Henon Map Dynamical Space: 1

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=-.4+.7i, a=.3), near the classic rabbit.

below: (c=-2.75,a =-.74). This map is a "complex horseshoe".

below: (c=-1.44, a=-.2). Karl Papadantonakis found these "cockroaches". The checkerboard pattern illustrates exernal rays (the "split" option in FractalAsm enables this coloration).

below: (c=-1.17, a=.3). This map appears to have attracting cycles of period 3 and period 1.

Page 2: Henon unstable manifold pics

Page 3: Henon unstable manifold pics

See also

• Complex parameter space pics:
  • Using various Papadantonakis programs
  • Using SaddleDrop
    
• Real parameter space pictures

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