FOTD -- April 01, 2013 (No Rating) Fractal visionaries and enthusiasts: Today's image is a new view of a minibrot hole on the main stem of the Mandelbrot set. The minibrot looks so unusual because it is sliced in the Rectangular orientation, which lies at a right angle to the Mandelbrot orientation and is determined by the imag(z) and imag(c) axes. The brilliant green bars slicing diagonally through the open area are actually Mandelbrot valleys viewed at a right angle. The bars are straight edged because regardless of where points in the M-set are initialized, they will eventually settle into the same orbits unless they escape first. There is no way I could give a rating to such an overworked theme, but being fascinated by things beyond visualization, I continue returning to the four-dimensional Julibrot for ever new surprises. The name "A Rectangular Set" is a bit misleading. The image is merely a small part of one of an infinity of Rectangular sets. The calculation completes in 25 seconds, fast enough to waste no one's time. The web sites are more convenient but probably no faster. When the official FOTD web site is back in operation, it will be found at: <http://www.crosscanpuzzles.com/Archives.html> Until then, the finished images may be seen in hi-def at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> The day began pleasant enough here at Fractal Central today, with breaking clouds and a temperature of 50F 10C, but by midday the clouds and rain had returned, and the temperature had dropped to 45F +7C. The fractal cat observed all this with dis-interest, while the humans made it through another day with no unexpected disasters happening. The next FOTD will be posted soon. Until we find out how long 'soon' is, take care, and when disasters happen, look to the bright side. But before you look, be sure a bright side actually exists. Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= A_Rectangular_Set { ; time=0:00:25.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/10166.07\ /1.3984/29.6185420924715608/28.9858769262522351 params=90/90/0/90/-1.690128/0/-1.690128/0/2/0 float=y maxiter=3200 inside=0 logmap=28 periodicity=6 colors=000BamCalD`kE_jFZiGYgHXeIWcJVaIU_ISYHQVHOSG\ MQGKNFIKFGIDDGBADA89846713940B72E94HC6KF8OHARKCUME\ YPG_SGbUFdXEf_DiaCkdBmfAlgClhDkiEkjFjkHjlIilJimKhn\ LhoNgpOgqPfrQfrRhoUjmXlk_nibpgerehtckvanx_qqXlkUgd\ RbZOYSLTMIONJJOLPWSUpfGoaHnYHmTHlPHkLHgNIcOI_PIWRJ\ SSJPTJSPGVMEYIC`FAaJDaNGbRJbVMcYOcaRdeUdiXem_epadm\ bdjbdgbLTRLUQKVQKWQJXPJYPIYPIZPH_OH`OGaOGbNGcNFcNF\ dMEeMEfMDgMDhLCiLCiLBjKBkKBlKAmJAnJ9oJ9oJ8pI8qI7rI\ 7sH6tH6uH6uH7tI7sI8sJ8rJ9rK9qK9qLApLApMBoMBnNBnNCm\ OCmODlPDlPDkQEkQEjRFjRFiSFhSGhTGgTHgUHfUHfVIeVIeWJ\ dWJdXJcXKbYKbYLaZLaZM`_M`_M_`N_`iSVgTVeTVdTVbUV`UV\ _VVYVVWVVVWUTWURWUQXUOXUMYULYUJYUHZUGZUE_UC_UB_U9`\ U7`U6`U7aT8bT9bT9cTAcSBdSCdSCeSDfSEfRFgRFgRGhRHhQI\ iQIjQJjQKkQLkPLlPMlPNmPNmPOnOPoOQoOQpORpNSqNTqNTrN\ UsNVsMWtMWtMXuMYuLZvLZwL_wL`xLaxKayKbyKczKczKbxLaw\ L`vM`uM_tNZsNYrNYqOXpOWoP } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================