Editing Lyapunov fractal (section)

==Properties==
Lyapunov fractals are generally drawn for values of ''A'' and ''B'' in the interval <math>[0,4]</math>. For larger values, the interval [0,1] is no longer stable, and the sequence is likely to be attracted by infinity, although convergent cycles of finite values continue to exist for some parameters. For all iteration sequences, the diagonal ''a = b'' is always the same as for the standard one parameter logistic function.

The sequence is usually started at the value 0.5, which is a [[critical point (mathematics)|critical point]] of the iterative function.<ref>See {{Harvnb|Markus|1990|p=483}}.</ref> The other (even complex valued) critical points of the iterative function during one entire round are those that pass through the value 0.5 in the first round. A convergent cycle must attract at least one critical point.<ref>See {{Harvnb|Markus|1990|p=486}}.</ref> Therefore, all convergent cycles can be obtained by just shifting the iteration sequence, and keeping the starting value 0.5. In practice, shifting this sequence leads to changes in the fractal, as some branches get covered by others. For instance, the Lyapunov fractal for the iteration sequence AB (see top figure on the right) is not perfectly symmetric with respect to ''a'' and ''b''.