[Fractint] Web Rings

13 Nov 2012

      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:

http://dl.dropbox.com/u/33642054/image/web_rings_1200_5.jpg

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\
 HU4ET0BR3DS6GT9IUDLWGOXJQYNT_QW`TYaX`c_bdbeefhgijh\
 lmippkpnipkgphepecpcap`_pYYoVWoTUoQSoNQoKOoIMoFKoC\
 In9FnBGnEInGJnJLnLNnOOnRQoTSoWToYVo`XobYoe_phanjak\
 lbincfpdcseasfZrgWriUqjRplOpmMooJopGnrEmsBmu8lv5kx\
 7kw9kvBluDltFmsHmrJnqLnpNnnPomRolTpkVpjXqiZqh`rgbr\
 fesdcpeamfZjgXfiUcjS`kPXmNUnKRoIOpFKrDHsAEt8Av57w3\
 4x00z33y67x9AvCEuFHtILrLOqOSoRVnUZmXak_ejbhielghof\
 lsdjqegofdmgajiZhjWfkTdmQanO_oLYqIWrFTsCRu9Pv6Nw3K\
 y0Iz3Ky6Mx9OvCQuFTsIVrLXqOZoSanVclYek`gjcjhflginel\
 pdtsiqphnlfkiehfcecbb`aZX_WUZTRYQOWNKVKHUHESEBRA8Q\
 85PA8QEBRHESKHUNKVQOWTRYWUZZX_b`aecbhfckienlfqphts\
 iurhvpfwneylcyk`yjYxiVxhTxhQxgNwfKweHwdFvdCvc9vb6u\
 a4vb6vc9vdCwdFweHwfKxgNxhQxhTxiVyjYyk`ylczlfzmiwmh\
 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
}

-- 
Mike Frazier
www.fracton.org