; Date: Thu, 20 Sep 2007 22:17:56 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 21-09-07 (Squarely Rooted [5]) ; ; Id: <1.5.4.16.20070920221837.0da7baf4@pop.mindspring.com> ; --------- ; ; FOTD -- September 21, 2007 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; Today's image takes us back to the MandelbrotBC2 formula and the ; complex logarithmic hyperspiralling ladder. Today however we do ; not need the ladder, since we explore the Z^(sqrt(2))+C fractal ; at its ground level. ; ; The parent fractal is a most curious Mandeloid, with a triangu- ; lar period-2 bud as large as the main bay and an unusually long ; zig-zagging main spike extending far into positive-imaginary ; territory. ; ; Today's scene is located deep in a valley separating the large ; triangular bud from a large sub-bud on its northern edge. The ; depth of the scene in the valley makes today's image much slower ; than the FOTD images of recent days. ; ; I named the image "Squarely Rooted" because its exponent is the ; square root of 2. I rated it at a hum-drum 5 because it is ; plagued by the excessive chaos that is so typical of fractals ; with exponents of Z in the range between 1 and 2. ; ; The calculation time of 12 minutes on the P4-2000mhz computer ; would be near one hour on the old P200mhz unit. So why not ; visit the FOTD web site at: ; ; ; ; and view the image effortlessly there. ; ; Another typical end-of-summer day prevailed here at Fractal ; Central on Thursday. The morning fog lifted by 10am, leading to ; a sunny afternoon with a temperature of 82F 28C. The fractal ; cats made the most of it by lounging in the sun streaming in the ; southwest window for most of the afternoon. My day was neutral. ; ; The next FOTD will be posted for all it is worth right here in ; 24 hours. Until then, take care, and remember Fractint in your ; will. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Squarely_Rooted { ; time=0:12:11.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=-0.1234698959\ 7/+1.53149499923/3184551/1/90/3.88578058618805e-016 params=1.4142/0/0/-97.25 float=y maxiter=7200 inside=0 logmap=1174 periodicity=10 colors=00060K60K60K70K70J70I80H80I80J80K90L90M90NA\ 0OA0PA0Q90RA0SA0TA0UB1TB2SB3RB4QC5PC6OC7ND8ND9NDAN\ DBNECMEDMEEMFFMFFMFFMFGLHHKIIJKJJLKINLIOMHQNHROGTP\ GUQFWRFXSEZTE_UDaVDbWCdXCeYBgZBh_Aj`Aka9la9la9j_6h\ Y3fW6dU9cSBdQEeOGfMJhKLiKOjLQkMTlNVmOYoQ_pRbqSdrTg\ sUitVlwVquWnsWlqXjoXhmXfkYdiYbhY`fZZdZXbZV`_TZ_RX_\ PV`NU`LS`JQaHOaFMaDKbBIb9Hb7F_6EY6DW5CU5AS49Q48N37\ L35J24H23F12D14E35E47E58E6AF7BF8DF9EFAGGCHGDJGEKGF\ MHGNHHPHIQHJSILTIMVINWIOYJPZJQ`JRaJScOPdTMeXJgaGhe\ DijAkn7ls4lz0mw2nt3oq4pn5qk6rh7se8tbAu_BvXCwUDxREy\ OFzLGzJHzGEpDBgB8Y85Q52K30E73BA6CD9EGCGKFHNIJQLKTO\ MWQO_TPbWRfcSjmUnzWkzXfzZ`z_VzbUzbPZbKRbKJaK9`KB_K\ D_KFZKGYKIYKK_OLbNNbSPbRQdQScQUcPWbOXaOZaN``Ma`Mc_\ LeZKfZKhYJjYJk_Oj`SiaWhc`gddfehfhcikZkmUnpPptBzrKr\ qSjp_bngVmoNcxChwFmwIrwLvwOzwRzwUzwXzvWzvWzuVzuVzt\ UztUzsUzsTzrTzrSzqSzqRzQH } 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|