June 2003 - Fractint - mailman.xmission.com

The "bug "is not a bug!!! Is not! Is not!
by Tim Wegner 26 Sep '03

26 Sep '03

OK folks, listen up. :-) For you Fractint is a fractal program, for me it is the World's Best Quick And Dirty Reference to Complex Transcendental Functions. Press F1, go to "Fractals and the PC", and navigate down to trig identities. I put these in the help because I went through a LOT of books finding these and wanted to collect them all in one place in order to code them up. Some books are too simple and so don't have the formulas, and other more advanced books are too abstract and so don't have them either. The formula for the complex power is as follows: z^w = e^(w*log(z)) (here"^" is ASCII text shorthand for exponentiation, in this case z^w means "raise the complex number z to the power of the complex number w") where: e^(x+iy) = (e^x) (cos(y) + i sin(y)) and log(x+iy) = (1/2)log(x^2 + y^2) + i(atan(y/x) + 2kPi) for k = 0, -1, 1, -2, 2, ... (The log function refers to log base e, or ln. The expression atan(y/x) is an angle between -pi and pi in the quadrant containing (x,y) implemented in C as the atan2() function.) The point of these formulae from a programmer's perspective is that they define the complex valued power function in terms of the real versions of e^x, log(x), sin(x), and cos(x) that are available to the C programmer. The interesting and important thing here is that the value of the complex log is not unique. There are infinitely many different values, with the imaginary members. Put another way: the complex log is not single valued. Let's look at the log. In the "bug" illustration, the complex argument is: (-5.0, 0.0) The assembler log function gives: (1.6094379124341,-3.141592653589793) Coding by hand in C gives: (1.6094379124341, 3.141592653589793) BOTH ANSWERS ARE RIGHT!!! The imaginary parts differ by 2*PI, which is acceptable. What actually causes this is that the log implementation normalizes the result to a particular 2*PI segment. Jim's fatal mistake was when he assumed that given a = 1, b = -5, g = 1, h = -1, j = 1/6, that (-a*b*g*h) is -5. Yes, it's very close to -5 in the actual computer calculation, but "close" wins only in horseshoes. The problem is that the complex logarithm of (-5,0) has an imaginary part exactly on the logarithm software implementation's boundary of 2*PI normalization (namely PI). So if the calculation (-a*b*g*h) drops a bit here or adds a bit there, even a bit of the lowest significance, it can change the imaginary component from ~ PI to ~ -PI. I leave it to the reader to plug both these logarithm values into the rest of the formula for the exponential power, and see that the result is (1.132467200411351, -0.653830243005915) in the one case and (1.132467200411351,+0.653830243005915) in the other, as Jim discovered. Here's the main point - a recurring theme in trying to create fractals with complex transcendental functions. The complex power function x^y is discontinuous because of the ambiguity in the many- valued complex log. Each decision to normalize the log to a particular 2*PI interval in an effort to define a single-valued function creates a discontinuous tear in the result in a different way. The "bug" Jim found had values right on the boundary of the tear, so that tiny perturbations and rearrangements of the code pushed the calculation over the edge of the discontinuity. Fractint is cleared of the unjust accusation! The verdict: INNOCENT! All is well with the fractal world :-) One single absolute truth of the universe is thus upheld again. It is this: There are NO software bugs, ONLY USER ERRORS!!! (Sorry Jim ... -no, not *really* sorry, I lied :-) I suggest the future Fractal of the Day explore a fractal based on a discontinuous complex transcendental function in such a way that the fractal itself has visually manifest tears. There are several examples in Fractal Creations, and I am sure many of the artists here, including the honorable Mr. Muth, know of or can discover examples. Tim Wegner

