; Date: Fri, 15 Apr 2011 22:07:21 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 16-04-11 (Blithe Eidolon [5]) ; Id: <1.5.4.16.20110415220725.14f714fa@pop.earthlink.net> ; --------- ; ; FOTD -- April 16, 2011 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; In today's image we venture into the parent fractal that comes ; about when the formula Z^(1.15)+C is calculated at a level 11.5 ; turns down the complex logarithmic hyperspiral when no function ; is applied. ; ; The name "Blithe Eidolon", is a fancy way of saying 'happy ; ghost'. It refers to the parent fractal, which resembles a ; chubby but happy ghost flitting merrily off to the east- ; northeast, its short plump arms protruding through its sheet. ; Today's image is located in a stream of chaotic debris extending ; from the ghost's upper arm. ; ; Actually, it's a bit incredible that such fractals exist at all. ; The value of iterated Z in today's generating expression is ; 1.15, which is perilously close to unity, a value that cannot ; create fractals unless it is combined with some other value. ; ; There might or might not be a minibrot at the center of today's ; image. The signs are there, and all the way down it has ; appeared as though a minibrot would become visible on the next ; dive, but here we are at the limit of resolution and no minibrot ; has yet appeared. ; ; Actually, we need no minibrot. The image stands on its own ; merits, and rates a 5, which on the old scale would be a 7. ; ; The calculation time of 4-1/3 minutes borders on slowness, ; leaving it to the individual fractal visionary to decide whether ; the result might be worth the effort. For those in doubt, the ; finished image may be viewed on my FOTD web site at: ; ; ; ; The image is also available for viewing on Hal's web site at: ; ; ; ; Paul's venerable FOTD web site is still up at: ; ; ; ; Though it is currently inactive. ; ; Another fine spring day prevailed here at Fractal Central on ; Friday, though with a temperature of 61F 16C, it was not quite ; as warm as on Thursday. The fractal cats did not concern them- ; selves with the outside conditions, but enjoyed the inside ; conditions to the best of their ability. Their only excitement ; came in the afternoon, when Nicholas sensed a stray cat passing ; through the yard and leaped to the window to be sure the cat ; continued on its way. ; ; The day of the humans was about average. The next FOTD will be ; posted in 24 hours. Until then, take care, and when was it ; determined that ghosts do their haunting wearing old bed-sheets ; instead of regular clothes? ; ; ; Jim Muth ; jamth@mindspring.com ; ; ; START PARAMETER FILE======================================= Blithe_Eidolon { ; time=0:04:20.68-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.8500552192825902/+1.261034003596572/\ 2.19456e+011/1/-157.25/0 params=1.15/0/-11.5/36 float=y maxiter=640 inside=255 logmap=375 periodicity=6 mathtolerance=0.05/1 colors=000HTMGSLFRKEQJEPIDOHCNGCMFBLEAKD9JC9IB8HB7\ GA7FA6E05C04B0490370260240130010YZJxVzpRrhNjaJbUFV\ MBNF7F73AKvgJsdIpbHn`GkUFiaEfVDdTDaQCZOBXMAUK9SI8P\ G7N96K76H45F24C03A0270150020k_CaS7SL3KE0D70x50u40r\ 40p40m40k30h30f30c30a30Z20X20U20R20P20M10K10H10F1m\ C1mA0m70m50m20mICmGAmE9mD8mB7m96m85m64m43m32m11uP6\ uN5uM5uL5uK4uJ4uI4uH4uG3uZDpfJpnPpmSplVpkXpjUpjUpi\ UphUpgUpgUpfUpeUpdUpdUpaUpZUpXUpUUpSUpPUpNXpKTp53z\ HPpFMpCIzAEz7Bz57z23zfGpbEpZDpWCpSApP9pL8pH6pE5zA4\ z72z31zUUpcUpcUpcUpaUp_UpYYpWWpTTpRRpPPpNNpLLpJJzH\ HzEEzCCzAAz88z66z44z22zDEzABz78z55z22zI0pEKpAYp7Np\ 3BzC2zA1z91z71z61z40z30z10zG0pF0pEcpEcpDcpCcpCcpBc\ pAapAZp9Xp8Up8Sp7Qp6Np6Lp5Jp4GpmUzmUzmUzmUzmUzmUzm\ UzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUz\ mUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmUzmU\ zmUzmUzmUzmUzmUzmUzmUzmUz } 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|