If we have the iterative functions X= X2+Y, where X is complex number and Y constant complex number. Can one find the Y and initial value of X in iterative function from generated sequences mathematically in order to generate next values?
I look forward your comments.
Best wishes.
Dear Qasim Mohammed Hussein, I suppose you are referring to the difference equation zn+1=zn2+c, with c being a complex constant. But, what do you mean by "generated sequences"? Do you have some terms of some solution of the difference equation and you want to calculate the constant c and the inintial condition z1? If this is the case, then the constant c is the difference of any term from the square of the previous term; i.e., c=zn+1-zn2. Next, to calculate the initial condition z1, you may solve the difference equation for zn; thus, obtaining zn in terms of zn+1 and the constant c that you have calculated, and going backwards to successively calculate zn,zn-1,...,z1.
It may be useful to note that the difference equation zn+1=zn2+c provides the famous Mandelbrot set; see, https://mathworld.wolfram.com/MandelbrotSet.html.
- Badges
- Science topic
- Similar topics
- Filing