FOTD -- April 12, 2007 (Rating 8) Fractal visionaries and enthusiasts: Today we introduce a new formula, which will replace the old MandelbrotMix4 formula. The new formula is named MandAutoCritInZ. This is short for "Mandelbrot -- Automatic Critical value of Initial Z". And this is exactly what the old M-Mix4 formula did. The new formula adds an additional variable parameter to the old formula, which allows an extra adjustment to initial Z. This is necessary because some functions of the type handled by the new formula have two critical points, and the formula calculates only one of them. A drawback of the new formula is that it can not initialize Z to the second critical point automatically. To do this, both critical points must be manually calculated and the difference entered as the adjustment to Z. This may be done graphically or mathematically. The graphic method is far more fun. Sometimes both critical points produce identical fractals; sometimes the identical fractals are mirror images of each other; sometimes the two critical points produce totally different fractals. Finding out is much of the fun of the new formula. Today's image was created by subtracting Z^(2.6) from Z^(2.4) and adding C. I named it "Spider Web Arms" because the pattern in the four angular arms around the central midget reminds me of spider webs. The spider-webs are actually open-inside areas decorated by the 'fmod' inside fill. I rather like the image, so I rated it at an 8. Today's image is a slow one, with a calculation time of over 43 minutes. But the wait may be avoided by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completely rendered image is or soon will be posted for instant viewing. In tomorrow's FOTD I'll discuss all the MandelbrotMix formulas and what they are supposed to do. A sunny mild morning turned into a cloudy mild afternoon here at Fractal Central on Wednesday. The temperature reached 52F 11C, which is still well below normal. Rain moved in at nightfall, but by then the fractal cats had finished their evening treats and were more concerned with washing each other's faces and chasing each other up and down the hallway. My day was actually not too unpleasant. And the above-average fractal for today shows it. The next fractal, hopefully also above average, will appear here in 24 hours. Until then, take care, and don't get lost in an ocean of iterations. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Spider-Web_Arms { ; time=0:43:47.58--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=t center-mag=-2.14487395538943600/+0.299702679142293\ 80/4.74766e+008/1/25/9.6356e-006 float=y logmap=228 params=1/2.4/-1/2.6/0/0/0/0 maxiter=5000 inside=fmod proximity=0.05 periodicity=10 colors=0000009L0BO0CR0DU0EY0G`0Hc0If0Jh0Pj0VkA_nKe\ pUksfpxmuzszzztwzotjjqiemh`hgWcfRZeMUdHPcCKbAOd8Te\ 7Yf5bg4gh2li1qj2lh3gf3bd4Yb4Ua5P_5KY6FW6BV9GSCLPEP\ MHUJKZGMbEQ`JTZOWYTZWYbUbeTghRlkPqnOvIJPJKNJKMJKLJ\ LKJLJJLHJMGJMFJMEJMDNUMR`VK4IKAMKIQKMSKPXKS_KVcKYg\ K`gKchKehKhiKkjKnjKqkKskSeCUbBV`BWZBYXBZVB_SBaQBbO\ BcMBeKBfHBgFBiDBjBBk9Bl7BkAEkDHjFJjIMiKPiNRhPUhSXg\ VZgXaf_dfafediefkY_wXYoWXhVWaUUUTTNSSGQSJPSLOSNNSP\ LSSKSUJSWISYGS`FSbESdDSfImYHnVHoTHpRHpPGqNGrLGsIGs\ GFtEFuCFvAFv8ZuCNcFQmIUkMYhP`eSdbVh`ZkYaoVdrTgqVfw\ XfcZfp`foafocfzzfngfnhfmdgm`hmXilTjlPklLllHmhJkeLj\ bMi_OhXQgURfRTeOVdLWcIYbFZaLV`RR_WNZaJYfFXaD_XBaSA\ dO8fJ7iE5kA4mFK`K_OOnBJhCEbD9YEATNBOWARTATRAWPAYMA\ `KAbI9eF9gD9jB9l89o69q49s28r28q28q28p28o28o28n28m2\ 8m2Dn6HnALnE`s9ox4nhHnUUmFfm0sl4pl7nkAkkDijGgjKdiN\ biQ_hTYhWWg_TgbRfeOfhM8Vb } frm:MandAutoCritInZ {; 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)+(p4)), 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=========================================