This fractal is one I found while exploring variations of the parallel resistor formula with 3 terms. The formula in this case mixes cosh, sinh, and z:

z=1/(1/((cosh(z)-1)+pixel+1) + 1/(z*sinh(z)+pixel-1) + 1/(z*z+pixel))

The equation was constructed so that the minimum power of z representing the series for each term is 2. Thats the reason for the -1 after the cosh and the extra z* in front of the sinh. I haven't made any conclusions about whether or not 3 terms is better than 2 terms but it certainly is different.

I liked how the inside stuff in the image was filled with the "webs". Even the arms of the webs have little webs along the sides.

The parameter file for the fractal is:         

petal_webs { ; Exported from Fracton.
 reset=2004 type=formula formulafile=fracton.frm
 formulaname=F_20150208_1101 passes=1 float=y
 center-mag=-6.997039369982983/0/2222.22225/1/0/0
 params=0/0/0/0/-1/0/1/0/0/0 maxiter=10000
 inside=0 logmap=10 periodicity=6
 colors=000APIAPIAPIAPIAPIARLARLARLARLBTOBTOBTOBTOB\
 TOBVRBVRBVRBVRBXUBXUBXUBXUBXUBZXBZXBZXBZXB`_B`_B`_\
 B`_CabCabCabCabCabCceCceCceCceCehCehCehCehCehCgkCg\
 kCgkCgkCinCinCinCinCinCkqCkqCkqCkqDlsDlsDlsDlsAKAA\
 KAAKAAKAAKAAKAAKAAKADMDDMDDMDDMDDMDDMDDMDDMDFPGFPG\
 FPGFPGFPGFPGFPGFPGIRJIRJIRJIRJIRJIRJIRJIRJLTMLTMLT\
 MLTMLTMLTMLTMLTMNWPNWPNWPNWPNWPNWPNWPNWPQYSQYSQYSQ\
 YSQYSQYSQYSQYST`VT`VT`VT`VT`VT`VT`VT`VWbYWbYWbYWbY\
 WbYWbYWbYWbYYe`Ye`Ye`Ye`Ye`Ye`Ye`Ye``gc`gc`gc`gc`g\
 c`gc`gc`gccjfcjfcjfcjfcjfcjfcjfcjfelielielielielie\
 lielieliholholholholholholholholkqokqokqokqokqokqo\
 kqokqomsqmsqmsqmsqmsqmsqmsqmsqkqokqokqokqokqokqokq\
 okqoholholholholholholholholelielielielielielielie\
 licjfcjfcjfcjfcjfcjfcjfcjf`gc`gc`gc`gc`gc`gc`gc`gc\
 Ye`Ye`Ye`Ye`Ye`Ye`Ye`Ye`WbYWbYWbYWbYWbYWbYWbYWbYT`\
 VT`VT`VT`VT`VT`VT`VT`V000 }

frm:F_20150208_1101 {
 ; Similar to the parallel resistance formula
 z=0,c1=pixel-p3,c2=pixel-p4:
 z=1/(1/((cosh(z)-1)+c1)+1/(z*sinh(z)+c2)+1/(z*z+pixel)),
 |z|<100
 }