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\ fZbgZbg_ch_ch`ch`diadiaeibejbfjcfjcgkdgkdhlehleilfimfjmgjmgknhknhlniloim\ ojmpjmpknpknqloqloqmprmprnqsnqsorsortpstpstqtuqturuuruvsvvsvwtwwtwwuxxux\ xuxxvyyvyywzzvyyvyyuxxtxxtwwsvwsvvruvquuqtupstostorsnqsnqrmprlpqloqknpjn\ pjmoimohlnhkngkmgjmfjleilehkdhkcgjcfjbfibeiaeh`dh`cg_cgZbfZbfYaeX`eX`dW_\ dW_cVZcUYbUYbTXaSWaSW`RV`RV_QU_PTZPTZOSYNSYNRXMQXLQWLPWKPVKOVJNUINUIMTHL\ TGLSGKSFKRFJREIQDIQDHPCHPBGOBFOAFN9EN9EM8DM8CL7CL6BK6AK5AJ49J49I38I37H27\ H16G16G05F05F05F16G16G16G16G16G27H27H27H27H27H38I38I38I38I38I49J49J49J49\ J49J5AK5AK5AK5AK5AK6BL6BL6BL6BL7CM7CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9E\ O9EOAFPAFPAFPAFPAFPBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJ\ TFKTGKUGLUHLVHMVIMVINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_ } 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