; Date: Fri, 25 Jul 2008 21:28:35 -0400 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 26-07-08 (The Forest Floor [8]) ; ; Id: <1.5.4.16.20080725212904.2bd7d97a@pop.mindspring.com> ; --------- ; ; FOTD -- July 26, 2008 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; Our asymptotic approach to unity continues today as we investi- ; gate the fractal that results when the formula Z^(1.025)+C is ; calculated 43 levels up the complex logarithmic hyperspiral with ; no function applied. Actually, I am not certain which, if any, ; function is the 'correct' one to use with the MandelbrotBC3 ; formula, or even if there actually is a correct way to deal with ; the infinity of 'correct' solutions to the multi-valued complex- ; logarithm. ; ; Today's parent fractal is an oversized parabolic-shaped thing ; with the focus of the parabola on the east-southeast side. This ; parent requires a bailout radius of 3600 to give it room to ; spread to its full extent. An area of chaos appears at its ; northwest extremity, with today's scene located in this chaos. ; ; There is a minibrot at the center of the image, but don't waste ; time trying to reach it. It lies far beyond the limit of resolu- ; tion. At the magnitude of the actual image, the picture reminds ; me of a scene in a forest, looking upward from the forest floor ; toward a mighty fir tree. I named the image "The Forest Floor". ; ; If I had more time, I might have made the fir tree likeness more ; convincing. As it is, even with its flaws, the image rates an ; 8, which is pretty good as fractals go. ; ; The calculation time of just under 6 minutes can be eliminated ; by viewing the already-calculated image on the FOTD web site at: ; ; ; ; Tomorrow's FOTD will be posted in 24 hours. Just for the fun of ; it, I'll reduce the exponent to 1.00625 to see if I can find ; anything. But with an expression whose graph is virtually a ; straight line, I can guarantee no success. Regardless, until ; then, take care, and stay on the straight and narrow fractal ; path. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= The_Forest_Floor { ; time=0:05:55.52-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=-26.71933195088172/+9.587738968748848/\ 2.907681e+010/1.0234/-22.5/0 params=1.025/0/43/3500 maxiter=2800 inside=255 logmap=455 periodicity=10 colors=000KbzKczKdzKezKfzKgzKhzKizKjzKkzKlzKmzKnzK\ ozKpzKqzKrzKszKszKrzKqzKpzKozKnzKmzKlzKkzKjzKizKhz\ KgzKkzKizKgzKezKczKazKazKYzHgzCUz2_z8QzEOzKOzPRpPQ\ nOPzNUzMOzLWzKNzJMzILzHLzGKzFVzEJzDIzCHzCCzFHzHMzK\ MzMRzOWzR`zTez_jzgozntzwyzzxzzwzzxzzyzvzzrzzmzzhzz\ czzZzzUzzPzzJzzHzzGzzEzzCzzBzz9zz8zzAvzBrzCmzDhzEc\ zDZzCUzRUTRUTRUSQUSQUSQURQURPURPUQPUQPUQOUPOUPOUPN\ UONUONUOzcOzcNzcNzcNzcMzcMzzMzzLzzLzzLzzKKKKJKKJKK\ JKJJKJIKJIKIIKIHKIHKHHKHHKHGKGGKGGKGFKFGKGGKGGKGHK\ HHKHHKHIKIIKIIKIJKJJKJJKJKKKKKKKKKLKLLXLLYLMYMMZMM\ _MNaNM`MM`MM_MM_MLZLLZLLYLLYLLYLKXKKXKKWKKWKJVKJVJ\ JVJJUJJUJITJITIISIISIHRIHRIHRHHQHHQHGPHGPHGOGGOGGO\ GFNGFNFFMFFMFELFELFEKEEKEEKEDJEDJEDIDDIDCHDCHDCHDC\ GCCGCBFCBFCBECBEBADBADBADBACBACA9BA9BA9AA9A99A9899\ 89988988877877876876876765765764764753653653652652\ 6415415405405405516516527 } 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|