; Date: Tue, 10 Sep 2013 21:00:13 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 10-09-13 (Points Revealed [A-7,M-8]) ; Id: <1.5.4.16.20130910210122.2a9f1624@earthlink.net> ; --------- ; ; FOTD -- September 10, 2013 (Rating A-7,M-8) ; ; Fractal visionaries and enthusiasts: ; ; While yesterday's fractal was a non-critical loser, today's ; fractal, which is critical, is a notable improvement. It is a ; scene in the fractal that is generated when yesterday's fractal ; is re-calculated with Z initialized to the first of the three ; critical values of the iterated expression. This value appears ; as the real(p5) parameter of today's image. ; ; At first glance, today's parent fractal, which is critical, ; appears little changed from yesterday's image. In its depths ; however it is totally different, with intact minibrots lurking ; where least expected. Today's image, which I named "Spiraling ; Onward", lies on the west side of the north branch of what could ; be called a kind of Seahorse Valley. ; ; The math value remains a superb 8, while the artistic value has ; risen from an abysmal 3 to a very respectable 7. ; ; The three critical values of initial Z in yesterday's loser ; image were found by entering the same parameters into the ; CriticalPoints formula, which appears in today's parameter file. ; This calculates the Parabolic plane of the iterated expression ; and creates an image that is a rough graph of the expression. ; All that is then necessary is to find the 'Y' coordinates of the ; tips of the three obvious though distorted parabolic curves. I ; always choose the place where the default red adjoins light ; blue. The tedious part is continually stretching the curves ; horizontally to determine the exact 'Y' coordinates. The second ; image, named "Points Revealed", shows the resulting image-graph ; that must be analyzed. ; ; The method is tricky, especially with negative and fractional ; exponents, and sometimes does not work, but it is still better ; than trying to write a formula to do the job or finding the ; points by hand calculation. ; ; The calculation time of 2-2/3 minutes is somewhat slow, and I'm ; not sure the result is worth the wait. Luckily, the web sites ; can speed up the viewing. ; ; Save time and effort by checking the finished images at: ; ; ; ; ; ; ; ; ; ; A mix of sun and clouds, and a temperature of 88F 31C made today ; quite summer-like here at Fractal Central. The fractal cat was ; undecided whether to stretch out or curl up, and finally settled ; half stretched in my favorite chair. The fractal people passed ; the day getting things done. ; ; The next FOTD will soon be posted. To see how soon, check back ; here frequently, and before you know what happened, the next ; fractal will be here. Until whenever the fates decide, take ; care, and let's admit it -- according to science, objective ; reality is probably an illusion, which means that our mighty ; scientific method is founded on nothing more than an illusion. ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= Spiraling_Onward { ; time=0:02:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident passes=t center-mag=-0.511568295107038/+0.05469492019194518\ /1.23e+010/1/140/0 params=0.1/2/1/3/0.5/6/0.01/-1/\ 0.2246790860663939/0 float=y maxiter=1750 inside=0 logmap=138 periodicity=6 mathtolerance=0.05/1 colors=000AIA8J68K3CL2JK2QK2WK1bK1iK1oK1VG6XF7ZG7`\ I3aL0eP6eVBcYFdZJeZMfZPgYSgWVhUYiR_jObkLekJhlGkkEn\ iBqe9saAlWBfNB`IBWFAQC8O87K65G44C420228zz4rp5mk4if\ 4ea3dX3cU3cQ2cM2cI1cF1UB1K70c306m55h45c44Z44U34P33\ K33I23G22E22C11A1181160040020ZyFWoEThDRcCPZBNUALR9\ JP8HM7GK7EI6CG5AD48B3793562341120M`zKYmJWcHUUGRKFP\ ADN1CK1BI19G08D06B0590460240120PmVNiTLfRKcPI`NHYLF\ VJESHCPFALD9IB7F96C7495363131SqTQmROjPMfNLcLJ`JHXI\ FUGERECNCAKA8G97D75A5363131pQjjNddK_ZHVTEQNBKH8FB5\ A5256zn5ti4nd4h`3cW3YR2SN2MI1HD1B9054KK0II0HH0FF0E\ E0CC0BB0AA0880770550440220110ltcOSKjceNKLQzbMqXIhR\ E_MBRG7IB395Xw7Mc4BK2oPukNpgLlcJh`UdXU`TUXQUTMUOIU\ KEcGBcC7c83c4xchhmXUmMFmBwmcdmlczhczdcz`czXmzUmzQm\ zMmzImzFmzBmz7mz3mzSmznzzizzdzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } Points_Revealed { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=CriticalPoints function=ident passes=1 center-mag=0/0/0.6666667 params=0.1/2/1/3/0.5/6/0.01/-1 float=y maxiter=500 inside=0 periodicity=6 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\ zLzzz000555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmsss\ zzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0Gz\ 00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbz\ VVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhz\ lhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhz\ lhzqhzuhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70S\ E0SL0SS0LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLES\ OESSESSEOSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLES\ OESSEOSELSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKS\ SKQSKOSKMSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0G\ G0CG08G04G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0C\ G08G04G88GA8GC8GE8GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8C\ G8AG88G88GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBGGBFGBD\ GBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBFGBDGBC\ G000000000000000000000000 } frm:CriticalPoints {; Jim Muth z=imag(pixel), c=fn1(real(pixel)) a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4): z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| < 10000 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;