FOTD -- April 14, 2007 (Rating 7) Fractal visionaries and enthusiasts: Today's image mixes Z^(1.95) with Z^(2.05) before adding C, making the overall power an average of 2. The parent fractal created by this formula resembles a perturbed Mandelbrot set. And today's scene is located on the edge of what appears to be the remains of Seahorse Valley. The things in this valley are like nothing found in the real Seahorse Valley however. The peanut-shaped hole at the center of the image lies at the center of what I call a dry valley. Dry valleys are areas that start out with 2-way symmetry, giving the impression that a quadratic midget lies at the center, but they come to dead ends. Today's dry valley is unusual in that a peanut-shaped hole lies at its center. The peanut shape is actually two circular holes which have partially merged. The edge of the hole is actually a discontinuity, making a greater maxiter useless. No more detail can be found inside the peanut hole regardless of how high the maxiter is raised. I named the image "Merging Dry Valley", which is a full descrip- tion of what we are looking at. I rated it at an above-average 7. Unfortunately, the calculation time is a rather slow 14-1/2 minutes. But this wait may be bypassed by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the pre-rendered image there. In my collection I have 6 MandelbrotMix type formulas. 'MandelbrotMix1' has long been discarded. It simply combines 2 powers of Z and always initializes Z to zero. It makes no effort to find a critical starting point. 'MandelbrotMix2' appears to be identical to the 'MandAutoCritInZ', which I just wrote. It automatically initializes Z to a critical value and allows initial Z to be manually reset to a second critical value. If I had checked this formula carefully, I would have had no reason to write the 'MandAutoCritInZ' formula. 'MandelbrotMix3' mixes 4 powers of Z and allows Z to be initialized manually to a critical value that has been determined by calculation. 'MandelbrotMix3a' is the same as 'MandelbrotMix3' with the added ability to change the escape radius. 'MandelbrotMix4' is the workhorse formula, which automatically calculates a critical value of the entered formula and initializes Z to this value. 'MandAutoCritInZ', the newest formula, takes the 'MandelbrotMix4' formula and adds the ability to manually initialize Z to a second critical point, which must be calculated separately. I also have a 'JuliaMix1' formula, which calculates the Julia sets of the fractals crated by the MandelbrotMix family. This formula can draw some very attractive fractals. It has been grossly under-used. And finally, there is a formula named 'ParabolicMix3', which graphically and rather laboriously determines the critical values of entered formulas. Heavy clouds, blustery winds, occasional sprinkles of cold rain and a temperature of 43F 6C kept spring at bay here at Fractal Central on Friday. The two fractal cats sat on their shelf by the sunniest window in vain. They never got the warm sun they were waiting for. They consoled themselves with an extra treat of tuna in the evening. My day was notably average. Saturday will likely be the same. The next FOTD will appear in 24 hours. Until then, take care, and walk with your head in the stars and your feet on a fractal. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Merging_Dry_Valley { ; time=0:14:25.24--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.36696528477454960/+0.086040053843335\ 20/6.461328e+010/1/11.5/-9.95185134476730959e-005 params=1/1.95/1/2.05/0/0/0/0 float=y maxiter=1800 inside=0 logmap=220 periodicity=10 colors=000KGRKHSKITKJUKKVKLWKMXKNYLOZLP_LQ`LRaLSbL\ TcLUdIVfKWeLXeMYeNZeO_dP`dQadRbdSccUdcVecWfcXgbYhb\ Zhb_ib`jaakabladmaen`fo`gp`hq`ir_js_kt_lu_mt_ls`lr\ `lq`loalmalkaliblhblgbkfckeckdckcdkbdkadk`ek_ekZej\ YfjXfjWfjVgjUgjTgjShjRhjQhlPkkOijNhiMghLfgKefKdeLc\ dMbcNacN`bO_aPZ`QY_RXZSVYTUXUTWVSWVRVWQUXPTYOSZNR_\ MQ`LPaKObJPdJObINaIN`IM_IMZILYIKXHKWHJVHJUHITHHSHH\ RGGQGGPGFOGENGEMGDLGDKFCJFBIFBHFAGFAFF9EE8DE8CE7BE\ 7AE69E57C68D68E68E68F78F78G78G78H88I88I88J88J98K98\ K98L98MA8MA8NA8NA8OB8OB8PB8QB8QC8RC8RC8SC8Stjlvklx\ llwmmvnmuomtpmsqnrrnqsnqtnpuoovonwomxolypkzpjzpjzp\ iMmhLkgLhfKfeJcdJacIZbIXaHU`GS_GPZFNYEKXEIWDFWDDYH\ H_LK`ONbSQcVTeZWfaZheaihdklglojnsmryrozpmznjzmhzke\ ziczh`zfZzeWzcUzaRz`PzZMzXKzWHzUEzRFzTFzUFzWFzXFzZ\ Fz_FzaGzbGzdGzeGzgGzhGzjGzkGzlIzhJzeizOkzNlzMnzLoz\ KqzJrzJlzHfzG`zFVzDPzCJzB } 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=========================================