FOTD -- November 14, 2009 (Rating 7) Fractal visionaries and enthusiasts: I'm writing this on Friday the 13th, a supposedly unlucky day. I think the bad reputation came about when, on this day six- or seven-hundred years ago, the king of France ordered the Templars to be eliminated. The day is probably no more unlucky than any other day. I also still hear rumors that the world will end in December 2012. I think both Nostradamus and the Mayans predicted it. Of course, Nostradamus's writings are so ambiguous that they can be made to have predicted anything desired, just as long as the event has already happened. And as for those Mayans -- I think they had a calendar that ran in repeating cycles of 5000 years or so, and not in the linear way we keep track of our time. One of the Mayan cycles is supposed to end in December 2012, and a new cycle is supposed to begin. I doubt that they expected the entire world to end. At any rate, all the end-of-the-world stuff on TV and in the movies will certainly help sell the sponsors' products. Today's image lies in the 'Seahorse Valley' of the parent fractal that comes about when the formula Z^(1.618034)+C is iterated 33 levels up the logarithmic ladder and the reciprocal function is applied. (I used this function by mistake, but the result is still worth the effort.) I named the image "Dancing in Darkness" because this phrase was the first thing that came to mind when I turned off my thoughts. The rating of a 7 was earned when I livened up the colors a bit in a separate graphics program. Unfortunately, with a calculation time of a full 18 minutes, the image is quite slow. But fortunately, the finished product is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I see that the 3-D fractals on the web are wowing the fractal- ists on this list. I checked the images, which are impressive indeed. They remind me of the ink-blot images created by the artist Max Ernst. The type=julibrot in Fractint also draws 3-D fractals, but this type is so slow that I rarely check it. I wonder what could be done with it -- most likely nothing close to those surreal 3-D images on the web. Friday here at Fractal Central featured variably cloudy skies and a temperature of 63F 17C, which made the fractal cats happy. The unexpected amount of work left me with mixed emotions. The next FOTD is due to be posted in 24 hours, but FL is getting an antiquing look in her eye, and if an unexpected expedition develops on Saturday, the FOTD for November 15 might be late. Until whenever, take care, and now that we've seen the 3-D Mandelbrot set, let's see the 4-D Julibrot. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= DancingIn_Darkness { ; time=0:18:06.10-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip inside=0 center-mag=-0.483202805468211/+0.5648328233695159/\ 3.24576e+011/1/-40/0 params=1.618034/0/33/0 float=y maxiter=32767 periodicity=10 mathtolerance=0.05/1 colors=000PPePPePSePSePUeNXgPSeSUbUUbXX__X___Xb_Ue\ bUgbSjeS0Fz0Fz0Iz0Kz0Nz0Nz0Pz0Sz0Sz0Uz0Xz0_z0_z0bz\ 0ez0ez0gz0jz0mz0mz0pz0rz0uz0pz0pz0pz2pz4pzApzCpzIp\ zKpzPpzSpzXpz_pwepugppmpmppjupgwpezpbzp_zzmzzhzwcz\ tNzrKzqIzpFzmAzmFzjIzgIzeKzbNu_NpUPgSPbPSUNUPKUIIX\ CF_4A_07b04b02e00g00g00j00m00g00e00_00X00U00P00N00\ K00F00C00A204702A00C00F00I00N00P00S00U00_00b00e00g\ 00m00m00j00g00e00b00_00X00U00S00P00N22K47I4CF7IC7K\ AAP7AU4C_4Fb2Fg0Im0Ip0Ku0Nz0Nz0Pz0Pz0Sz0Sz0Uz0Xz0X\ z0_z0_z0bz0ez0ez0ez0ez0gz0gz0gz0gz0jz0jz0jz0jz0mz0\ mz0mz0mz2pz4pz7pzArzCrzFrzIrzKuzNuzPuzSuzUwzXwz_wz\ bwzezzgzzjzzmzzpzzrzzuzzzzzmwzgpzbgrX_gSSXNKNICCC4\ 2400IFCKKAKNANS7PX4P_4Se2Uj0Um0Xr0_w0_z0bz0ez0ez0g\ z0jz0jz0mz0pz0mz0jz0jz0gz2gz7ezCeUKbOPb7U_0__0eX0j\ U0r_0e_0e_0e_0e_0eX0eX0eX0eX2eX2eX4eU4eU7eU7eUAeUC\ eUCeSFeSFeSIeSIeSKeSNePNe } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================