This fractal has circles, ovals, rounded rectangles, diamonds, and a square.

Here is a link to an image:

The Fractint compatible PAR file for the image is:

Orbicular { ; Exported from Fracton.

 reset=2004 type=formula formulafile=fracton.frm

 formulaname=F_20121123_2022 passes=1 float=y

 center-mag=-3.953281687312188/-5.224562695854533e-\

 15/888888900000/1/0/0

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

 inside=0 periodicity=6

 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\

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 0zy0ym0ua0oS0hI0ZA0O40C10 }

frm:F_20121123_2022 {

; 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*z*(cos(z)-1)*sin(z)+c1)+1/(d*(z^f)+c2)),

|z|<100

}