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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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=========================================