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Gingko leaf is a "living fossil," and has been declared as "tree of the millennium." Malischewsky gave the Gingko leaf iteration method for its generation. In this paper, the authors show that there are many ways instead of one way to generate Gingko leaf. [ABSTRACT FROM AUTHOR]

Julia sets have been widely generated and analyzed in the fractal theory for Qm c(z) = zm+c, where m ≥ 2 and the cubic polynomial Qa,b(z) = z³ + az + b. In 2004, Rani and Kumar introduced superior iterates in the study of Julia sets [J. Korea Soc. Math. Educ. Ser. D; Res. Math. Educ. 8(4):261-277, 2004] and gave superior escape criterions for Qa,b and Qm c and generated superior Julia sets for the same. In this paper, we consider higher degree polynomials of the form Qm a,b(z) = zm + az + b, where m ≥ 3, and obtain some results regarding the superior escape criterion for the polynomial Qm a,b. Further, we obtain some beautiful superior Julia sets for the same. [ABSTRACT FROM AUTHOR]

Parrondo's gave a paradox, where two losing games together yields winning game when played alternatively, called as Parrondo game (a switching strategy). Rani first time studied superior iterates (i.e. superior orbit) in discrete dynamics and proves that it increases the solution domain of dynamical system. In this paper, we have studied and analyzed the stability of modified and extended logistic map for describing the dynamics of multi-scaled population (sexual reproduction) in superior orbit. We have shown that the stability of above maps is extended, and also we found some examples of “ chaos 1 + chaos 2 = order ” or “ undesirable 1 + undesirable 2 = desirable ” dynamic behavior in superior orbit. [ABSTRACT FROM AUTHOR]

Rational maps and its generalizations have been evolved extensively using the function iteration. In this paper, we introduce superior iterations in the study of Julia sets for rational maps of the form fλ(z) =z2 + λ/ z2 when λ≠0. Our new Sierpinski curve Julia sets are effectively different from those obtained by others. [ABSTRACT FROM AUTHOR]