; Date: Thu, 12 Apr 2007 00:04:56 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 12-04-07 (Spider-Web Arms [8]) ; ; Id: <1.5.4.16.20070412000848.2a7711b2@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint