FOTD -- July 02, 2002 (Rating 7) Fractal visionaries and enthusiasts: Fractals of the Mandel-Julia variety are filled with holes, especially when the iterated expression contains more than one power of Z. These holes come in many varieties. There are the obvious Mandelbrot midgets and Julia sets, and then there are the other types of holes that defy description. Today's image features one of these 'other' holes. The area in question was pointed out to me by Lee Skinner in an image he sent privately several days ago. The orange-colored holes near the center are of a type I have seen in images created with the branch-cuts formula when the exponent of Z is in the area of 1.15, but in today's image, several things appear to be happening at the same time. It almost appears that the two different powers of Z are doing things independently of each other. A math expert might be able to tell what is going on in today's image, but not being a math expert, I have no idea. While studying the image, I had the distinct impression of a frog staring back at me. I promptly named the image, "One Froggy Morning". The rating of 7 is justified because the image is a bit -- well -- cute. The render time of over one hour on a P200 machine is not cute however. I advise letting Paul and Scott do the heavy work and downloading the completed image from their one of the web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday at Fractal Central was typical summer fare for these parts of the world -- HHH -- hazy, hot and humid. The temperature of 92F 33C, combined with the high humidity and foul air, made the outdoors unpleasant for most of the day. The dynamic duo of cats must have agreed, for they stayed on the porch only a few minutes before coming in and asking for their tuna treat. As for me, it's another Tuesday, even hotter than yesterday, and I've got a bit of work to finish before returning to the FOTD CD, which should be ready for distribution by the end of summer. But the end of summer is still over 2-1/2 months away, and before then we'll have many more fractals added to the ever- growing list. The next fractal will appear on July 4. Until then, take care, and digress but don't egress. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ One_Froggy_Morning { ; time=1:09:42.15--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip center-mag=6.57209/0.000937142/22.6787/1/-80/-1.23\ 37353361147052e-014 params=-0.2/-1.25/-0.2/-0.8/0/0 float=y maxiter=160000 inside=0 logmap=19 periodicity=20 colors=000j85Q85h96g96fA6eA7eB7dB7c\ C8bC8aD8`D9_E9ZE9YEAXFAWFAVGBVGBUHBTHCSICRICQJDPJD\ OKDNKEMLELLEKMFKNFKNFLOFLOFLPFLPFMQFMQFMRFMRFMSFNS\ FNTFNTFNUFOUFOVFOVFOWFOWFPXFPXFPYFPYFQZFQZFQ_FR_FR\ `FR`FRaFRaGSaGSbHTbITbJUbJUbKVbLVcLWcMWcNXcNXcOYcP\ YdQZdQZdRZeS_eT_eU`eU`eV_eV_eX`fZ`f_`gaagcageahfah\ hbhjbilbimcjocjqckrcktdlvdlxemzgnzhozjpzlqzmrzoszp\ tzruztvzvwzwxzyyzxxywwxuwwtvvsuurutqtrosqnrpmrolqn\ jqmipkgojfniemhcluckfnmtakhchWahlZZZb`_eb`idamgcni\ goklpmpqpupotonrnlqmkoljnjhligkgfjfeiddhccgaaf``eZ\ _dYZcWXaWW_VUYUTWTRUSPSSOQRMOQLMPJKOIINGGLEEKCCLDC\ NEDOEDQFDRGESHEUHEVIFXJFYKG_KG`LGaMHcNHdNHfOIgPIiQ\ JjRJlSKnTLoULqVMsWNuXOwZPw`QwbRwdRxfSxhTxjUxlUxnVx\ pWyrXytYzvZzx_zz`zw_zuYzrXzoVzmUzjSzgRzePzbOz_MzYL\ zVJzSIzQGzNFzKDzHCzFAzC9yA7y75y54y32z00y00x11yA1zK\ 1zN1zQ2zT2zU2zU3zU3zU3zU4zU4zU4zU4zU0zU0 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================