; Date: Sun, 04 Apr 2004 10:50:53 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 04-04-04 (Star of the Ages [7]) ; Id: <1.5.4.16.20040404105404.390f9f28@pop.mindspring.com> ; --------- ; ; FOTD -- April 04, 2004 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; Today's image takes us to the land created when 0.2 parts of Z^3 ; are subtracted from Z^2, where we further study the possibili- ; ties of the 'fmod' option. We also make use of the 'bof61' ; inside coloring option, which is effective because a good part ; of the image consists of areas of trapped 'inside' points. ; ; Yes, I do feel a bit guilty about the departure from fractal ; reality that took place when I decided to use these two options ; rather than outside=iter, inside=0, but the image is not bad, in ; fact it rates a 7, and is worth its moment in the sun as FOTD ; for April 4. ; ; I saw a letter on the fractint list recently wondering whether ; formulas other than Z^2+C will produce undistorted Mandelbrot ; sets. I would say the answer is yes. I have been producing ; them for years with the MandelbrotMix series of formulae. A ; formula as simple as Z^2+Z+C will merely shift the M-set around, ; while leaving it otherwise unchanged. ; ; Curiously, when Z is added to any power of Z other than 2, an ; entirely new fractal will result. See what happens when the ; formula Z^(2.5)+Z+C is calculated. And the formula Z^2+2Z+C has ; no effect whatsoever, producing a Mandelbrot set that is both ; undistorted and in its proper position as well. ; ; When searching for a name for today's image, I was struck by the ; eight-pointed star, and thought of the name "Star of the Ages". ; The name has a kind of religious sound to it, but no connection ; to religion was intended. ; ; When combined with the render time of over 5 minutes, today's ; image has an overall value of 131. For convenience, the ; completed GIF image will soon be posted on the FOTD web site at: ; ; ; ; Though the weather was improved here at Fractal central on ; Saturday, it was still too wet and chilly (50F 10C) for the cats ; to remain in the yard longer than 30 minutes. They spent the ; remaining 23-1/2 hours sleeping. The problem this morning is ; more rain, colder temperatures, and high winds, so I doubt that ; the day will be any better. ; ; For me, it might be an afternoon of 'antiquing' as the fractal ; lady calls examining the junk that others have thrown away. ; When the crisis has passed, I'll return to fractal land. Until ; tomorrow, take care, and I have yet to see a discarded fractal ; in one of those antique shops. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ Star_of_the_Ages { ; time=0:05:19.73--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.89130860945648100/+0.000079946227141\ 96/1464693/1/15/-1.43131317909e-008 params=1/2/-0.\ 2/3/0/0 float=y maxiter=1500 inside=bof61 proximity=0.3 outside=fmod periodicity=10 colors=050BLrBLrBLrBLrBLrBLqBLqBLqBLqBLoALnALnALnA\ LnALnALmALmALmALmALmALm8Lk8Lk8Lk8Lk8Lk8Lj8Lj8Lj8Lj\ 8Lj6Li6Li6Li6Li6Li6Lg6Lg6Lg6Lg6Lg3Kf4Lg4Lg6Lg6Lg6L\ g8Lg8Lg8LgALgALgALaBLgBLgDLgDLgDLgFLgFLgFLhGLhGLhG\ LhILhILhILhJLhJLhLLhLLhLLhMLhMLhMNhONhONhONhPNhPNh\ RNhRNhRNhSNhSNiSNiUNiUNiUNiVNiVNiVNjWNjWNjYNjYNjYN\ jZNjZNjZNj`Nj`Nj`NjaNjaNjaIjaKiaLgaLfaNeZNcYOZWQTV\ QNSOGRNGPLHMKIOIJOGKOFLPDMPBNP9OP9PR9QR9RR9SR9TSDU\ SGVSIWSKXUKYUKZUK_VK`VKaVLbVLcWMdWNeWOfWPgYQhYRiYS\ jYSkZTlZTmZTn`To`Tp`Tq`TraUsaTtaTuaTvcTwcTxcTxcTxd\ UxdUxdVxcWydWydXydXzfYzfYzfZzgZzh_zi`zj`zkazlazmby\ nbyocypcxqdxrdxsewtewufwvfvwgvxhvziozkrzluznuzouzq\ uzruztuzuuzsuzsuzquzquznuznszlqzkozhmxhjwgivgftees\ ebrdapcZoaXnaUl`Rk`Qj_Nh_MgYJfXHdWEcWEcVDcVDdVDdWD\ dXDfXBfZBg_Bh`BibBibBjcAkeAkfAmhAnhAniApk8rl8sm8um\ 8vo8wp8IKkGKjGKjFKjDKjDKj } 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================================== ;