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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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 20.0 PAR-FORMULA 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 20.0 PAR-FORMULA FILE==================================