thank you! I didn't see much pictures of multifractals before! -david ----- Original Message ----- From: <fractint-request@mailman.xmission.com> To: <fractint@mailman.xmission.com> Sent: Wednesday, February 02, 2005 6:53 AM Subject: Fractint Digest, Vol 24, Issue 2
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Today's Topics:
1. Fractint_Multifractal (Albrecht Niekamp) 2. FOTD 02-02-05 (Triple Beast [5]) (Jim Muth)
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Message: 1 Date: Wed, 2 Feb 2005 05:00:50 +0100 From: Albrecht.Niekamp@t-online.de (Albrecht Niekamp) Subject: [Fractint] Fractint_Multifractal To: <Fractint@mailman.xmission.com> Message-ID: <002301c508db$c9256ba0$78b4fed9@homerwq09jetk> Content-Type: text/plain; charset="iso-8859-1"
Hi,
I´m back again. There are several reasons. The first one is that I managed to boot Windoze98 as additional OS. As you know this OS has a perfect DOS support and allows switching between DOS and windows vv. Also I like it because it is compact and easy to handle. All the hardware, AGP, USB, DVD, Firewire etc is there. For Fractint I use an ancient Nvidia G-force 4 video card which has full Vesa support, also 1600/1200. The second reason is that I have some ideas how to improve and complete my multifractal formula. There is another one not mentioned today.
In my email archive dated July19 I found a request by David Lowenstein asking for multifractals composed of different fractals at the same time. Maybe this is an answer, although possibly not the one you expected.
Multifractal_10 composes images using max 5 different formulas simultaneously. There are 9 frms to choose from. There are five "channels": basic shape, outside and inside 1-3.The transitions are controlled by an iteration counter or by border (z) values, in and out (bigger or smaller), or iteration and border simultaneously. At the transition points optional resets are provided, either of the iteration counter or the z-value (or both), which affect the coloring and further iteration. Five different bailout values can be applied, ranging from 1 to one million. The effect is compression or expansion of the colours.
A unique programmable "warp-effect" can be applied to each channel. It changes the behaviour and looks of the channels, pending on previous iterations, a choosable function and a "warp" factor. Maybe this just means a distortion, maybe a 3d effect.
Sylvie Gallet´s lake effect is optional, fully integrated and works with all formulas, inside3 is shut off if activated.
There now is a second basic "Double mandel" which allows the creation of "mandscapes", 2 samples with different insides, symmetric or asymmetric are provided.
The par-files are demos for the contributing formulas to give you an impression about their looks, mostly with activated lake effect. "Pandemonium" is a basic image with lots of zooming spots. I gave it that name because so many different structures are hidden somewhere.
"Debugflag=322" must be deactivated. Please check your SS-tools.ini.
Any questions are welcome, of course.
Attached is a printable wordpad file which is handy if you should want to compose your own image. If it does not get through, please paste the following part to an editor, using size9 to make it small enough for one sheet of paper.
Sincerely, Al. ---------------------------------------------------------------------------- -
Multifractal_10 Inputs
Real P2 First Input (before the dot) 5 Digits : Channels : 1_Basic Shape 2_Outside 3_Inside1 4_Inside2 Inside3 Frms: 1_Secant 2_Mandel(2) 3_Bees 4_Julia 5_Many Mods 6_Phoenix 7_Newton 8_Spider Second Input (after the dot) 2 Digits_Many Mods_Number of sides 2 Digits_Phoenix 2 Digits_Spider 1 Digit_Reset on Transitions (Shape) 0_no 1_Dble Mandel 2_Iter-reset 3_both +5_warp 4 Digits_Reset Channels 2-5 0_no 1_z-reset 2_Iter-reset 3_both +5_warp
Imag P2 First Input 5 Digits_Colour (Bailout) Number for each channel (5 available) Second Input Variables : 4 Digits_Mand/Jul (2 var) 2 Digits_Secant 4 Digits_Bees
Real P3 First Input 2 Digits_Newtonvariable 4 Digits_Colour1 Second Input 5 Digits_Colour2 5 Digits_Colour3
Imag P3 First Input Basic Shape : Warp-factor (fn1 is used) Second Input 5 Digits_Colour4 6 Digits_Colour5
Real P4 First Input Outside : Warp-factor (fn2 is used) Second Input Outside : 4 Digits+1fractal digit_Border-out 4 Digits+1 fractaldigit_Border-in
Imag P4 First Input Inside1_Maxiter Second Input Inside1 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border 5 Digits_warp factor (fn2 is used) 4 Digits+1 fractaldigit_border1
Real P5 First Input Inside2_Maxiter Second Input Inside2 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border 5 Digits_warp factor (fn3 is used) 4 Digits+1 fractaldigit_border2
