Backward iteration algorithms for Julia sets of Möbius semigroups

Stankewitz, Rich; Sumi, Hiroki

doi:10.3934/dcds.2016079

Cited by 2 publications

(1 citation statement)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This variety of Julia sets is easier to grasp, if one looks at them as corresponding to the topological semigroup generated by infinite compact families of proper polynomial mappings. This is consistent with the point of view adopted by a number of researchers in one complex variable (see [2] and, e.g., the work of Stankewitz and Sumi [3][4][5]).…”

Section: Introductionsupporting

confidence: 90%

Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings

2018

View full text Add to dashboard Cite

We investigate the metric space of pluriregular sets as well as the contractions on that space induced by infinite compact families of proper polynomial mappings of several complex variables. The topological semigroups generated by such families, with composition as the semigroup operation, lead to the constructions of a variety of Julia-type pluriregular sets. The generating families can also be viewed as infinite iterated function systems with compact attractors. We show that such attractors can be approximated both deterministically and probabilistically in a manner of the classic chaos game.

show abstract

Section: Introductionsupporting

confidence: 90%

Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings

2018

View full text Add to dashboard Cite

show abstract

Public Art Design Practice under Visual Communication Design

Huang,

Hao,

Jin

2024

Applied Mathematics and Nonlinear Sciences

View full text Add to dashboard Cite

The expansion of visual communication design in public art makes the scope of visual communication wide. This new art form reflects the cross and integration of disciplines but also makes the form of public art in our life richer, and people can get more beautiful enjoyment. Research on the fractal algorithm in the escape time algorithm studied the Julia set in different function conditions of the fractal graph of the change and the function of different indices of the joint. The fractal graph obtained a colorful, more tense structure. Subsequently, it is applied to public art design, and after testing its performance, the fractal design of visual communication is combined with the IPA model to explore the practical effect of the fractal design in public art design. The results show that the improved fractal algorithm proposed in this paper increases the pattern generation rate from 61.5% to 92.6%. The fractal dimension measurement of 15 typical batik patterns shows that more than 85% of the batik patterns have an average value of more than 15000.

show abstract

Backward iteration algorithms for Julia sets of Möbius semigroups

Cited by 2 publications

References 25 publications

Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings

Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings

Public Art Design Practice under Visual Communication Design

Contact Info

Product

Resources

About