Henon Map Dynamical Space Pics: 2

The following images were all created using FractalAsm, and the Henon_Unstable_Manifold definition.

These images show parameterized slices of the
unstable manifold of a saddle fixed point of a Henon map, *H*.
Points are drawn black if their forward orbit under *H*
appears to be bounded, or else they are colored according to rate of
escape. The saddle fixed point is the rightmost tip of the black.

above: (c=0.15625+0.5423i, a=0.2375+0.90625).

You will need something
like 1000 iterations to see the channels.

below: (c=0.362+0.3414i,a = 0.3). We smell period 5.

The checkerboard pattern illustrates exernal rays

(the "split" option in
FractalAsm enables this coloration).

below: (c=-3, a=-.34). This is a "real horseshoe".

below: (c=0.1+0.7i, a=.3). Another interesting horseshoe, with external angles checkered.

Page 1: Henon unstable manifold pics

Page 3: Henon unstable manifold pics

See also

- Complex parameter space pics:
- Real parameter space pictures