Imag P5 First Input Inside3_Maxiter Second Input Inside3 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border 5 Digits_Warp factor (fn4 is used) 4 Digits+1 fractal digit_border3 Alternate Input Imag P5 First Input : 1_Lake effect enabled (Inside3 disabled) Second Input : 2 Digits_Frequency 2 Digits_Waterlevel 2 Digits_Amplitude
------------------------start-pars-----------------------------------------
Secant_basic { ; Lake effect active ; Time 0.42.00.86 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/sin/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/10000.32595700022/55234.0\ 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200A85<17>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ 0s00<3>z00<25>C00A00800<3>000<12>NNNPPPQQQ<8>fffgggiiijjjlll<3>sss<25>BB\ B999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<2>864 }
Bees_Basic { ; Lake effect active ; Time 0.09.10.85 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/sin/exp/sin passes=t center-mag=1.00827/0.00308737/0.6630435/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/30000.32595700022/35234.0\ 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200A85<17>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ 0s00<3>z00<25>C00A00800<3>000<23>fffgggiiijjjlll<3>sss<25>BBB999777<2>22\ 2000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<2>864 }
Julia_Basic { ; Lake effect active ; Time 0.31.26.42 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/sin/exp/sin passes=t center-mag=0.0659115/0.0324086/1.087898/1.0222/90/3.88578058618804789e-0\ 16 params=-0.05825983458967864/0.3785210730307932/40000.32595700022/25234.0\ 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000047049<5>0BL0DN0DP<4>0KZ0L`0Mb0Nd0Of0Qh<3>0Up4Yr8atCgvGkxKqz<3\
4_s0Vq0Uo<12>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R0LT0NV0PX0P<3>\ d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y0SW0RU0O<5>I0F\ G0EE0CC0A<3>304102010<4>0B10D10F10H20J20L20N2<2>0T40V40X3<3>0d40f50h5<3>\ 0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>\ 0000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_\ Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<5>121000\ 001023025 }
Phoenix_basic { ; Lake effect enabled ; Time 0.19.25.24 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=exp/sin/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/60000.32565700023/25234.0\ 506030602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter logmap=5 periodicity=0 rseed=-2436 colors=200432<20>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ 0s00<3>z00<25>C00A00800<3>000<7>FFFHHHJJJ<9>___aaaccc<3>iiijjjlll<3>sss<\ 25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211 } Newton_Basic { ; Lake effect active reset=2004 type=formula formulafile=mfr9n.frm formulaname=multifractal_10 function=exp/sin/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/70000.32595700023/55234.0\ 506030602/152048.0404808048/384.1604894048/384.00482000595/256.1007683/5\ 12.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=2 periodicity=0 rseed=-2436 colors=200432<20>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ 0s00<3>z00<25>C00A00800<3>000<9>IIIKKKLLL<9>bbbdddfffgggiiijjj<3>qqqsssq\ qq<24>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211 }
Spider_Basic { ; Lake effect active ; Time 0.09.42.76 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=exp/sin/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/80000.32595700023/25234.0\ 506030602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=2000NU<8>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7\ A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<11>LLLNNNPPPQQQSSS\ UUU<6>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<\ 15>0OW } Many_mods_basic { ; Lake effect active reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/sin/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/50000.16595700022/55234.0\ 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=20009C<19>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3\
unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<23>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<3>07A } Pandemonium { ; Time 0.21.15.48 ; reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.489028/0/0.6666667 params=-0.05825983458967864/0.3785210730307932/21225.64595718025/21235.0\ 311030602/150056.0204808192/384.32768524288/384.00482000595/256.10076830\ 01/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000gt<22>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB\ 7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>fffgggiiijjjll\ l<3>sss<25>BBB999777<2>222000012<22>0_k0am0bo0cq<4>0kz0jx0hv } Mandscape2 { ; asymmetrical inside ; Time 0.14.07.06 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=exp/exp/exp/sin