; Date: Thu, 26 May 2011 22:13:52 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 27-05-11 (An Incredible Hole [8]) ; Id: <1.5.4.16.20110526221353.1177f5d0@pop.earthlink.net> ; --------- ; ; FOTD -- May 27, 2011 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; Today's image shows one of the many holes that lie near the base ; of the hook in the image of May 23, when the exponent of the ; image is lowered from 1.08 to 1.078 and the minibrot tracked ; down. ; ; I named today's image "An Incredible Hole" because in some ways ; the attributes of the central hole are as unbelievable as some ; of the kooky claims now circulating among the credulous. (But ; remember that a claim is not necessarily false simply because ; rationalists disbelieve it.) ; ; To emphasize the hole's unusual qualities, I brought it to ; active life by rendering the scene with the inside set to ; 'bof61'. (When the hole appears as a flat black area, some of ; its impact is lost.) The bluish-pink coloring of the hole is ; unintentional. It came about by lucky accident. ; ; The hole is a true hole, and not simply an artifact of too low ; a maxiter. I tested the scene with a maxiter of 1,000,000 and ; found the hole unchanged. ; ; The amazing thing about this hole became obvious when I decided ; to count the number of large lobes around its edge. After ; several failed attempts to get an exact count, I realized that I ; would never get the count correct, for the large and small lobes ; with all their sub- and sub-sub-lobes, are of one and the same ; series. The total number of lobes is therefore infinite. ; ; The inside of the hole in today's image is actually an extension ; of the minibrot in the original 'minibrot for the ages' image. ; The original minibrot extends invisibly under the surface debris ; of the original image, well beyond the hook. ; ; The rating of an 8 seems justified. If I had put a bit more ; effort into the coloring, I might have rated it an 8-1/2. ; ; The finished image is available on the internet at: ; ; ; ; and in high definition at: ; ; ; ; The original web site may be accessed at: ; ; ; ; Thursday turned into a midsummer-like day here at Fractal ; Central, with enough heat, haze and humidity to satisfy the most ; ardent hot weather lover. The high temperature of 90F 32C ; totally satisfied the fractal cats, who stretched to their full ; cat lengths to show their pleasure. As of post time, a warning ; on the TV Weather Channel (I call it the Commercial Channel) of ; possible tornadoes in the area had proved to be a scare rather ; than a forecast. ; ; The humans had a relatively slow day, which was good in some ; ways, but not so good in others. If nothing goes wrong, which ; is usually the case, the next FOTD will be posted in 24 hours. ; Until then, take care, and yesterday's kookiness sometimes ; proves to be today's scientific fact, but before the question is ; settled scientifically, how does one tell the true kookiness ; from the kooky kookiness? ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= An_Incredible_Hole { ; time=0:08:12.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-0.000750885846/+1.174041344618/144809\ /1/-47.5/0 params=1.078/0/16/525 float=y maxiter=4000 inside=bof61 logmap=-250 periodicity=6 colors=000zf0ze0ze0zc0yb0yb0wa0va0v_0tZ0tZ0sX0qX0q\ W0pW0pU0oT0mT0mR0lR0zhvjQ0iO0zaohN0hM0zUhfK0eI0vNU\ cH0oFNoF0h7F_E0a07ZC0Z07aB0W00W00U70U00T60R00R40Q2\ 0Q00O00N00N00L00J00H00G00F00F00C00A007009005005002\ 00300800A00H00H20N40N60O70Q90QB0RC0TC0TE0UF0UH0WI0\ XK0XM0ZN0_O0_Q0aR0aT0eU0hW0mX0rX0vZ0z_0za0zb0zd0zg\ 0zi0zl0zm0zm0zm0zm0zm0zm0zm0zl0zk0zj0zi0wh0wh0yh0y\ h0zh0zh0zh0zh0zh0zh0zh0zh0zh0zh2zh2yh4wh4ehZehZfh_\ fh_hh_hhaihaihaihajhbjhbjhblhblhblhcmhczUczUczUczU\ czUezUezUezUezUezUfzUfzUfzUfzUfzUfzUhzehzchzbhzahz\ _izZizXizWizUizTizRjzQjzOjzNjzMjzKlzIlzHlzFlzElzCl\ zBmz9mz7mz6mz4mz2oz0oz0oz0oz0zz0zzKzzKzzKzzKzzKzzK\ zzKzzKzzKzzKzzKzzKzzKzzKzzKzzKztKzvKzvKzvKzwKzwKzw\ KzyKzyKzzKzzKzzKzzKzzKzzKzzKzzUzzUzzUzzUzzUzzUzzUz\ zUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzUzzUzzUzzUzzUzzUzzUz } 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|