Period doubling and Feigenbaum's scaling
("Anatomy" of the Mandelbrot and Julia sets)

In the following Demo, you can see doubling of the period of the attractive stationary points (z1=f(z1), z2 =f(f(z2), z4=f(f(f(f(z4))))... ) Turn on "grid" and zoom in (click mouse + <Alt> + <Shift>) the picture at the cross position (in the center one of black circles - "mu-atom"). You'll see the M-set self-similarity near the Feigenbaum point when the magnification increases by 4.6692 (the Feigenbaum Constant) and period is doubled each time. Increase "It" (max iterations number) to get deeper zoom. See also "MuEncy".

The same Feigenbaum's scaling symmetry with period doubling presents near every "mu-atom" (black circle).

You can also see amazing similarity between the Mandelbrot set filamentation ("antenna") near the cross position and the Julia set ("aeroplane").

Controls
Click mouse into the Julia-set to stop animation or Demo.
Click mouse into the M-set to stop "animation" and go to the mouse position.
Click mouse + <Alt> to Zoom In (the applet stops animation before Zooming!).
Click mouse + <Ctrl> to Zoom Out.
<Shift> to modify Zoom In/Out 2 (Feigenbaum's zoom).
<Enter> to set new parameters from text fields.

Steps - number of steps in animation
It - max iterations number
Delay - delay between two frames
no label - the cross position
Period - an orbit period at the cross position


Contents updated 3 November 1999