Julia 4D - Comparing Quaternion and Hypercomplex

[7NTM61Ic]

Would it be possible to generate a 3D picture such as in your video for the specific hypercomplex numbers discussed on Wikipedia under the heading "Multicomplex Numbers" within the subhead "Basic Form and Representations"? These numbers are of special interest to me (see my Video Response above) and I would be very curious what such an animation would show, if indeed it is possible! Perhaps you could direct me to where I could look at such a plotting, if not a video.

[ImpoliteFruit]

It would possible, yes.

I'm not aware of any videos done with these (I have thought about the bicomplex numbers, but haven't gotten around to writing the render code for it).

One way to display the numbers, would be as a combination of points and vectors (for the coefficients).

[7NTM61Ic]

Fascinating!

PS: I have found that some use the term "hypercomplex number" more generally, encompassing systems with different multiplication rules.

[ImpoliteFruit]

Hypercomplex numbers is a term (correctly) used for several types of constructs (the definition varies among various sources). It is commonly used to refer to one specific type of number (as in the multiplication table), which adds to the confusion. While the difference between quaternion (Q) and "hypercomplex"(H) is subtle, it have several consequences, H is commutative while Q isn't. Despite this, the two fractal sets generated from these numbers share some similarities (as show in the video).