I've been playing with the Burning Ship fractal type in Fractint. I changed z^2 to z^3 and came up with a version which has x-axis symmetry, though it needs rotating 45 degrees. Is this the "M-set" of the Burning Ship type? Has it been found before? The whole fractal reminds me of a Klingon Bird of Pray, by the way.
Begin .par file
BShip4 { ; 45 degrees & symmetry
; Tony Hanmer 23/7/2012
; Fractint Version 2099 Patchlevel 8
reset=2099 type=formula formulafile=T-frms.frm
; paste the below formula (minus the "frm:") into a new *.frm file if you like,
; & remane T-frms.frm to that .frm name.
formulaname=BurningShip4 passes=1
center-mag=-0.108695/0.108695/0.4303211/1/44.999999999999993 float=y
maxiter=250 inside=fmod sound=off
colors=000<8>KN_MPcOSg<3>Xaw<9>CawA`w8`w<3>0`w<9>HgRJhOLiK<3>Sl7<9>ks2ms\
2ot2<2>uv0ww0wu1<8>we9wcAwaB<3>wVF<9>ybFycFydF<3>zhF<3>`ZBVWAOUA<2>5M7<5\
>Nd3Qg3Tj2<3>ew0<12>DJ0BF08C0<2>230000000<118>000
}
frm:BurningShip4 { ; Tony Hanmer 23/7/2012
z = (0,0): ; x-axis symmetry at last, though at a 45-degree angle:
z = abs(z) ; the "M-set" of the Burning Ship fractal?
z = z * z * z - pixel ; instead of z^2, z^3.
|z| < 100
}