FOTD -- March 23, 2007 (Rating 6) Fractal visionaries and enthusiasts: The formula behind today's image mixes 3 parts of Z^(-1.5) with 0.6 part of Z^(-7.5), then adds (1/C). Using (1/C) rather than plain C turns the already inside-out parent fractal inside-out again, which gives a fractal with the inside where it should be -- on the inside. Curiously, the 'evaporated' version of today's image is virtually the same as the image itself when the 'bof61' inside fill is used. The parent fractal somewhat resembles a snowman with his head facing east and his fat bottom on the west end. A little stretch of the imagination will also reveal two Mickey-Mouse ears sprouting from the snowman's head. The scene of today's image is located in a spiral in a disconnec- ted bit of fractal debris in the interior of the southern branch of the valley that defines the snowman's neck. (Of course, all proper snowmen have necks.) Though I did not give today's image a name, I did give it a rating of a 6. The calculation time of 24 minutes is slower than FOTD average, but not outrageously so. And the calculation may be totally avoided by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is posted ready for viewing. I was recently asked how I find good parameters for the formula that I use so often -- the MandelbrotMix4. A number of years ago I described how I find good parameters for this formula, but I have advanced since then. As soon as the current busy period here at Fractal Central slows down, I'll describe my method of finding parameters and include it in a FOTD discussion. But I will admit now that some degree of luck is involved. Tuesday was sunny but chilly (43F 5C), Wednesday was partly cloudy and chilly (45F 6C), Thursday was mostly sunny and mild here at Fractal Central, with a midday temperature of 66F 19C. Clouds arrived in the afternoon however, and light rain set in during the evening. During this time, I was too busy at the computer to be concerned with the outside conditions. (I did check the waether records however.) The fractal cats were equally unconcerned. They never seem to concern themselves with the outside weather as long as it is warm inside. The present big rush is down to manageable proportions, so there should be no immediate interruptions in the steady flow of FOTD images. The next FOTD will be posted in 24 hours. Until then, take care, and I often wonder about the meaning of fractals. Their existence was barely suspected before Julia first realized that something surprising happens when certain complex numbers are reiterated. But maybe the very concept of ultimate meaning is only another human invention. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= FOTD_for_Mar_23_07 { ; time=0:24:12.55--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip inside=0 center-mag=+1.53544097882177/-0.39073195036567/\ 3.29e+008/1/138.5/1.32634158e-006 params=3/-1.5/\ 0.6/-7.5/0/0 float=y maxiter=4500 periodicity=10 colors=000aIYiIYqHYyHYzIZzIZzJ_zJ_zKazKazMbzMbzMbz\ NczNczOezOezQfzQfzQfmYf_efMZYOkfRwnUzvOrkKbbFMSB6J\ HISKU_QegUooQ_bNKQMNRKORJRRJSRIURHXRHYSF_SEaSEbSDe\ SBfSDfOBgSAgV8gY7i_6ic4if3ji2jk0jo0kr0ku0iz0kw0mq2\ nk6oe8q_BrUFsOIuIKvD_q8nm4zg0zi2vi7oiDiiIbjOXjUQjZ\ IuzKjcKb8MaBMaDNaENaFOaIOaJOaKQaMQaNRaQRaRSaSSaUYe\ USaVOZVJVVFSVBOV6MV2IV08S0FV4KYDQ_08HJVaXiseovmuwu\ zyzzzzzzzzvzzqzzmzvgzrbzoZzkUziQyeKwaFvZBuV6wU0sS2\ qS6nSAjSFgSJeRNaRSZRXXR_MBgURcae_gfYgfUfXRfSNeHKeI\ HaI7bIBbF7aD4a70a20a00Y20X43Y76YBAYEEYHHVJKRNOOVcM\ VXJZaHceEfjBjo6oy8msAjnBfiEckF_YHYSIUNK`mMMFNJAQH6\ RE2SB0S70U80VA0VB0XB2YD6YE8ZFBZFE_HIaIKaJNbJQcKUcM\ XeNZuQceNaQKZAIXOsi0HU0KS6NSBRRFURKYRQ_QVcQZfQcjOi\ mOnrQmoOkmNjkMiiKigJgeIfcIeaHcZFcYEbVDaUB_RAf0I_QA\ Qz0Uv3XnA_fHacHbZMbUQbOUkKrbJYaRvYQsUQrQOoMOmIOjEN\ iANf6Mc2Ma0M_6KZEKZMJZUJZ } frm:MandelbrotMix4 {; 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, 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=========================================