What-If-Not: Complex Number Lyness Sequence

This is the same iteration as before, but now, all the points are complex numbers. Point A is the first complex number in the sequence, and B is the second complex number in the sequence. Point K is the the complex number added in the numerator.[br][br]Drag the ORBIT slider to reveal the points in the sequence one-by-one.[br]Drag the STEP slider to reveal the order of the points in the sequence one-by-one.
[list][*]Are there any special values of A, B, or K? [br][/*][*]Are there any values of A, B, or K that induce a high degree of symmetry?[br][/*][/list]
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Information: What-If-Not: Complex Number Lyness Sequence