Today's fractal is a remix of my Oct. 24 post. Same formula and palette, different parameters.
Like the Oct.24 post ready made at http://maxitersfractalfollies.blogspot.com
Twilight Remix { ; fract484.gif
; blank
; calctime 0:17:07.88
; created Oct 26, 2010
; Fractint Version 2004 Patchlevel 10
reset=2004 type=formula formulafile=kerrym.frm
formulaname=hermanm_man-polar
center-mag=-1.89610111352240000/+0.00222840388810970/9616.574/1/22.49999\
99999827232/-2.86882184674652763e-011 params=4/2/1/60/3/0 float=y
maxiter=1500 inside=0 proximity=1 outside=fmod decomp=256
colors=000302403503504604705805806907A07B08B08C09D1AE1AF1BF1BG1CH1CI1DI1\
EJ1EK1FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21w00z03\
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z0fz0dz0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0Iz0Gz0Ez0Cz0Az08z06z04z02z00z00\
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9E1AF1AF1BG1BH1CI1DI1DJ1EK1EL1FL1FM1GN1HO2IO2JQ2IS2HV2GX2F_2Da2Cd2Bf2Ah1\
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0zH0zE0zB0z80z60z30z00x01v02s03q04n06l07i08g19e1Ab1B`1CY1EW1FT1GR1HO2JN2\
IM2HK2GJ2FH2DG2CE2BD2AB19A18817715514413212000000101201
}
frm:hermanm_man-polar { ; Kerry Mitchell 16feb98
;
; real(p1) = z exponent (use integer >= 2; m=n-1)
; imag(p1) = g exponent (integers)
; real(p2) = alpha magnitude (try 1)
; imag(p2) = alpha polar angle (try integers)
; real(p3) = critical point selector (>0 for positive root)
; imag(p3) = unused (<0 for negative root)
; use decomp=256
; zero and infinity bailouts hardcoded to 1e-6, 1e6
; coloring speed hardcoded to 4
;
c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1
maxr=1e6, minr=1/maxr, speed=4*pi/128
r=real(p2), t=imag(p2), alpha=r*(cos(t)+flip(sin(t)))
oln=1/log(n), fac=log(0.5*log(maxr))
c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1
hypden=sqr(n-m), hypfac=hypnum/hypden
if (real(p3)<0)
pn=-1
end if
if (real(c2)>hypfac)
pn=-pn
end if
if (imag(c)<0)
pn=-pn
end if
afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n
d=sqrt(bfac*bfac-4*afac*cfac)
z=(bfac+pn*d)/(2*afac)
:
g=(z-c)/(1-c*z), z=alpha*z^n*g^m
iter=iter+1, r=|z|
;
; orbit trap around 0
; renormalize iteration count via decomp angle
; set "iteration done" flag (iter=-1)
;
if (r<minr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
z=cos(angle)+flip(sin(angle))
iter=-1
end if
;
; orbit trap around infinity
; renormalize iteration count via decomp angle
; add pi to angle to separate from 0 orbit trap
; set "iteration done" flag (iter=-1)
;
if (r>maxr)
angle=(iter+oln*(fac-log(log(cabs(z)))))*speed
angle=angle+pi
z=cos(angle)+flip(sin(angle))
iter=-1
end if
iter>0
}
Roger Alexander