That's one of the nicest fractals I've seen Jim. I know you have the copyright to all these images but I'd really like to use that particular one for the hundred or so Christmas cards we will be sending out this year. Can I have your permission to print it? I'll put an acknowledgment on the card anyway. "Fractal image courtesy and copyright of Jim Muth" or something similar? Chris ----- Original Message ----- From: "Jim Muth" <jamth@mindspring.com> To: <fractint@mailman.xmission.com> Cc: <philofractal@lists.fractalus.com> Sent: Friday, July 08, 2005 2:59 PM Subject: [Fractint] FOTD 08-07-05 (Old Lace [7])
FOTD -- July 08, 2005 (Rating 7)
Fractal visionaries and enthusiasts:
The lacy effect of today's image inspired the name "Old Lace", though in this case no arsenic is involved. What is involved is a combination of negative Z and (1/Z), with C added.
It is curious that this combination would produce any fractal at all. By itself, negative Z does not make a fractal, and (1/Z) makes a simple vertical row of small flat disks. (In the odd orientations of the Julibrot, (1/Z) produces some striking effects, but this is another story.) When negative Z and (1/Z) are combined however, some very interesting Mandelbrot things can happen.
In today's image, I added (1/Z) to negative Z. The resulting parent fractal is a rough hyperbola with Mandelbrot buds along its edges, and a small valley at the apex. Today's scene lies in the vicinity of this valley.
I rated the image at a 7. The coloring, which is about as smooth as can be achieved with only 256 colors to work with, adds to the impact, and raises the rating from a 6 to the 7. The render time of 26 minutes is admittedly slow. But relief may be found on the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
where the completed image is posted, ready for download.
The clouds remained thick all day Thursday here at Fractal Central, while the temperature reached a high of 81F 27C. Luckily, the rain held off until after dark, which gave the cats a pleasant afternoon in the yard. They became alert when two unwanted neighborhood stray cats wandered by, but the other cats moved on without coming within confrontation range. Today is starting with heavy rain however. Unless it ends in a hurry, the cats' day will be spoiled. My day will consist of the usual work and fractals, the next of which will appear in 24 hours. Until then, take care, and where do fractals come from?
Jim Muth jamth@mindspring.com jimmuth@aol.com
START PARAMETER FILE=======================================
Old_Lace { ; time=0:26:18.44--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.00697239427666942/+2.648103091012842\ 00/7219667/1/2.5/-2.90142841345708558e-006 params=-1/1/1/-1/0/525 float=y maxiter=2200 inside=0 logmap=569 periodicity=10 colors=00001P01N07M08L08R09P09S0AQ0AT0BR0BU0CS0CV0\ DT9DWAEUAEXBFVBFYCGWCGZDHXDH_EIYEI`FJZFJaGK_GLaHLa\ GMbGNbGNcGOcGOdGPdFPeFQeFQfFRfFRgFSgFShEThETiEUiEU\ jEVjEVkEWkDWlDXlDXmDYmDYnDZnDZoC_oC_pC`pC`qCaqCarC\ brBbsBcsBctBdtBduBeuBeuDfvFfvGgvIgvJivLhvNjvOjvQkv\ RkvTmvVmvWovYowZpw`pwbrwcrweswftwhtwjuwkvwmvwnwwpx\ wryxqxwpxwoxwnxwmxwlxvkxvjwviwvhwvgwufwuewudwucvub\ vtavt`vt_vtZvtYvtXvsWusVusUusTusSurRurQurPtrOtrNtq\ MtqLtqKtqJtqItqGurFusEusDvtCvtBvuAwu9wv8wv7xw6xw5x\ x3yz4xx4xw5wu5wt6vr6vq6uo7un7ul8tk8ti8sh9sf9reArcA\ rbAq`Bq_BpYCpXCoVCoUDoSDnREnPEmOEmMFlLFlJGlIGkGGkF\ HjDHjCIiAIi9Ii8IhAJhBKhCLhDMhENhFOhGPhHQgIRgJSgKTg\ LUgMVgOWgPXgQYfRZfS_fT`fUafVbfWcfXdfYeeZfe_geahebi\ ecjedkeelefmdgndhodipdjqdkrdlsemtgnuilvkjwmhxogyqe\ zsczubzz`zxZzyYzzWzzUzzTzzRzzPzzOzzMzzKzzKzzJzzJzz\ IzzIzzHzzHzzGzzGzzFzzRzzQ }
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 PARAMETER FILE=========================================
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