 terms, the fractal is 4-dimensional. We manage to display them by taking 3D "slices" of the fractals at certain places. The following picture is an example of quaternion: