Spiral structures in the Julia sets

It is evident, that if φ = 2π m/n + δ,   δ « 1, then mapping
    zk = f ok(z + ε) ~ z + |λ| k eikφε
generates spiral structures in the neighbourhood of the fixed point z. Some of these spirals are shown below.
wait
wait
0.0000  0.1000  2.5000   36ms
wait

Next we can investigate stability of fixed points and period 2 orbit of quadratic mappings analytically.


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updated 12 Sep 2013