passes=t center-mag=-0.504822/4.44089e-016/0.9463538 params=-0.05825983458967864/0.3785210730307932/20227.32595710661/25255.1\ 111020602/151024.0204808192/384.32768524288/384.00482000595/128.10076800\ 01/512.10076800005/768.10076800002 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000376<2>121000001023025047049<5>0BL0DN0DP<4>0KZ0L`0Mb0Nd0Of0Qh<3\ 0Up4Yr8atCgvGkxKqz<3>4_s0Vq0Uo<12>0FQ0DO0DM<3>08E06C06A0480460240120001\ 00<12>R0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_\ e0Z<3>Y0SW0RU0O<5>I0FG0EE0CC0A<3>304102010<4>0B10D10F10H20J20L20N2<2>0T4\ 0V40X3<3>0d40f50h5<3>0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>\ 0I20G20E20C20A1081<3>0000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM\ <3>DdTDfVEhWFjYFlYGn_Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK\ <3>7KE6IC5GB5DA4B9497 }
Mandscape1 { ; symmetrical inside ; Time 0.14.02.12 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=exp/exp/exp/exp passes=t center-mag=-0.504822/-3.9968e-015/1.1027/0.8582 params=-0.05825983458967864/0.3785210730307932/20222.32595710666/25234.1\ 111020602/151024.0204808192/384.32768524288/384.00482000595/128.10076800\ 01/384.10076800005/512.10076800002 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200A85<17>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ 0s00<3>z00<25>C00A00800<3>000<23>fffgggiiijjjlll<3>sss<25>BBB999777<2>22\ 2000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<2>864 } Lite_Zoom { ; Different outside ; Time 1.51.37.67 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50466/1.66533e-016/4.219409/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21225.64595767025/13234.0\ 311030602/151024.0204808192/384.32768524288/384.00482000595/256.10076830\ 01/512.1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000LS<11>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3\
unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<11>LLLNNNPPPQQQSSSUUU<6>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012\ <11>0JQ }
Multimix { ; Lite zoom ; Time 3.23.44.07 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_9 function=sin/exp/exp/sin passes=t center-mag=-1.22699/8.32667e-017/13.33333/1/90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21225.64595718025/23434.4\ 911030602/152048.0409608192/384.3276898304/384.00482000595/256.100768300\ 1/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000KQ<6>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7\ A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<9>IIIKKKLLL<9>bbbd\ ddfffgggiiijjj<3>qqqsssqqq<24>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<1\ 7>0LS } Hades { ; The gate to the underworld ; Time 2.09.12.02 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=cos/sin/sin/sin passes=t center-mag=-0.188053/0.00113846/24.61324/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21222.32595700021/22222.0\ 506020602/551024.0204808192/384.32768524288/384.0048000545/256.100768555\ 55/512.10076855555/768.10076855555 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200222<24>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3\
0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3\ 000400<23>o00q00s00<3>z00<31>000 }
-----------------------------------------start frm--------------------------- FRM:Multifractal_10 { ; Albrecht Niekamp Jan2005 ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ;0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2: 2digits_many-mods 2digits_phoenix 2digits_spider ; 1digit_shapereset:0_no 1_dblmandel 2_iter-reset 3_both +5_warp ; 4digits reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 6digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ; optional: 1_lake effect, 2digits_frquency 2digits_level 2digits_ampl ;fn(1) shared by many-mods+bees ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Qusinewton Pusk s Istv n z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } -----------------------------------------------end-frm---------------------- -
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Message: 2 Date: Wed, 02 Feb 2005 09:52:53 -0500 From: Jim Muth <jamth@mindspring.com> Subject: [Fractint] FOTD 02-02-05 (Triple Beast [5]) To: fractint@mailman.xmission.com Cc: philofractal@lists.fractalus.com Message-ID: <1.5.4.16.20050202095518.2ac7fde6@pop.mindspring.com> Content-Type: text/plain; charset="us-ascii"
FOTD -- February 02, 2005 (Rating 5)
Fractal visionaries and enthusiasts:
Today is the next to last time we will meet the fractal beast that has been prowling the neighborhood for the past two days. The beast is actually a four-dimensional thing with more aspects than it has fleas. I named today's view of the critter "Triple Beast" because the beast appears to have been stretched in three different directions.
