FOTD -- August 22, 2003 (Rating 6) Fractal visionaries and enthusiasts: I heard two interesting rumors yesterday. Rumor number 1 is that Microsoft is using Linux!!! on its web servers to protect them from worms and hacker attacks. Rumor number 2 is that the world of fractals is filled with surprises. I don't know about rumor number 1, but rumor 2 is certainly correct. I have discovered many surprising things in the 16 or so years I have been exploring the fractal world. Fractal trees, one of which appears in today's image, are only one of these surprises. The trees lurk in and near the Julia sets of the Julibrots with an exponent of Z between 1 and 2. The orientation of today's image lies 0.65 degree from the Julia direction, and the expo- nent is 1.5, making the conditions perfect for the generation of fractal trees. Since the 'tree' in today's image is but one of an infinity of similar trees in the vicinity, I named the image "Only One Surprise". I rated the final result at a 6, which is just slightly above average. BTW, perhaps the greatest fractal surprise of all came when I discovered that there are two ways in which the Z^2+C Julibrot can be sliced to give a perfect Mandelbrot set, and the second M-set has twice the area of the more familiar classic set. But that's a story for another day. Right now, it's time to give the good news that today's image renders in less than 3 minutes from the parameter file, and the equally good news that the finished GIF image is available on the W.W.Web at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Typical summer heat and humidity with ample sun and a tempera- ture of 90F 32C gave the fractal duo a pleasant day Thursday in the shadier parts of the yard. By the time the end of the day came, they had worn themselves out, and came indoors to eat with no coaxing. Today promises to be a repeat, with the chance of showers added. We'll see how it goes. It will go well for me if I finish the day's work without any unexpected problems. (Such as a call complaining that I sent a job in CMYK instead of grey scale, from a customer who for some reason could not convert the file.) Regardless of any problems, I shall return in 24 hours with more fractal goodies and a few words of wisdom. Until then, take care, and be advised that one person's wisdom can be another person's kookiness. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Only_One_Surprise { ; time=0:02:41.64--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multimin-XY-ZW-new function=ident/flip passes=1 center-mag=0.380743/0.154547/41.90764/1/\ -32.5/-1.014e-013 params=89.35/90/1.5/0/-0.6391/0/\ -1.15/0 float=y maxiter=1200 inside=0 periodicity=0 colors=0007An6Ao6Ap5Ap5Aq4Ar4Ar3As2At3As3Ar4Ar4Aq4\ Aq5Ap5Ao6Ao6An6An7Am7Al8Al8Ak8Ak9Aj9Ai9AiAAhAAhBAg\ BAfBAfCAeCAeDAdDAcDAcEAbEAbEBaFC`FD`GE_GF_GGZHHYHI\ YIJXIKXILWJMVJNVJOUKPUKQTLRSLSSLTRMURMVQNWPNXPNYOO\ ZOO_NN`OOaNPbMQcMRdLSeLTfKUgJVhJWiIXjIXkHYlHZmG_mF\ `mFamEbmEcmDdlCelCekBfkBgkAhjAij9ji8ki8li7mh7nh6nh\ 6mg7lf7ke7jd7jc7ib7ha7g`8f_8fZ8eY8dY8cX8cW8bV8aU9`\ T9_S9_R9ZQ9YP9XO9XO9WNAVMAULATKATJASIARHAQGBPFBPEB\ ODBNDBMCBMBBLABK9CJ8CI7CI6CH5CG4CF3CG2DF3CF3CF3CF3\ CF3CF3CF3CF3CE3CE3CE3CE3CE3CE3CE3CE3CD3CD3CD3CD3CD\ 3CD3CD3CD3CC4CC4CC4CC4CC4CC4CC4CC4CB4CB4CB4CB4CB4C\ B4CB4CB4CA4CA4CA4CA4CA4CA4CA4CA4C938A4CA5FA6JA7MA8\ PA9TAAWAB_ACbADe9Cf9Cg9Cg8Ch8Ch8Ci8Ci7Cj7Cj7Ck7Ck6\ Cl6Cm6Cm6Cn5Cn5Co5Co5Cp4Cp4Cq4Cq4Cr3Cs3Cs3Ct3Ct2Cu\ 2Cu2Cv2Cv1Cw1Cw1Cx0Bz1Cx1Dw1Ev1Fu1Gt2Hs2Ir2Jq2Kp2L\ o3Mn3Nm3Ol3Pk3Qj4Ri4Sh4Tg } frm:multimin-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=(-z)^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================