This fractal makes a web of interconnected rings. You can see the pattern I used to add the rings by zooming out. The technique is the same one that usually adds longer arms to a fractal. To perform the technique, you repeatedly zoom in on ever smaller self similar structures. In this fractal, each time you do that it adds one more ring. The equation is:

z = 1 / (1 / ((z ^ 3) * sinh(z) + pixel + 1) + 1 / (z ^ 4 + pixel - 1))

Here is a link to an image:

The Fractint compatible PAR file for the image is:

Web_Rings { ; Exported from Fracton.

 reset=2004 type=formula formulafile=fracton.frm

 formulaname=F_20121113_0850 passes=1 float=y

 center-mag=-2.730493261162895/-4.958068276404781e-\

 14/44444445000/1/0/0

 params=1/1/4/4/-1/0/1/0/0/0 maxiter=2000 inside=0

 periodicity=6

 colors=000mnjjligihcgg`deYadU_cRXaOU`KS_HPYEMXAKW7\

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 tlfqlenkcliaif_fcXd`VaZTZWQWTOUQMRNJOLHMIFJFCGCAD9\

 7FB9IEBLHEPMJUSPZYUcb_hhd }

frm:F_20121113_0850 {

; Similar to the parallel resistance formula

a=real(p1),b=real(p2)-1,d=imag(p1),f=imag(p2),

z=0,c1=pixel-p3,c2=pixel-p4:

z=1/(1/(a*(z^b)*sinh(z)+c1)+1/(d*(z^f)+c2)),

|z|<100

}