FOTD -- October 10, 2013 (Rating A-6,M-6) Fractal visionaries and enthusiasts: In today's image I mixed straight Z with 0.5 part of Z^2, 0.333... part of Z^3 and 0.25 part of Z^4 and then set initial Z to -1, the critical point of the mixture. (I entered the value as -0.999... because of a program glitch.) The resulting Mandeloid resembles a Mandelbrot set with two large wings sprouting from the north and south sides of the East Valley, which is grossly enlarged but, at least on the surface, not very interesting. Today's image does not lie in this area however. It is located very deep, near a larger minibrot in a minor valley on the east shore line of an oddly shaped minibrot on a filament extending from the large period-3 bud on the northwest shore line of the main bay. The art and math aspects both rate a 6, which is a little above average but nothing to get excited about. The colors clash too much and are too splotchy to rate anything higher, and the math is nothing new either. I might have done better with the colors if I had not become preoccupied with four-dimensional stuff. The name I gave to the image, "The Worm has Turned", had some meaning when I thought of it, but I have since lost track of whatever the meaning might have been. The slow calculation time of 7-1/4 minutes may be avoided by checking the FOTD web sites. The web sites may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> A cloudy sky with a temperature of 59F 15C kept spirits under wraps here at Fractal Central today. The fractal cat hid his depression under the chair cover; the fractal humans had too much other stuff to do to feel very depressed. The next FOTD will be posted before long. The discussion should include a bit about four-dimensional curiosities, especially the weird motion possible only in space of more than three dimensions known as double rotation. Until then, take care, and this Saturday we will see what the wooly bear caterpillars have to say about the weather of the coming winter. Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= TheWorm_Has_Turned { ; time=0:07:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident float=y center-mag=-0.7389306041414476/+0.6651148962222097\ /3.193439e+013/1/132.5/0 params=1/1/0.5/2/0.333333\ 33333333/3/0.25/4/-0.999999999999999/0 maxiter=2000 logmap=448 periodicity=6 mathtolerance=0.05/1 colors=00000300600A00D00H00L10O40R70V92XB3ZB5`B5cB\ 5dB5fB5gB5gB5hB5jB5jB5gB5fB5eB5eB5dB5cB5bB5_B5YB5X\ B5VC5SD6QF7OG8LHAIKBGMDDOEBRF8TG6WJ3YL0_O0bQ2dS3cW\ 6bY8``A_bCZdDYeGYfGXeHWdHV`HUWHTRHSMHRIHQDHO7HM25K\ 05I03G02F02E00D00C00B00A00900800700600500400300200\ 10000000000000000000010010010020020020032042042042\ 0430430430000430F60O30M70LB0IF2HJ6FMADQDBTH9XL7`Q5\ cT3fX1j_0mc0pf0sj0wm0zr0zp0yn0yl0xk0wh0wfWjSImG4p3\ 0s03s0Ds8NsHXsQesYnseppgrmjtjlvfnxcpzaqx`lv`gv`ctZ\ YsZTqZPpZKoYDnY8mY3kY0hX0fW3cV6`V7YTAWSCTSDQRGNQIK\ PLHPMDOPBMR8MSDKTIITMFTRETWBVZ8Vc6Vf5VeBPdIKcODcT8\ bZ3`d0ej0kn0ql0vj0vg0qe0kc0fa2bZ5bX7bVAbSCbQFbOHbM\ I`OL_OOZOQYOSXOTWOWUPYTP_SP`RPcQPeOPgNPhOMjQLkRJlS\ ImSGmTEnUDoWApX8qX7qW8oUAmTBlTDjSEgRFfRFdQGbOI`NJZ\ NKXMLWLMTLMSS`nXXk_VgcSdfP`iMYmKVpIRsEOvBKz8Gz6DtV\ YkppfflbXhYOeSM_MLVGLPZdb } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END PARAMETER FILE=========================================