I was experimenting with formulas to see what would happen when mixing large exponents of z with trigonometric functions. The changes weren't really that different from smaller exponents. I did notice a small area that looked totally different than the rest of the fractal and I zoomed in there to find this.

Here is a link to an image:

The Fractint compatible PAR file for the image is:

Funneled { ; Exported from Fracton.

 reset=2004 type=formula formulafile=fracton.frm

 formulaname=F_20121122_0942 passes=1 float=y

 center-mag=-0.5347914944581987/9.38169058092517e-1\

 3/4938271666666.666/1/0/0

 params=-1/1/0/100/-1/0/1/0/0/0 maxiter=2000

 inside=0 logmap=20 periodicity=6

 colors=bbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooop\

 ppqqqrrrssstttuuuvvvwwwxxxyyyzzzrrrsssqqqooommmkkk\

 iiigggeeecccaaa___YYYWWWUUUSSSQQQOOOMMMKKKIIIGGGEE\

 ECCEAAE88E66E44E22E00F00G00I00K00M00O00P00R00T00V0\

 0X00Z00`00b00c00e00g00i00k00m00o00q00r00t00v00x00z\

 01z13z25z37z39z4Bz5Dz6Fz7Hz8Jz9Lz9NzAPzBRzCTzDUzEW\

 zFYzF_zGazHczIezJgzKizLkzLmzMozNqzOszPuzOtyNsxNqwM\

 pvLntKmsKkrJjqIhpHgoHenGdmFbkEajE_iDZhCXgBWfBUeATd\

 9Rb8Qa8O`7N_6LZ5KY5IX4HW3FU2ET2CS1BR09P19Q3AR4BT6C\

 U7DW9EXAFZCG_DG`FHbGIcIJeJKfLLhMMiONkQPkSSlVUmXXn_\

 Zoaapdcqffrhhskktmmuppvrrwuuxwwyzzzzwxzsuzoszkpzgn\

 zckz_izWfzSdzOazK_zGXzCVz8Sz4Qz0Nw1Mt1Mp2Lm2Kj2Jh3\

 Ie4Hb4G_5GX5FU6ER6DP7DM8CJ8BG9AD99AA97A84B75D86FA7\

 IB8KD9ME000111222333444555666777888999AAABBBCCCDDD\

 EEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUU\

 UVVVWWWXXXYYYZZZ___```aaa }

frm:F_20121122_0942 {

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

|z|<100

}