; Date: Mon, 25 Nov 2013 18:01:02 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 25-11-13 (Toothache [A-7,M-8]) ; Id: <1.5.4.16.20131125180051.2a2f1674@earthlink.net> ; --------- ; ; FOTD -- November 25, 2013 (Rating A-7,M-8) ; ; Fractal visionaries and enthusiasts: ; ; Today's image is the parent fractal that results when the ; expression Z^(1.09+C is iterated at ground level of the ; hyperladder with no function applied. I rarely use parent ; fractals as FOTD's, but today's parent struck me as having ; enough bite to earn the honor of being declared FOTD for ; 25-11-13. The reason for the name "Toothache" is now obvious. ; ; As the exponent of Z is decreased toward unity, the resulting ; parent fractals tend ever closer to a circle. But this tendency ; can be avoided for a while by calculating the fractal as it ; appears on one of the remote levels of the hyperladder. In ; today's image however, we need no remote level. The fractal is ; interesting enough right at the ground level, where we find a ; Mandeloid that resembles nothing as much as a newly extracted ; tooth. ; ; Despite surface appearances, the image is filled with well ; hidden and quite hard to find smaller minibrots. I will present ; a few of these in future FOTD's, though do not expect any ; paradoxical images to magically appear. ; ; The art rating of the image is a reasonably respectable 7. The ; math rating is a very respectable 8, mostly due to the ; unexpected richness of the outer filaments of the fractal. ; ; The calculation will cause no problems. The image will finish ; in less than one minute on most units, at least those that do ; not panic at the sight of a DOS prompt. Panicky units can be ; spared the panic by checking the finished image on the FOTD web ; sites. ; ; The finished image is online at: ; ; ; ; with grand themes and symphonic variations at: ; ; ; ; ; ; ; ; After a morning low of 16F -9C the temperature rose to a not ; very warm afternoon peak of 34F +1C. Helped by hazy sun, it ; felt almost comfortable after the biting winds of yesterday. ; The fractal cats agreed, as did the fractal humans. ; ; The next FOTD will be posted when both it and I are ready. ; Until that marvelous moment arrives, take care, and how could ; one communicate the directions of left and right to an alien ; imprisoned in a ship in outer space, with no knowledge of the ; outside universe? ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= Toothache { ; time=0:00:55.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=-3.94562/-2.28956/0.2032885/1/-45/0 params=1.09/0/0/525 float=y maxiter=13000 inside=0 logmap=7 periodicity=6 colors=00000E00I00M00Q10U20Y30`40g50i60m70q80q90sA\ 0rC0qE0oG1nI2mK3kL4jM5iN6gO7fP8eQ9cRAbS9aTBZUCWVEU\ WFRaHPmIMzJKzLHrMEzOCrP9zR7rS4zT2rW4mY6m`8mbAmeCmg\ EzzGzzIzzKzzMzzOzzQzzOzzNzzMzzLzzJzzIzzHzzGzzEzzDz\ jCziBzh9zg8zf7ze6zjKznYzrkzvyzJXzKZzL_zLazMbzNdmUe\ mOgmUhmUjmQkmUmmUnmUomUpmUpmUpmUqmUqmUqmUqmUmccicc\ fccbcc_ccWccTccPccMccIccFccBcc8cc4cc1cc4cc6Im8ImAI\ mCImFImHImJImLImNImQImSImUImWImYIm_ZmXomUmzWlzXjzY\ izZgz`fzaezbczcbze`zf_zgZzhXzgVzgTzgRzgPzzNzzLzzJz\ zHzzFzzDzzBzzZzzZzzZzzZzzZzzZzzZzzZzzczzczzczzczzc\ zzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczz\ czzczzczzczzczzczzczzczzczzczzczzmzzmzzmzzmzzmzzmz\ zmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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|