Powered by OpenAIRE graph
Found an issue? Give us feedback
addClaim

From Newton Fractals to Gradient Fractals in Addition to Zhang Fractals

Authors: Yunong Zhang; Tianjian Qiao; Bolin Liao; Long Jin 0001; Junwei Chen;

From Newton Fractals to Gradient Fractals in Addition to Zhang Fractals

Abstract

The paper employs gradient dynamics (GD), in addition to Zhang dynamics (ZD), to generate new fractals which are quite different from the conventional Newton fractals (NF). The proposed gradient fractals (GF) have three types. Specifically, via appropriate iterative formulas derived in complex domain, the first-type and second-type fractals are generated, i.e., 1GF and 2GF. By expanding the conventional gradient formula from real domain to complex domain, the third-type fractals are thus obtained, i.e., 3GF. Besides, Zhang fractals (ZF) are yielded via solving static and time-variant equations using ZD. Numerical experiments substantiate the effectiveness of complex-valued GD and ZD for generating new fractals. Connections and differences among NF, GF and ZF are also revealed.

Related Organizations
  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    1
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!