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c4 = -1.3125... (in the center of the "secondary"
(1/2, 1/2) M-bulb) is periodic point with period 4 .
fc4o2 is renormalizable (see the picture to the
left). The critical point has period 2 under iterations of
fc4o2, therefore you see a small "embedded"
homeomorphic copy of J(-1) in the center of the picture. J(-1)
midgets appear in every bulb of "initial" J(-1) set.
fc4o4 is renormalizable too (see below) and z = 0 is its superattracting fixed point, therefore the red bulb in the center of J(c4) is a homeomorphic copy of J(0). |
In a similar way one can obtain any (m/n)
bifurcation. E.g. this complex (1/3,
1/2) J-set is constructed of the two "primary"
(1/3) and
(1/2) J-sets.
At laste the (1/2, 1/2,
1/2) Rabbit.