FOTD -- March 22, 2005 (Rating 6) Fractal visionaries and enthusiasts: With today's image we leave the Rectangular orientation of the Julibrot and turn to the orientation I call the Elliptical, which is determined by the real(c) and imag(z) axes. I gave it this name because when the Julibrot is sliced through its origin in this direction, the resulting figure resembles an ellipse that has been squashed on one end and stretched on the other. The Elliptical orientation is completely perpendicular to the Oblate orientation and simply perpendicular to the remaining four orientations. The scenes found in it are as varied as those found in all other aspects of the Julibrot. I was about to name today's image "Forever Amber", but then I remembered a naughty novel with that name, and decided to protect the children. I named the image "Forever Waffling", which can be taken as a swipe at certain politicians who can't make up their minds, or as a plug for a particular type of breakfast food. The waffling scene is located in the part of the Julibrot connected with East Valley of the Mandelbrot set. A large degree of stretching and skewing was needed to bring it to a recognizable form. Most of the effect of solidity was achieved by rendering the image with the outside set to 'fmod' and the proximity set to 0.115, which produces the effect of overlapping bubbles. The brilliant sky-blue background is a result of a low proximity factor. It is not a true area of trapped points. If the proxim- ity, which appears at the bottom of the X screen, is increased, the amber elements will thicken and the blue background will fill in. If the value of the proximity continues to be raised, the image will quickly turn into a screen filled with a single flat color. In certain fractals, such as today's, the proximity is an important parameter. The image appears unusually brilliant, and I am not sure of the reason. Maybe this effect is peculiar to my particular monitor, which has at least 8 years of age on it but appears to be operating as good as it did on the day I unpacked it. Or maybe it is due to the coloring, on which I actually spent less than the normal amount of time. Regardless, the final result is an image that earns a slightly above average rating of 6. The render time of just under 8 minutes borders on unreasonable slowness. But relief for impatience is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a high temperature of 50F 10C and limited sun, Monday proved barely acceptable to the fractal cats at Fractal Central. They spent about 90 minutes in the yard, but were a bit upset about the marginal conditions. They cheered up when the tuna appeared however. Today is starting sunny, but it is quite chilly, and clouds are due to move in by afternoon. The cats had best take their outdoor time early. I have only a small amount of work to finish before I enter Fractal Land. The next glorious image will appear in 24 hours. Until then, take care, and is it possible for a universe to exist in which there is no potential Mandelbrot set? Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Forever_Waffling { ; time=0:07:58.51--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=-0.78417915215484530/+0.250205105304999\ 00/7771140/1.89e-005/0.00515606886434218266/89.920\ 4269909497214 params=0/90/2/0/0.5/0/0/0 float=y maxiter=12000 proximity=0.115 outside=fmod logmap=yes periodicity=10 colors=000htzT_UV_UW`UY`UZ`V`aVaaVcbWdbWfcWgcWicXj\ dXldXmeXoeYpfYrfYreXsfYtgZthZui_uj`vj`vkawlbwmbxnc\ xncyodzpezqezrfzsgzsgzthzuizvizwjzwjzuhzsfzqezoczm\ azk`ziZzgYzeWzcUzaTz_RzYPzWOzUMzSLyQJyOHyMGyKEyJDv\ LEtMErOFpPFnRFlSGjUGhVHfXHbXGcYHdYHdYIeYIeYJfZJfZK\ gZKhZKhZLi_Li_Mj_Mj_Nk_Nl`Nl`Om`Om`Pn`PnaQoaQpaQpa\ RqaRqbSrbSrbTsbTpiZreWsbTtZQuWNvTKwPHxMEyIBzF8zC6z\ D6zE6zF6zG6zH6zI6zI7zJ7zK7zL7zM7zN7zN7zO7zP7zQ7zR7\ zS7zT7zT8zU8zV8zW8zX8zY8zZ8zZ8z_8z`8za8za8zd8x`8rW\ 8mR8gM8cH7XA9UJ8XL7_O6cQ5fT4iV3lX2mY3mZ4m_5m`6m`7n\ a7nb8nc9ncAndBneCofCofDogEohFoiGoiHpjHpkIplJplKpmL\ pnMqoMqoNqpOqqPqrQstRqrQpqPooOnnOmlNlkMkiLjhLifKhe\ JgcIebId`Hc_GbYFaXF`VE_UDZSCYRCXPBWOAXK7WM9VNAVOBU\ PCTQDTRFSSGSTHRUIQVJQWKPYMOZNO_ON`PNaQMbRLcTLdUKeV\ KfWJgXIiZIj_Hk`GlaGmbFncFoeEpfDqgDrhCsiBuiCtjDVREV\ RGWRHWSJXSKXSMYSNYTPYTQZT } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================