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
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