Control of Julia sets (Q2484712)

The authors use a proper mathematical transformation on the complex iteration \(z_{n+1}= z^2_n+ c\) to realize the whole magnification and minification, extension along the \(X\)- or \(Y\)-axis and rotation of Julia sets, without changing the characters of the Julia set. As the Julia set is defined as a closure of period repelling points, the authors realize controlling the stability of the iteration function by means of controlling the Julia set.