It's busy at Action Central and this post is short. It's a minibrot today, check it out at
http://maxitersfractalfollies.blogspot.com and as a bonus there is an intriguing video from
You Tube on manipulating statistics.

fract284.gif       { ; minibrot appears to be slightly perturbed
                     ; blank
                     ; calctime   0:06:15.14
                     ; created Jul 01, 2010
                     ;  Fractint Version 2004 Patchlevel 9
  reset=2004 type=formula formulafile=kerrym.frm
  formulaname=hermanm_man-cart
  center-mag=1.79491/1.13844/14.97396/1/60.0000000000000995/-1.26836041669\
  520228e-013 params=3/2/0.5/0.5/2/0 float=y maxiter=1500 inside=0
  outside=atan
  colors=00000000200400600800A00C00E00G00I00K00M00O00Q00S00U00W00Y00_00a00\
  c00e00g00i00k00m00o00q00s00u00w00z01z03z05z07z09z0Bz0Dz0Fz0Hz0Jz0Lz0Nz0P\
  z0Rz0Tz0Vz0Xz0Zz0`z0bz0dz0fz0hz0jz0lz0nz0pz0rz0tz0vz0xz0zz0zz0yz0xz0wz0v\
  z0uz0tz0sz0rz0qz0pz0oz0nz0mz0lz0kz0jz0iz0hz0gz0fz0ez0dz0cz0bz0az0`z0_z0Z\
  z0Yz0Xz0Wz0Vz0Uz0Tz0Sz0Rz0Qz0Pz0Oz0Nz0Mz0Lz0Kz0Jz0Iz0Hz0Gz0Fz0Ez0Dz0Cz0B\
  z0Az09z08z07z06z05z04z03z02z01z00z00z03z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0j\
  z0nz0rz0vz0uz1tz1sz2rz3pz3oz4nz5mz5kz6jz7iz7hz8gz9ez9dzAczBbzB`zC_zDZzDY\
  zEWzFVzFUzGTzHSzHQzIPzJOzJNzKLzLKzLJzMIzNGzNFzOEzPDzPCzQAzR9zR8zS7zT5zT4\
  zU3zV2zW0zW0zV0yV0xU0wU0vT0uT0tS0sS0rR0qR0pQ0oQ0nP0mP0lO0kO0jN0iN0hM0gM0\
  fL0eL0dK0cK0bJ0aJ0`I0_I0ZH0YH0XG0WG0VF0UF0TE0SE0RD0QD0PC0OC0NB0MB0LA0KA0\
  J90I90H80G80F70E70D60C60B50A509408407306305204203102101
  }
frm:hermanm_man-cart { ; Kerry Mitchell 16feb98
        ;
        ; real(p1) = z exponent (use integer >= 2; m=n-1)
        ; imag(p1) = g exponent (integers)
        ; p2 = alpha
        ; 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, alpha=p2
        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

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