; Date: Tue, 21 Feb 2012 18:00:06 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 20-02-12 (Scattered Trunks [8]) ; Id: <1.5.4.16.20120221180200.2ba7df3e@earthlink.net> ; --------- ; ; FOTD -- February 21, 2001 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; The valley on the east side of the Z^2 Mandelbrot set is ; sometimes called Elephant Valley. The radicals found there ; rather convincingly resemble elephants. Every bud has one ; elephant standing over it, trunk raised and curled in defiance. ; The Z^3 Mandeloid has two elephants guarding every 2-lobed bud ; in its Elephant Valley; the Z^4 Mandeloid has three elephants ; guarding every 3-lobed bud, etc. The series continues, with the ; elephants growing ever more numerous and smaller, always ; numbering one less than the exponent of Z. But what happens ; when the exponent of Z is reduced? ; ; The same series continues. Today's image shows the elephants, ; or what is left of them, in the Elephant Valley of the Z^(1.5) ; Mandeloid. We have half an elephant guarding every half-bud. ; And it happens to be the front half of the elephants that ; remains. The image shows disembodied elephant trunks scattered ; everywhere, but not a single whole elephant. With little ; thought, I named the image "Scattered Trunks". ; ; The parent Mandeloid is a rather shapeless thing that came about ; when I returned to the 'MandelbrotBC2' formula and checked East ; Valley of the fractal that results when the expression Z^(1.5)+C ; is calculated 1.5 levels up the logarithmic ladder. ; ; Today's scene lies on the south side of the valley, where the ; front halves of the elephants remain. (On the north side of the ; valley their rear halves remain, but elephant rumps are far less ; impressive than elephant trunks, so I chose to check the trunks.) ; ; I rated the image at an 8, mostly for its mathematical interest. ; The coloring is a bit flat, though it is smoother than usual and ; its flatness does give an atmospheric effect. ; ; The calculation time of 2-3/4 minutes is rather slow by FOTD ; standards. This is where the FOTD web sites stampede to the ; rescue. ; ; The trunks are on display at: ; ; ; ; where they may be seen without the task of calculation. ; ; High-definition trunks may be seen at: ; ; ; ; Over 4-thousand FOTD images may be seen at: ; ; ; ; Cloudy skies and a temperature of 42F +6C made today an un- ; notable one here at Fractal Central. The fractal cats disliked ; the lack of sun, and settled by the house heat early in the ; afternoon. ; ; FL and I had a day as uneventful as the weather. Yes, I know it ; makes boring reading, but I have to tell it like it is. The ; next FOTD will be posted in 24 hours. Until then, take care, ; and one thing absolutely certain is that the end of the world is ; coming, just like those 'scare' shows say. The only question is ; when. ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= Scattered_Trunks { ; time=0:02:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=+0.17056338/\ -0.00784447/757/1/33.1/0 params=1.5/0/1.5/0 float=y maxiter=15000 inside=0 logmap=30 periodicity=6 colors=00010c20d31e42f54g66h79i8Cg9FfBIeCLdEOcFRbH\ UaIW`JY_K_ZLaYMcXPeWPgVOiULkTGmNBoIApJCqLFrQLsWSta\ Ytgcsmiqskprlnqmlpnkpokopknqknrkmskltllulkvnjwpjxq\ iyrhzrhpvQmsTkpWinZfkadidbig_ijYimWioXilXiiXifYidY\ iaYiZZjXZlUZnRZoP`jUbfZdbbfZghVljRphSlfShdSdbS``TY\ ZTUXTQVTMUTJTSKSSKSRLRRLQQMQQMPQNOPNOPONOOMOPMNPLN\ QLNQKORKPSKQSKRTKRTKSUKTVKUVKUWKUWJUVJUVJUVJUVJUVJ\ UVJUVJUVJUVJUVJUVJUVJUVJUVIUXHUYGU_FU`EUbDUcCUdBUf\ AUg9Ui8Uj7Ul4Uq6Um5Uo4Up`XE_WFZVGYVHXUIWTJWTKVSLUS\ MTRNSQORQPRPQQORPOSONTNNUMMVMLWLLXKKYUJZUJ_UI`UIaU\ HbUGcUGdUFeUEfUEgUDhUDiUCjUBkUBlUAmU9nU9oU8pU7lU6m\ U5mU5mU4mU5mU5mU5mU5mU5mU5mU5mU5mc5mc6mc6mc6mc6mc6\ mc6mc6mc6mc6mc7mc7mc7mc7mc7mc7mm7zm7zm7zm8zm8zm8zm\ 8zm8zm8zm8zm9zmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAz\ mAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmAzmA\ zmAzmAzmAzmAzmAzmAzmAzmAz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(p/(2*PI)), r=real(p2)-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|