; Date: Fri, 13 Apr 2007 22:54:25 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 14-04-07 (Merging Dry Valleys [7]) ; ; Id: <1.5.4.16.20070413225817.29afdc12@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint