; Date: Sun, 28 Aug 2005 10:10:26 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 28-08-05 (Octoflake [5]) ; Id: <1.5.4.16.20050828101245.298f9944@pop.mindspring.com> ; --------- ; ; FOTD -- August 28, 2005 (Rating 5) ; ; Impatient fractal visionaries and enthusiasts: ; ; Today's image was originally dated August 27, but it is now so ; late that the image has been re-classified as the FOTD for ; August 28. The computer problem that caused the delay has ; finally been remedied, and the machine is once again behaving ; like it should. In a day or so, I'll try to post another image ; to fill the gap of the 27th, but there is no guarantee. ; ; Today's fractal is a scene in the parent fractal that results ; when various portions of Z^(2), Z^(3), Z^(-1.5) and Z^(4) are ; combined. The formula that did all the work is named ; MandelbrotMix3a, which works much the same as the M-Mix4 formula ; except that it combines 4 powers of Z instead of 2, and the ; critical points must be calculated separately and entered by ; hand. ; ; I have written a Fractint formula that draws rudimentary graphs ; of the entered expressions and finds some critical points ; graphically, but it is awkward to work with and problematical in ; its results. My ultimate goal is a formula that finds all the ; critical points of a function without the need to analyze a ; graph, and can at once calculate the fractal associated with any ; critical point that the user chooses. ; ; One of the critical points the awkward formula found for today's ; expression is 0.754232105. I have entered this value as ; real(p5), where it acts as the starting point of Z. The parent ; fractal consists of a fairly undistorted M-set with cantor-dust ; debris fields scattered about. Today's image is located near ; the northern branch of Seahorse Valley of the M-set. There are ; midgets scattered through the debris fields, but experience has ; shown that such midgets are usually not very interesting. ; ; I named the image "Octoflake" because it resembles a snowflake ; with 8 arms instead of the normally expected 6. After careful ; non-consideration, I rated the image at a 5, a rating that is ; not great, but at least is not below average. ; ; The render time of 2 minutes is fast enough, and can be ; eliminated entirely by going to the FOTD web site at: ; ; ; ; and downloading the finished image from there. ; ; The skies turned cloudy on Saturday here at Fractal Central, ; but the temperature never rose higher than 75F 24C and it ; remained dry. These conditions were well within the comfort ; zones of the fractal cats, who spent the entire afternoon ; hiding in the holly patch. They came inside without coaxing ; when evening arrived. Today is starting with clouds and ; showers, which will likely cause the cats to have an inferior ; day. For me, the day will be rather uneventful. ; ; The next regularly scheduled FOTD will appear in only 24 hours. ; An extra FOTD dated August 27 might appear when least expected. ; Let's hope that the next image, whenever it arrives, rates ; better than just average. Until then, take care, and don't let ; a fractal get the better of you. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Octoflake { ; time=0:02:16.38--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=-0.6565220055047544/+0.1099144662045948\ /210172.3/1/10/0 params=1/2/-1/3/0.5/-1.5/1/4/0.75\ 4232105/0 float=y maxiter=1000 inside=0 logmap=21 periodicity=10 colors=000aK2ZJ2VH2QE2JA2662KHBXSKjbTztagdSSXJO`MK\ cPGfSDjU9mX5p_2sa5lb7fc9`cBVdDPeFJeCLa9MY6OU3PQ1QN\ dtaarZ_qXYpVWoTUnRSmPQlNWjS`hXegajefodktbpyauu`kr`\ ao_Sl_IO4kzSBrUFkWJcYNX_RQ`UQaVQaWQbXQcZyRRyn4onGe\ nRibSlRTdZaYfiRnqKuyOnzRhzVazYWzUTwRQtNNqKKnGHkDFh\ EEZEEQEEGEE7MVUTkppB8iTRbihoEor5qAKbwvUxlYybauYbqU\ bmPciLceHdaCdY8eV4eZBhbIkfPnjWqnbtlcsjdsherffrRlme\ fqcgqahp_ipZioXjoVknTlnDoBEnDFnFGnHGnJHnLInNJmPJmR\ KmTLmVMmXMmZNm`OlbPldPlfQlhRljSllWUqVWpVXpVZpU_pUa\ oUboTdoTeoTgnShnSjnSkn`ov_nuZntZntYnsXmsXmrWmrVmqV\ mpUlpTloTloSlnnOilQjkRjjSjiTjhUkgWkfXkeYkdZlc_laal\ `bl_cmZdmYemXgmWhnVinUjnTknB2zD6zE9zFCzGFzHIzILzJO\ zLSzMVzNYzO`zPczQfzRizzmzzmzzmzzmzzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzzmzznzzozzpzzozzozzozzozznzznzznz\ znzzmzzmzzmzzZzzgzzozzlzzizzfzzdzzazzZzzXzzUzzSzzP\ zzNzzKzzIzzKzzMzzOzzQzzSz } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } ; END PARAMETER FILE========================================= ; ;