[Fractint] Fmod Minibrot

21 Oct 2010


      Minibrots-if the iteration loop has x^2 + c its got a minibrot! Another pre-calculated
nomadic mandelbug at http://maxitersfractalfollies.blogspot.com. 
    
Fmod Minibrot     { ;   fract481.gif
                     ; blank
                     ; calctime   0:17:12.49
                     ; created Oct 20, 2010
                     ;  Fractint Version 2004 Patchlevel 10
  reset=2004 type=formula formulafile=kerrym.frm
  formulaname=hermanm_man-cart passes=1
  center-mag=+1.10021739445293500/+0.02785688062135686/341530.1/1/-167.500\
  000001965589/7.71297616053434609e-010 params=4/3/1/0/2/0 float=y
  maxiter=1500 inside=0 proximity=2 outside=fmod logmap=14
  colors=00101211312412413523624724825935936A36B37C47D48E48F49F59G5AH5AI5B\
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  G48F48E47D37C36B36A35A259248247236135124124113012001000
  }

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