|
To plot the first iteration we draw vertical red line from the
starting point xo = 0 toward the blue curve y = f(x) =
x2 + c, where yo = f(xo).
To get the second iteration we draw red horizontal line to the green
diagonal y = x, where x1 = yo =
f(xo). Then draw again vertical line to the blue curve to get
y1 = f(x1) and so on.
Points fc: xo → x1 → x2 → ... for some c and xo values make orbit of the point xo (it is plotted in the right part of this applet). |
| To the left on complex plane are shown: fractal basin of attractor z1 (the blue region), repeller z2 and two points of unstable complex cycle z3 , z4 . |
| For C = -1 the map has attractin period-2 cycle (the left picture above). The second iteration of the map f o2 has two attracting fixed points z3 and z4 . The basin of the cycle is shown to the left. f o2 attract the red regions to z3 and the blue ones to z4 . z1 becomes a repeller. |
For attracting cycle below L is negative