Journal article
Pickover biomorphs and non-standard complex numbers
- Abstract:
- In this study Pickover biomorphs are analysed as being dependent on the chosen complex number system in which iterations of analytic functions are performed. Moran’s spatial autocorrelation function and two forms of entropy, the Shannon entropy and the sample entropy, are chosen in order to find correlations and measure complexity in Pickover biomorphs. These turn out to be strongly correlated and low-entropy objects with a fractal dimension between 1.4 and 2. It is shown that there is a strong maximum in correlation and a strong minimum in entropy for the case of Galilean complex numbers corresponding to the square of the generalised imaginary unit being equal to zero.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Accepted manuscript, pdf, 1.1MB, Terms of use)
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- Publisher copy:
- 10.1016/j.chaos.2018.05.001
Authors
- Publisher:
- Elsevier
- Journal:
- Chaos, Solitons and Fractals More from this journal
- Volume:
- 113
- Pages:
- 46-52
- Publication date:
- 2018-05-27
- Acceptance date:
- 2018-05-01
- DOI:
- ISSN:
-
0960-0779
- Pubs id:
-
pubs:854775
- UUID:
-
uuid:2760b8ae-5cdd-40fd-b4fb-37cd4eb62c27
- Local pid:
-
pubs:854775
- Source identifiers:
-
854775
- Deposit date:
-
2018-06-04
- ARK identifier:
Terms of use
- Copyright holder:
- Elsevier Ltd
- Copyright date:
- 2018
- Notes:
- Copyright © 2018 Elsevier Ltd. This is the accepted manuscript version of the article. The final version is available online from Elsevier at: https://doi.org/10.1016/j.chaos.2018.05.001
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