Most of the features that appear in the Mandelbrot aspect of the scene are still recognizable, though some have been stretched almost beyond recognition. And one of the green inner spirals has apparently split into a double spiral.
The double spiral is only an accidental effect. It appears because the calculated slice of the Julibrot that we see on the screen cuts twice through a curved four-dimensional tube-like feature something like a rolled-up scroll that has been bent in the middle.
Since the beast is starting to become boring, and we have seen such distorted Mandelbrot features quite a few times before, I could rate the image no higher than a 5, which is average. But the beast is near the end of its life, and will make only one more appearance before being sent to the oblivion where all the undiscovered fractals are awaiting it.
The beastly fractal may be glimpsed by running the included parameter file, or by downloading the finished image from the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
The next installment of philosophy is but two days off. So be patient. Enlightenment is nigh.
Tuesday was another perfect day for this time of year here at Fractal Central. Warm sun and a temperature of 39F 3C made conditions near ideal, at least in the places where the snow had melted and the ground was bare. The fractal cats enjoyed conditions to the best of their ability, and when they finally came indoors, were ready to curl up and sleep. Today is starting the same. Another good day would appear to be in store for the duo.
For me, the work is normal. It looks like the day will be neutral. This means ample time for the last of the beastly images. Until the final beast appears in 24 hours, take care, and be ready for new ideas.
Jim Muth jamth@mindspring.com jimmuth@aol.com
START PARAMETER FILE=======================================
Triple_Beast { ; time=0:02:41.04--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 center-mag=-0.000003485\ 49440916/-0.00000142882743436/518039.3/0.05033/\ 156.558086503412028/-40.9116101381892818 params=55/-157/-81/166/0.288136932805/0.4826454054\ 09/0.288136932805/0.482645405409 float=y maxiter=5000 inside=0 logmap=288 periodicity=10 colors=000SYsSXrSWqSVpSUoSTnSSmSQlTOkUMjVKiWIhXGgY\ Ef_CeaAdcAceAbgAaiA`kC_mEZoGYqIXrKWsMTrOSqQRpSQpUP\ oWOnXNnYMmZLl_KlaJkcIjeHjgHkhGkgFlfEldDmbCm`BnZAnX\ 9kV8hT8eR8bP7_N7XL7UJ6RH6OF6LD5IB5FC5CC49D46D43D45\ E57F59G6AH6CI6EJ7FK7HL8JM8KN8MO9OP9QQARRATSAVTBWUB\ YVC_WC`XCaYEbZGbZHc_Jd`Kd`MeaNebPfbQgcSgdThdVheWif\ YjgZjh`kiakjclkdmlfmlgmmimminmjomjpmjqnjrojtpjuqjv\ rjwsjxtlxujwtivshurgtqftpdsocrmbqlapk`oj_oiYnhXmgW\ lfVkdUjcTjbRiaQh`Pg_OfZNfYMgXKgVJgUHhTGhREhQDiPBiN\ AiM8jK7jJ5jI4kG2kF1kE0gH1dJ1aM2ZO2WR3TT3QY4Na4Kf5U\ o5cs2mz5mz8mzBhtEcrHZqKUoNPnQLmTMkWNjZOiaPidQhgRhj\ SgmTgpShsTgrTfrTfqTeqUepUbpU_pUZoUUoVTnVTnVSnVSmVR\ mWRnWQoWQpWPqWPsXOuXOwXNxXNzXMzYMzYLzYLzYKzYKzVOzS\ SzQWzN_zLczPgzUkzZozcszhvzmuzmwzmvzmvzmuzmuzmtzmtz\ mszmszmrzmrzmrzmqzmqzmpzmpzmozmozmnzmnzmmzmmzmmzml\ zmlzmkzmkzmjzmjzmizmizmiz }
frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 }
END PARAMETER FILE=========================================
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End of Fractint Digest, Vol 24, Issue 2 ***************************************