"Reverse" period n-tupling cascades

Reverse period tripling cascades

Here periodic orbits and corresponding tiny Mandelbrot set copies undergo period tripling cascades around the limiting period tripling point c3 = -0.023638805 + 0.7836616i with the universal scaling constants. Remember that
    1/3| = 10.09,   Arg(δ1/3 ) = +-117.1o .
You can see period 4, 12, 36... M-set copies. Each view is centered at the c3 point and the magnification increases by 10 each time (Zoom = 2). You can watch cascades 5, 15, 45... and 6, 18, 54... too.

Many other structures undergo the same bifurcations, e.g. preperiodic points (one of these points in the main antenna is marked by M).

You see here period-4 and 12 critical orbits. In the third picture only 1,4,7,10 points of the period-12 orbit are ploted. Then we get a small period-4 orbit.

The last two pictures illustrate ordinary period doubling bifurcation of the critical period-4 orbit (only 1,4,7,10 points of period-12 orbit are ploted in the last image again). Compare this to the real Reverse period doubling cascades.


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updated 17 June 2002