[Fractint] Field Line Variations

9 Nov 2010


      Today's blog post of Fractint compatible gifs and anti-aliased jpgs is of two versions of
the field4_jul formula by Kerry Mitchell. They are identical except for the imaginary P2
values. I calculated with values of 0 and 12. Available at http://maxitersfractalfollies.blogspot.com
I've posted only one version of the par file, just vary imag(P2) if regenerating.

 Field Line Variations             { ; fract506.gif 
                     ; blank
                     ; calctime   0:03:55.63
                     ; created Nov 08, 2010
                     ;  Fractint Version 2004 Patchlevel 10
  reset=2004 type=formula formulafile=*.frm formulaname=field4_jul
  center-mag=0.048197/0.607759/3.404629 params=0.375/0.375/1000000/0
  float=y maxiter=1500 inside=0 decomp=256 periodicity=0
  colors=00101211312412413523624724825935936A36B37C47D48E48F49F59G5AH5AI5B\
  J6BK6CK6CL6DM7DN7EO7EP7FP8FQ8GR8GS9HT9HU9IUAIVAJWAJXBKXBKYBLYCLZCMZCM_DN\
  `DN`DOaDOaEPbEPbEQcFQcFRdFReGReGSfGSfHTgHTgHUhIUiIViIVjIWjJWkJXkJXlKYlKY\
  mLZnLZnM_oM_oM`oN`pNapOaqObqPbrPcrPcrQdrQdsResRetRftSftSgtTguThuUhuUivVi\
  vVjvVjvWkwXkwYlwYlwZmxZmx_nx_nx`ox`oxapyapybqybqycrydryesyeszftzgtzhuzhu\
  zivzjvzkwzmwznxzpxzqyzryzuzzuzzuzzryzqyzoxznxzmwzkwzjvzivziuzhuzgtzftzfs\
  zesydrycrybqybqyapyapy`ox_ox_nxZnxZmxYmwYlwXlwXkwWkwVjvVjvVivVivUhvUhuTg\
  uTguSfuSftRetQesQdsQdrPcrPcrObqObqOapNapN`oN`oM_nM_nMZmLZmLYlLYlKYlKXkJX\
  kJWjJWjIViIViIUhHUhHTgHTgGSfGSfFRfFReFQdFQcEPcEPbEObDOaDNaDN`CM_CM_BLZBL\
  ZBKYAKYAJXAJWAIV9IU9HU9HT8GS8GR8FR8FQ7EP7EO7DN7DM6CL6CL6BK6BJ5AI5AH59G59\
  G48F48E47D37C36B36A35A259248247236135124124113012001000
  }


frm:field4_jul { ; Kerry Mitchell 20jan98
        ;
        ; Colors Julia sets by nearest approach to
        ;   period 4 field lines
        ;
        ; use decomp=256
        ; p1 = Julia parameter
        ; real(p2) = bailout (try 1e12)
        ; imag(p2) = number of field line to use:  0 - 15
        ; 4 iterations per pixel
        ; variable zc used for calculation, z for coloring
        ;
        zc=pixel, c=p1, maxr=real(p2), minr=maxr, iter=1
        fieldangle=tan(imag(p2)*2*pi/15):
        ;
        ; iteration
        ;   compare tangent of polar angle with desired
        ;   field line angle, update minimum if needed
        ;
        iter=iter+4, zc=sqr(zc)+c, zc=sqr(zc)+c, zc=sqr(zc)+c
        zc=sqr(zc)+c, rzc=|zc|, tanangle=imag(zc)/real(zc),
        r=cabs(fieldangle-tanangle)
        if (r<minr)
          minr=r
          end if
        ;
        ; bailout
        ;   set "iteration done" flag (iter=-1)
        ;   use log of minimum difference of angles as
        ;     decomposition angle
        ;
        if ((rzc>maxr)||(iter>=maxit))
          iter=-1
          angle=log(minr)
          z=cos(angle)+flip(sin(angle))
          end if
        iter>0
        }
Roger Alexander