[Fractint] Spirals With Spirals

17 Sep 2010


      A spiral with spirals. When I say fractal I say self-similarity. Fractint compatible gif
and re-sampled jpg at http://maxitersfractalfollies.blogspot.com. 

fract420.gif       { ; spirals
                     ; blank
                     ; calctime   0:09:55.07
                     ; created Sep 16, 2010
                     ;  Fractint Version 2004 Patchlevel 9
  reset=2004 type=formula formulafile=kerrym.frm
  formulaname=bubbleboth_jul center-mag=0.135169/0.511853/13.33333
  params=0.375/0.375/64/0.5/1/1 float=y maxiter=3600 inside=0
  outside=atan periodicity=0
  colors=05FOT_PT_PT`QU`QUaRVaRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYa\
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  }
frm:bubbleboth_jul { ; copy
        ; Kerry Mitchell
        ; color Julia sets with small bubbles
        ; filled with swirls (combination of rays and circles)
        ;
        ; use outside=iter, decomp=256
        ; p1 = Julia parameter
        ; real(p2) = bailout (at least 4)
        ; imag(p2) = radius of bubble (try ~ .1)
        ; real(p3) = amount of circles (0 for only rays, try 0.5)
        ; imag(p3) = amount of rays (0 for only circles, try 0.5)
        ; zc is the variable used for iteration, z for coloring
        ;
        zc=pixel, c=p1, maxr=real(p2), minr=imag(p2), scale=2*pi/minr
        minset=0, iter=1, rzc=cabs(zc), minzc=zc
        weight=real(p3)+imag(p3)
        weightc=real(p3)/weight, weightr=imag(p3)/weight
        ;
        ; initial check:  see if pixel magnitude falls within threshold
        ;   if so, set minset flag, update minimum to current magnitude
        ;
        if (rzc<minr)
          minr=rzc, minzc=zc, minset=1
          end if
        :
        iter=iter+1, zc=sqr(zc)+c, rzc=cabs(zc)
        ;
        ; iteration check:  see if iterate falls within threshold
        ;   if so, set minset flag, update minimum to current magnitude
        ;
        if (rzc<minr)
          minr=rzc, minzc=zc, minset=1
          end if
        ;
        ; bailout
        ;   set "iteration done" flag (iter=-1)
        ;   scale minr to find decomp angle for circles
        ;   take polar angle from minzc to ray decomp angle
        ;   final angle is weighted average of ray and circle angles
        ;   if a new minimum was never set (minset=0),
        ;   set z=0 (color 0 under decomp)
        ;
        if ((rzc>maxr)||(iter==maxit))
          iter=-1
          anglec=scale*minr, angler=imag(log(minzc))
          angle=weightc*anglec+weightr*angler
          z=(cos(angle)+flip(sin(angle)))*minset
          end if
        iter > 0
        }
Roger Alexander