FOTD -- August 26, 2002 (Rating 7) Fractal visionaries and enthusiasts: The midget at the center of today's image is located on the X-axis of its parent fractal, which has X-axis symmetry. This is demonstrated not only by the coordinates in the parameter file but by the straightness of the arms radiating from the midget. The 180 degree rotation of the image does not change the east-west orientation of the X-axis, so why do 2 out-zooms reveal a north-south oriented axis? The mystery is not very deep, a few more out-zooms reveal the true situation -- the X-axis is not continuous. Actually, only one out-zoom reveals an interesting scene -- a near-perfect array of square figures that almost made it as FOTD. The choice between the squares in the out-zoom and the octagons in today's image was a toss-up. The squares lost only because one of the two images had to lose. The generating formula subtracts 0.2 part of Z^(-3) from Z^(-2) before adding 1/C. If I had added the 0.2 part of Z^(-3) rather than subtract it, the resulting parent fractal would still have had X-axis symmetry, but its overall shape would have been totally different, and of course, today's image would not have existed. (More accurately, it still would have existed but it would never have been found.) I used the MandelbrotMix2 formula to find today's image. This formula works the same as the overworked MandelbrotMix4 formula, except that it includes the capability to change the starting point of Z. This capability is not used in today's image. The name of the image, "The Web of Terror", which sounds like the title of a horror movie, has no connection whatever to the appearance. I might have had a fleeting impression of a spider's web, but if so, I can no longer see the resemblance. The rating of 7 seems fairly accurate, and those who spend the 3 minutes to run the parameter file will not be disappointed. Those who download the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will not be disappointed either. The Sunday weather here at Fractal Central was perfect for most anything, with blue skies, puffy white clouds, gentle breezes, low humidity, and a temperature of 86F 30C. The fractal duo were happy all day, which is a rare event for them. My happiness however depends on finishing the work I now find before me. If I start now, I can be finished by 3pm. If I wait an hour, I will not finish before 4pm. If I put off some of the work until tomorrow, I can be finished by noon. Most likely, I'll choose the first option. Until next FOTD, which will arrive in all its glory within 48 hours, take care, and beware of fractals lurking in dark corners. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ The_Web_of_Terror { ; time=0:03:13.01--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+7.662161881652889/0/1.171407e+011/1/180 params=1/-2/-0.2/-3/0/0/0/0 float=y maxiter=500 inside=0 outside=tdis periodicity=10 colors=000z8z89S8AR9AP9BOACMADLADK9CJ9BI8AI89H78G7\ 8G77F66E65E54D53C53CB7EGBFLEHRIIWLJ`PLeSMkWNqZPwbQ\ zeRxcSrbSn`Sk_SgYScXS_VSXUSTSSPRSLPSIOSEMSALS6JS3I\ S4KQ5LP6MO6NM7OL8QK9RI9SHATGBUECWDCXCDYAEZ9F_8F`7I\ b6Kc6Md6Pe6Ug6ch6mi6wj6wl6wm6wn6mo6cjA`fDZbHWZKTUO\ RQROMVMIYKKVILSHMQFONDPLCQIARG8TD7UB5V84W6KdKZlXYj\ YXhYWgYWeYVdYUbYUaYT_YSZYSXYRWYQUYQTYRVXSXVTZUU`SV\ bRWdPXfOYhMZjLZkKWeOT_RQUUNOYKI`ICcJH_KMXKQUJSWJTX\ JVZJW_IX`IZbI_cI`dIbfHcgHdhHfjHgkHhlPilWilcjljjlqj\ leZgUObIDY62TEFPMRL8tF9qKAoOBmSBkWCi_DfdDdhEblF`pF\ ZtH`sIarJcqKdpMeoNgnOhmPilQkkSljTmiUohVpgWqfVpcVpa\ Vo_VoYVoWUnUUnSUnQUmNUmLTlJTlHTlFTkDTkBTk9ShASeARb\ BR`BRYCQVCQTDPQDPNEPLETJDWHD_FCbDCfBBi9Bm7Ap5As3Ap\ 6Cm9DjCFgEGdHHaKJZNKXPL_OIbNFeNDXMrYNsmL5lQAkVEj_J\ idNhiSgnWgq_eoaclcbhe`egZaiYZkWVmVSnWRpXQqYPsZOtZN\ uSWsMdrGmpAvoe1hO4b66X77V } frm:MandelbrotMix2 {; 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 20.0 PAR-FORMULA FILE==================================