FOTD -- March 11, 2012 (5) Fractal visionaries and enthusiasts: Today's fractal is an outzoom of yesterday's image, which lies in the fractal debris on the northeast side of today's minibrot. Today's FOTD is a close-up of a minibrot halfway through the process of morphing from quadratic to cubic, and doing so without discontinuities. The iterated expression is not the expected Z^(2.5)+C, it is sqr(Z)*(recip(Z^(3)+30))+C. And since no fractional exponents are involved, no discontinuities will appear in the fractals it creates. I have never understood exactly how the JulibrotMulti or similar formulas work, but today's image shows a perfect minibrot of order 2.5 without the frustrating broken-up bits and pieces that spoil so many otherwise good fractals. The name "No Discontinuities" simply describes the minibrot. I could give the image a rating no higher than a 5, which indicates its mathematical worth. I put almost no effort into the coloring, so the artistic worth is near zero. The calculation time of 45 seconds is blessedly brief, but viewing the finished image on one of the FOTD web sites is more convenient. The finished image, already calculated for maximum convenience, is posted on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Lots of sunshine and much warmer temperatures arrived at Fractal Central today. The fractal cats heartily approved of the high temperature of 57F 14C and showed their approval by sharing the sunny shelf without quarreling. The humans, FL and I, had an everyday day, whatever that might be. The next FOTD will be posted in 24 hours. Until then, take care, and when someone survives a tornado that destroys his town and kills his friends, why does he claim to have been blessed? If that person were realistic, he would think rationally. Before he assumed his survival was a blessing, he would wonder whether he would welcome a similar blessing next year. Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= No_Discontinuities { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=JulibrotMulti function=recip center-mag=-0.872575097/+29.735974572/5146/1/100/0 params=3/30/0/0/0/0/0/0/0/0 float=y maxiter=1500 inside=0 periodicity=6 colors=000UZYWaXZcX`fXchWejWhmWjoWmqVotVrvVtxVruXp\ sYnqZlo_jm`hjafhbdfccddabe_`fYYgWWhUUiSSjQQkIJsPOl\ VTeaYZgbSngLvkCtlEslGrlIpmKomMnmNlnPknRjnThnVgoXfo\ Ydo_cpabpc`pe_pgZqhXqjWqlVrnTrpSrrKArKBsKCtKDtKEuK\ FuKGvKHwKIwKJxKKzKLxKMwKNuKOtKQrKRqLSoLTnLVlLWkLXj\ LYhL_gM`eMadMbbMdaMe_MfZOfaMgYKgVIhRGhOEiLCiHAjE8j\ A6k70j05k59lADmFHnKLoPPpUTqZXrc`shdtmhurlvvmwzmxzm\ yzmwzmuvmtrmrmpqhnocmnaklZjjXhiUggSefPddNbcLaaI__G\ ZZDXXBWW8UU6ZN1TT4OZ6Id9y4ADiBJaEPVHiBEUOJF`O0mT5l\ R9kQDjPHiOLhNPgMOeONcPMaRM_SLZUKXVKVXJTYIR_HQ`HObG\ McFKeFJfHKdILbKMaLN_NNZOOXQPWRQUTRTURRWSQXTOZUN_UL\ aVKbWIdXHeYFgYEhZCj_Bk`9mb7l`8l_8lZ8kY8kX8kW9kV9jU\ 9jT9jS9jR9iQAiPAiOAiNAhMAhLAhKBhJBgIBgHBgGBgFBhEEi\ DHjDJjCMkBOlBRlATm9Wn9Yn8`o8bp7ep6gq6jr5lr4os4qt3t\ t3vrCjpK_nSOm_DlXDkVEkTEFPFFRIETLDVNDXQCZTC`WBbZBd\ aAfcCJZFLZHOZKQZMSYPVYRXY } frm:JulibrotMulti {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p2*0.0055555555555556), b=pi*imag(p2*0.0055555555555556), g=pi*real(p3*0.0055555555555556), d=pi*imag(p3*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), aa=-(real(p1)-2), bb=imag(p1)-0.0000000000000000001, c=p+flip(q)+p4, z=r+flip(s)+p5: z=z*z*fn1(z^(aa)+bb)+c |z|< 100000000 } END PARAMETER FILE=========================================