After reading the formula name of today's fractal (hermanm_man-cart) I realized
I had the pleasure of making the aquaintance of Herman Minibrot of the south-side Minibrots.
For an instant encounter with Mr. Minibrot go to http://maxitersfractalfollies.blogspot.com
no invitation required.

fract335.gif       { ; I like the colors
                     ; blank
                     ; calctime   0:08:07.84
                     ; created Jul 28, 2010
                     ;  Fractint Version 2004 Patchlevel 9
  reset=2004 type=formula formulafile=kerrym.frm
  formulaname=hermanm_man-cart
  center-mag=-1.98717456210925500/-0.00365303064774690/726.036/1/-97.49999\
  99999995168/3.88578058618804789e-016
  params=3/2/0.9481490524002808/0.4500259407330546/2.049745170445875/-0.59\
  7888119144261 float=y maxiter=1500 inside=0 outside=atan
  colors=000503504604705805806907A07B08B08C09D1AE1AF1BF1BG1CH1CI1DI1EJ1EK1\
  FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21w00z03z07z0B\
  z0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0zz0xz0vz0tz0rz0pz0nz0lz0jz0hz0fz0d\
  z0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0Iz0Gz0Ez0Cz0Az08z06z04z02z00z00y10x20\
  v20u30s40r50p50o61n71l81k91i91hA1gB1eC1dC1bD1aE1_F1ZF1YG1WH1VI1TJ2SJ2RK2\
  PL2OM2MM2LN2JO2IM2GJ2EH2CE1AC18916614312000101302503605806A07C19D19E1AF1\
  AF1BG1BH1CI1DI1DJ1EK1EL1FL1FM1GN1HO2IO2JQ2IS2HV2GX2F_2Da2Cd2Bf2Ah19k18m1\
  7p15r14u13w12z00z20z50z70zA0zC0zF0zH0zK0zM0zP0zR0zU0zX0zZ0za0zc0zf0zh0zk\
  0zm0zp0zr0zu0zw0zz0zw0zu0zr0zo0zl0zj0zg0zd0za0z_0zX0zU0zS0zP0zM0zJ0zH0zE\
  0zB0z80z60z30z00x01v02s03q04n06l07i08g19e1Ab1B`1CY1EW1FT1GR1HO2JN2IM2HK2\
  GJ2FH2DG2CE2BD2AB19A18817715514413212000000101201302403
  }
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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