Choosing a palette can be a distraction, I used a blue map for this fractal.
The URL http://maxitersfractalfollies.blogspot.com is still valid and active for those who want a pre-calculated gif

fract337.gif       { ; blue feathers
                     ; blank
                     ; calctime   0:17:32.09
                     ; created Jul 30, 2010
                     ;  Fractint Version 2004 Patchlevel 9
  reset=2004 type=formula formulafile=_t.frm formulaname=Tc03-12
  passes=1
  center-mag=+0.03819734590197747/+0.00956944867672783/1242099
  params=0/0 float=y maxiter=1500 inside=0
  colors=0Qk0Qj0Pj0Oi0Oi0Ni0Nh0Mh0Lg0Lg0Kg0Jf0Jf0Ie0Ie0He0Gd0Gd0Fc0Fc0Eb0D\
  b0Db0Ca0Ca0B`0A`0A`09_08_08Z07Z07Z06Y05Y05X04X04X03W02W02V01V00U01V03W05\
  X07Y09Z0A_0C`0Ea0Gb0Ic0Kd0Le0Nf0Pg0Rh0Ti0Vj0Wk0Yl0_m0an0co0ep0fq0hr0js0l\
  t0nu0pv0rw0qw0ov0mu0lt0js0hr0fq0ep0co0an0`m0Zl0Xk0Vj0Ui0Sh0Qh0Pg0Nf0Le0J\
  d0Ic0Gb0Ea0D`0B_09Z07Y06X04W02V00U00U00T00S00R00Q00P00O00O00N00M00L00K00\
  J00I00H00H00G00F00E00D00C00B00A00A00B00C00D00E00F00F00G00H00I00J00K00K00\
  L00M00N00O00P00P00Q00R00S00T00U01V03W05X06Y08Z0A_0B`0Da0Fc0Gd0Ie0Kf0Lg0N\
  h0Pi0Qj0Sk0Um0Vm0Xn0Zo0`o0bp0cq0er0gr0is0kt0mt0nu0pv0rw0tw0vx0xy0zz0zz0y\
  z0yz0xz0xy0wy0wy0vy0vy0ux0ux0tx0tx0sx0sw0rw0qw0qw0pw0pv0ov0ov0nv0nu0mu0m\
  u0lu0lu0kt0kt0jt0it0it0hs0hs0gs0gs0fs0fr0er0er0dr0dq0cq0cq0bq0aq0ap0`p0`\
  p0_p0_p0Zo0Zo0Yo0Yo0Xo0Xn0Wn0Wn0Vn0Um0Um0Tm0Tl0Sl0Rk0Rk
  }
frm:Tc03-12 {; V.1.1 - earlier versions may be discarded
         ; Copyright (c)1998,1999 Morgan L. Owens
         ; = 2(2z-1)Tc(2)-Tc(1)
  const=pixel, z=p1:
  z=((z+z)*(16*z*z-15)+8)*const
  |z|<100
  ;SOURCE: chby12.frm
Roger Alexander