We analyze the sequence Xn+2 = imXn+1 + Xn, with X1 = X2 = 1 + i, where i is the imaginary number and m is a real number. Plotting the sequence in the complex plane for different values of m, we see interesting figures from the conic sections. For values of m in the interval (−2, 2) we show that the figures generated are ellipses. We also provide analysis which prove that for certain values of m, the sequence generated is periodic with even period.
Duncan, David; Sansgiry, Prashant; Arslan, Ogul; and Meade, Jensen
"AN ANALYSIS OF THE SEQUENCE Xn+2 = i m Xn+1 + Xn,"
Journal of the South Carolina Academy of Science: Vol. 21:
2, Article 2.
Available at: https://scholarcommons.sc.edu/jscas/vol21/iss2/2