FOTD -- December 18, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image has been named "The Phantom Wave". Don't ask me why I gave it such a name -- I have no idea. The name might refer to a wave of bubbles or a wave of midgets, or even a wave of FOTD images calculated by the MandelbrotMix4 formula. More likely, it's a wave in my imagination. But whatever the reason, there must be some kind of wave connected with the image, which lies in the parent fractal created by subtracting 0.9 parts of Z^(1.2) from 2 parts of Z^(-1.2) and adding (1/C). The bubbly effect in the image was achieved by rendering the scene with the outside=fmod and the proximity=3. At the moment I am not sure how the 'fmod' option works and how the proximity affects it, but the information is somewhere in the monumental stack of help included with the Fractint program. I could rate the image no higher than a 5, a rating that is ho-hum average. No, I do not expect a rush to see the image when I admit in the discussion that it is un-exceptional, but the fun lies in finding the FOTD images and writing about them. Profit is obviously no motive in the creation of the FOTD. The render time on my worn-out P200 machine, which just barely keeps slogging along, is almost exactly 6 minutes. On the state- of-the-art units out there the image will render notably faster. The fastest way of all to see the phantom wave is to download it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and examine the image very carefully for any signs of a wave. The Wednesday rain here at Fractal Central changed to snow at 2pm, but ended within an hour before accumulating on the ground. The cats, who spent the entire day indoors, were not concerned with the change-over. They needed only a small treat of tuna in the evening to maintain their good spirits. Today is starting partly cloudy, breezy, and cold -- the kind of day that keeps fractal cats indoors and the fractal human busy working on the next FOTD, which will appear in 24 hours. Until then, take care, and be at peace. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ The_Phantom_Wave { ; time=0:06:00.08--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.38515755772367030/+0.157082089485032\ 80/89131.38/1/-30/2.018383862823e-010 params=2/-1.\ 2/-0.9/1.2/0/0 float=y maxiter=1200 inside=0 proximity=3 outside=fmod logmap=yes periodicity=10 colors=000pgopgmoglngknfkmfjlfilehkehjegjdfidfhdeg\ cdgccfccebbebadb`ca`ca_baZa`Za`Y``X__WZ_WZ_VYZUXZT\ XZTWZSVYRVYRUYQTXPTXOSXORWNQWMQWLPVLOVKOVJNUJMUIMU\ HLTGKTGKTFJSEISDHSDHRCGRBFRBFQAEQ9DQ8DP8CP7BP67O09\ O3BN6DN9FMCGLEIKHKKKMKNOKQOKRP9SP9SQ9SQ9TRATRATRAU\ SAUSAUTBVTBVUBVUBWUBWVCWVCXWCXWCXXDYXDYXDYYDZYDZZE\ ZZE__E__E__E_`F``F`aF`aFabGabGabGbcGbcGbdHcdHceHce\ HdeHdfIdfIegIegIehJfhJfhJfiJgiJgjKgjKhkKhkKhlJjkKh\ jKgiKehLdhLbgLafM`eMZdMYdMWcNVbNUaNS`OR`OP_OOZOMYP\ LXPKXPIWQHVQFUQEVRBUQCUQDTPETPFSPFSOGROHRNIRNJQNJQ\ MKPMLPMMOLNOLNNKONKPNKQMJRMJRLISLITKIUKHVJHVJHWJGX\ IGYIFZHFZHF_GE`GEaFCcGDbGDaGEaGE`GF`GF_GG_GGZGGZGH\ YHHYHIXHIXHJWHJWHJVHKUHKUHLTHLTHMSIMSINRINRINQIOQI\ OPIPPIPOIQOIQNGRPIQNJPMLPKMOJNNHPNGQMESLDTLBUKAWJ8\ XJ7ZI5_H4_I2`H3`H3`H3`H3`G3TnHUmJWmLXlNYlP_kR`kTbj\ VcjXeiZfi`ghbihdjgflghmfj } 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==================================