; Date: Thu, 23 Aug 2012 10:55:34 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 22-08-12 (Squarely Rooted [6.5]) ; Id: <1.5.4.16.20120823105907.30dfb71c@earthlink.net> ; --------- ; ; FOTD -- August 22, 2012 (Rating 6.5) ; ; Fractal visionaries and enthusiasts: ; ; We have had our share of PI. It's time to move on to the square ; root of 2. Today's image shows a sample of what can happen when ; the formula Z^(sqrt(2))+C is iterated sqrt(2) levels up the ; hyperladder when no function is applied. ; ; The first thing that happens is the parent fractal, which is a ; shapeless mass of large bays with a very long zig-zagging ; filament (main spike) extending north. Today's scene lies near ; the point where this filament connects to one of the smaller ; bays. ; ; The minibrot that lies at the center of today's image is even ; more shapeless than its parent, and to make things worse, it ; lies in a rather difficult area of the parent, where the very ; high maxiter makes the calculation go slow. Luckily, the web ; sites can speed up the viewing considerably. ; ; Considering all this, I rated the image at a 6-1/2, one-half ; point of which is a reward for the not-quite-successful coloring ; effort. ; ; The name "Squarely Rooted" explains itself. ; ; Get in there with the big-time thinkers by viewing the finished ; image on the official FOTD web site at: ; ; ; ; Become another Einstein by viewing the hi-def version at: ; ; ; ; Solve the ultimate mysteries of the universe and become a super ; hero by checking the FOTD back images and discussions at: ; ; ; ; Lots of sun and a temperature of 84F 29C made today's conditions ; near ideal here at Fractal Central. A few minor showers popped ; up in the afternoon around the area, but they stayed away from ; FC. The fractal cats were unusually restless most of the day, ; leading me to suspect that an unwanted cat was prowling nearby. ; ; The day of the humans was nothing at all like the day of the ; cats (or the night of the living dead). It consisted mostly of ; totally routine stuff made only a little more interesting by ; unwarranted references to flesh-eating zombies. The next FOTD ; will be posted when I consider it ready. Until that uncertain ; time arrives, take care, and fight for truth in advertising. ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= Squarely_Rooted { ; time=0:08:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.4396111301623483/+1.590005669004912/\ 21703/1/17.5/0 params=1.4142135624/0/1.4142135624/0 float=y maxiter=35000 inside=0 logmap=-753 symmetry=none periodicity=6 mathtolerance=0.05/1 colors=000KCTKDWKEYKF`KGcKHeMIgNJhPJiQKjRLkTLlUMnW\ MoXNpYOq_Or`Ps_PrZNpWLlTJhQHdNGaKEYHCUEAQB8M97JBAL\ CCMDENEGOFIPGLQINRKPSMRTOTUQWWSYXU_YWaZYc_`f`chafj\ bilcmndmlcqkbtiavh`wf_xeZycYzbYz`Xz_WzZVzXUzWTzUSz\ TSzRRzQQzOPzNOzLNzKMzJMzLLzNLzPKzRKzTKzUJzWJzYJz_I\ zaIzcIzdHzfHzhHzjGzlGznGzoFzqFzsFzuEzwEzxEziMzWUzZ\ WzaYzd_mgamjcmjcmjcmiccicciccicciccicTicSicSimRimR\ imQimPimPimOimOimNimNimOjmPjmQjmQkmRkmSkmSlzTlzUlz\ VmzVmzWmzXnzXnzYnzZozZoz_oz`pzapzapzbqzcqzcqzdrzer\ zfrzfszgszhszhtzitzjtzjuzkuzluzmvzmvznvzowzowzpwzq\ xzrxzrxzsyztyztyzuzzvzzvzzuyzuxzuwzuvzuvzuuzutztsz\ trztrztqztpztoztnztnzsmzslzskzsjzszzszzszzszzrzzrz\ zrzzrzzrzzrzzrzzrzzqzzqzzqzzqzzqzzqzzqzzqzzpzzpzzp\ zzpzzpzzpzzpzzpzzozzozzozzozzozzozzozzozzpzzpzzqzz\ qzzrzzrzzszzszzszztzztzzuzzuzzvzzvzzvzzuzzuzztzztz\ zszzszzrzzrzzrzzqzzqzzpzz } 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|