; Date: Thu, 05 Dec 2013 15:36:50 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 05-12-13 (On the Superspike [A-7,M-7]) ; Id: <1.5.4.16.20131205153647.2dafee82@earthlink.net> ; --------- ; ; FOTD -- December 05, 2013 (Rating A-7,M-7) ; ; Fractal visionaries and enthusiasts: ; ; Today's image shows a minibrot lying way out near the tip of the ; main spike of its parent fractal. But this parent is not the ; Mandelbrot set. It is a Z^(1.333)+C fractal with a spike that ; puts the spike of the M-set to shame. ; ; To begin, the spike is far longer than the M-set's spike, and it ; also points northwest instead of straight west, with far more ; fractal detail along its path. With all these superior ; features, I could consider the spike nothing less than super, ; which was reason enough to name the image for its location -- ; "On the Superspike". ; ; The parent fractal came about when I calculated the expression ; Z^(1.333)+C at a height of only one level up the hyperladder (or ; hyperspiral) with the cosine function applied. I think this is ; the first time I have applied the cosine function to the ; MandelbrotBC3 formula, and at today's hyperlevel it produces a ; rather scrambled parent with little but its one superspike. ; ; The image came about as a result of an effort to duplicate ; the rating of yesterday's image, but the final result was less ; impressive, rating only a 7 for both art and math worth. ; ; The image is a super fast one, finishing in 20 seconds or less ; on a SOTA (State Of The Art) machine. Even on older units it ; will finish very fast. ; ; Viewing the finished image is always more convenient than ; calculating it however, so enjoy the convenience of direct ; viewing by checking the FOTD web sites at: ; ; ; ; ; ; ; ; ; ; Heavy clouds spoiled the first half of the day here at Fractal ; Central today, while rain spoiled the second half. The ; temperature of 57F 14C was quite reasonable for the season ; however. ; ; The next FOTD will soon appear. Until the apparition happens, ; take care, and when a totally crazy man wins the mega-lottery ; and becomes unimaginably wealthy, should he then be considered ; merely eccentric? ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= On_the_Superspike { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=cos center-mag=-4.185306304415169/+6.636739950187376/\ 7253877/1/58.75/0 params=1.333/0/1/0 float=y maxiter=2500 inside=0 logmap=41 periodicity=6 colors=00000400500700810920A30A10B30C50D81AB27918C\ 24E35G45I55K65K65N66O86T86W96YA6_B7aB7cC7eD7gD7iC8\ kC9mBAjBBeAC`ACW9DR9EM8FH8GC8G79J4AM5BP7CU8DZ9EcBG\ hCImDKrFMvGOzHOwGMuFKsEJqDHmCGmBEmAClAAk98j86i75i6\ 4g53f42e31d30cB0XI0SQ7aX7Yd6Tk5Os4Jz4Fy8JyCMyFPxJS\ xMVxQYxT`wXdw`gwcjvgmvjpvnsvqvqpsmppipmepk`phXpeTz\ bPz`cz_czZczYczzczzczzczzczzczzctzmtzmtzmpzmmNmjKm\ gImcFm`DrYArV8rS6rW6rZ6ma6me6mh6mk6mo6mr6Ou6Os7Oq8\ Op9OnAOlAOkBOiCOgDOfEOdEObFOaGO_HOYIOXIRUKTSLVQMXO\ OZMP`KQcHSeFTgDUdBWa9XZ7YW5ZZ7_b9_fB_jC_iE_hG_fI`e\ J`dL`cN`bP`aQ`ZQgYTdXVbXX`WZYV`WVbUzdRzfPzhNzjKzlI\ znGzpEziUzcizYyz_vzatzcrzepzgnzikzzizzgzzezzczzfzz\ izzlzznzzqzztzzwzzyzzyzzyzzyzzyzzyzzezzMzz2zz5zz7z\ zAzzCzzFzzHzzJzzMzzOzzRzzTzzVzzYzz`zzczzfzzizzlzzo\ zzrzzuzzxzzvzzuzztzzrzzqzzpzznzzmzzlzzjzzizzhzzfzz\ ezzdzzizzmzzrzzvzzzzzpzzf } 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|