A question of nomenclature. Should these structures be called threads (or filaments) to
distinguish them from the linear structures such as found in the classic mandelbrot? And what
could the mandelbrot linear structures be called?
    Go to http://maxitersfractalfollies.blogspot.com to see what prompts this question.


fract234.gif       { ; filaments
                     ; blank
                     ; calctime   0:31:17.03
                     ; created Jun 01, 2010
                     ;  Fractint Version 2004 Patchlevel 9
  reset=2004 type=formula formulafile=2circles.frm
  formulaname=cenx=ceny_jul center-mag=0.0904633/-0.271478/13.83126
  params=-0.8416089358195745/-0.2229987487411115/-0.1370891445661794/0.368\
  1142612994781/0.5048982207708976/-0.5791192358165227 float=y
  maxiter=1500 decomp=256 periodicity=0 cyclerange=0/255
  colors=DHVCGUBET9DS8BR7AQ69P57O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAE\
  TBGUCHVDIWFKXGLYHMZIO_JP`KRaLSbMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`j\
  qakrbmscntepufqvgrwhtxiuyjvzjvziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVc\
  lUbkT`jS_iRYhQXgPWfNUdMTcLSbKQaJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47\
  O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAETBGUCHVDIWFKXGLYHMZIO_JP`KRaLS\
  bMTcOVePWfQXgRZhS_iTajUbkVclXemYfnZgo_ip`jqakrbmscntepufqvgrwhtxiuyjvzjv\
  ziuyhsxgrwfqvdoucntblsakr`jq_hpZgoYfnWdmVclUbkT`jS_iRYhQXgPWfNUdMTcLSbKQ\
  aJP`IN_HMZGLYEJXDIWCHVBFUAET9DS8BR7AQ58P47O36N24M13L02K02K13L25M36N47O69\
  P7AQ8CR9DSAETBGUCHVDIWFKXGLYHNZIO_JP`KRaLSbMTcOVePWfQYgRZhS_iTajUbkVclXe\
  mYfnZho_ip`jqalrbmscntepufqvgswhtxhtxiuyhtxgrwfqveoucntbmsakr`jq_ipZgoYf\
  nXdmWclVbkT`iS_hRZgQXfPWeOUdNTcMSbLQaKP`IO_HMZGLYFJXEIW
  }
frm:cenx=ceny_jul { ; Kerry Mitchell 26aug98
    ;
    ; "2 concentric circles" coloring method for Julia sets
    ; p1 = c = Julia parameter
    ; p2 = (both) circle center
    ; real(p3) = x circle radius
    ; imag(p3) = y circle radius
    ; bailout hardcoded to 10^12
    ; use "decomp=256" coloring
    ;
        zc=pixel, c=p1, bailout=1e12, iter=1, rmin=1e12
        cenx=p2, radx=real(p3), rad2x=radx*radx
        ceny=cenx, rady=imag(p3), rad2y=rady*rady:
        iter=iter+1, zc=sqr(zc)+c
        tempx=|zc-cenx|-rad2x
        tempy=|zc-ceny|-rad2y
        temp=tempx+flip(tempy), r=|temp|
        if (r<rmin)
          rmin=r, z=temp
          endif
        if ((|zc|>bailout)||(iter==maxit))
          iter=-1
          endif
        iter>0
        }
  Roger Alexander

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