Here is another fractal using the parallel resistor formula. The basic formula combines any two powers of z. It seems to make a fractal with pretty much any coefficients you pick. I wondered what would happen if I substituted a cosine for one of the z terms. The cosine seems to add a lot of intricate detail. Here is a link to a web page with an image and a description of what I found:

I will also list the PAR file here for people collecting them from the mail list:

Mixing_Cosine { ; Exported from Fracton.

 reset=2004 type=formula formulafile=fracton.frm

 formulaname=F_20121102_1156 passes=1 float=y

 center-mag=0.5475442691084866/-2.413982470836851e-\

 06/3333.333375/1/0/0

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

 inside=0 periodicity=6

 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\

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frm:F_20121102_1156 {

; Similar to the parallel resistance formula

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

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

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

|z|<100

}