A Concise Introduction to Hypercomplex Fractals by Andrzej Katunin

Author:Andrzej Katunin [Katunin, Andrzej]
Language: eng
Format: azw3, pdf
Publisher: CRC Press
Published: 2017-10-05T04:00:00+00:00

Figure 2.6 3-D projection of the M ℍ-set along the ℂ-plane.

Obviously, J -sets in ℍ can be considered in terms of higher-order polynomials that describe them. Let us first consider the recursive equation in the form (1.5), when z,c ∈ ℍ, p ∈ ℤ. The resulting slices for various values of p are presented in Figure 2.7, similarly to the case of J -sets on a ℂ-plane presented in Figure 1.7. One can observe that the 3-D projections of J p ℍ ( − 0.5 , 0.5 , 0 , 0 ) ) for increasing p tend to a 2-sphere. Indeed, when p → ∞, the shape of J p ℍ ( a 1 , a 2 , a 3 , a 4 ) tends to a 3-sphere for arbitrary an , which was proven in [66].

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.