2 1

FOTD 21-06-03 (Beware the Lava Pit [5])
by Jim Muth 02 Jul '03

02 Jul '03

FOTD -- June 21, 2001 (Rating 5) Fractal visionaries and enthusiasts: What do you get when you mix some Z^(1.1) with some Z^(-1.1)? A pit of boiling hot lava of course. I named the image "Beware the Lava Pit". Actually, I should have named it "Beware the Magma Pit" since the scene is underground, and molten rock is known as magma until it reaches the surface. Only then is it called lava. When the time came to rate the image, I studied it several minutes before realizing that it was merely an average image. The rating of 5 is average. There's nothing wrong with being average, it's just that I like my FOTD images to be above average, and the greater the number of above-average images I post, the higher the standard of average becomes. One thing that does not change however is the average render time of my FOTD's, which currently stands around 12 minutes on my tired, worn-out P200 machine with the exhaust fan that needs to be nudged before it starts turning. When I forget to nudge it, the smell of the over-heated power-supply unit soon reminds me to give it its nudge. Today's image requires 25 minutes to complete on my machine. It will finish faster on faster machines. But the fastest way of all to see the lava pit is to download the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Heavy rain fell during the day Friday here at Fractal Central. The cats, who were confined to the indoors, turned sullen in the afternoon. Several treats of tuna were needed to restore their spirits. Today is starting with a bit of sun, but heavy storms, and perhaps hail, are due this afternoon. I doubt that the cats will have a good day. If the grass dries enough, I'll trim it today. If not, I'll let it grow another couple inches. In any case, I'll visit Fractal Land to track down the next fractal. Until next time, take care, and beware. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Beware_the_LavaPit { ; time=0:25:44.24--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+0.15929781727837890/+0.033662025303030\ 13/7.522503e+007/1/52.5/4.46614381509335967e-006 params=-0.86/1.1/-0.53/-1.1/0.03/525/0/0 float=y maxiter=3400 inside=0 periodicity=10 colors=000pl8niAmeCkbFjZHhWJfSMePOcLQbIT`EV_BXgUZo\ l_dmNVqBWtDXwEYzFZzG_zH`zJazKbzLczMczN_zTWzYSzbOzh\ KzmHzrzkKziKzgKzeKzcKzaKz_KzYJzWIzUHzSGyQGxOGwMFvK\ FuFEtAEs5ErBJoFNnJ_hNWeRhbWcZ_mWclTgpQhtReqRfrRdrR\ aqR_qRYpRVpSToSRoSOnSMnSKmSHmSFlSDlRHmRKnQOnQRoQUp\ PYpP`qPcrOgrOesOksPcmQVhRLbSCYT3TUAXUTlUNdUZrU_kUe\ oUlsUjwUrzMlwFot7kq0gn1fk2ei3dg4cd5cb6b`6aY7`W8`U9\ _RAZPBYNBYLVMAmA0f63_25Z36Y37X38W39V3AV4AU4BT4CS4D\ R4ER4ET7FUAFVCFWFFXHFYKGZMG_PG`RGaUGbWGams_kqZjoXi\ mWhkVgiTfgSeeRddSbbSa`S_ZTZXTXVTWTUURUTQUSOVQMVPKV\ NIWMGWKEWJCWIBZKI`MPbNWePbgRiiSoeVmbXlZZkWaiSchPeg\ Q`aRXXSTRSPMQOKONJNMILLHKKGIJFHIEFHDDGCCFBAEA9D97C\ 86B7AF6DI6GM5JP5MT4PW4V`4_e4ei4jn4ps4uw4WoH6hUHXJR\ M8VJAZGCaDEeAGi7Il5JhJUdXc`jmXwwUrkRm_OhOLcCOVGRMJ\ UDMX5PeeUdbSc`QbYObWMaUK`RI_PG_MFZKDYIBXF9XD7WA5V8\ 3V62ZD3aK3eR4hX4lc5oj5rp5 } frm:MandelbrotMix2 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

9 13

Multifractal_5
by Albrecht.Niekamp＠t-online.de 30 Jun '03

30 Jun '03

Hi, Now a Newton formula is included. This was not easy as all newton types have a different bailout and generally they dont like to be mixed. The one I finally found is again by Pusk s Istv n, the third one I use in the multifractal series. A big Thank you! just in case heïs listening. The images really are unique for me and I guess for all of you. Fractals are fun! Al. ------------------------------start-par------------------------------------- Newtonflowers { ; Time 0.11.02.46 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.17906/-0.00478368/1.573582/1/-90/3.88578058618804789e-016 params=-0.1156346324045534/-0.5338602862636189/12482.00001/130000.321314\ 0212/2048.02048/384.000008/384.00024/128.0076800000001/512.0076800000001\ /768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200F00<4>500400200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HII\ FGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>\ jeOlgPniQpjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<22>H00 } Magic_circle { ; Time 0.25.12.59 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.17906/-0.00478368/1.573582/1/-90/3.88578058618804789e-016 params=-0.1156346324045534/-0.5338602862636189/14282.3200001/130040.1314\ 021203/2048.02048/384.000002/384.00024/128.0076800000001/512.00768000000\ 01/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200332<21>jeOlgPniQpjRrlStnT<2>ysX<25>BB7996775<3>000<24>n00p00r0\ 0<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFG\ GEFF<3>677455344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111 } Newtmand { ; Time 0.32.45.46 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.1197/-0.00478368/1.573582/1/-90/-1.23373533611470521e-014 params=-0.1156346324045534/-0.5338602862636189/14282.3200001/2540.131402\ 0602/2048.02048/384.0000045/384.00024/128.0076800000001/512.007680000000\ 1/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=2000Wd<14>09C08A068<2>022000111<22>jeOlgPniQpjRrlStnT<2>ysX<25>BB\ 7996775<3>000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18\ >hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0cq0es<3>0kz<9>0Xf } Mixdown2 { ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=exp/exp/exp/sin passes=t center-mag=1.1197/-0.00478368/1.573582/1/-90/-1.23373533611470521e-014 params=-0.1156346324045534/-0.5338602862636189/14237.3200001/72500.13140\ 216052/2048.02048/384.0000049/768.00024/128.0076800000001/768.0076800000\ 001/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455\ 344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>jeOlgPniQpjRrlS\ tnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<30>200 } Mixdown3 { ; Time 0.38.29.40 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=1.1197/-0.00478368/1.573582/1/-90/-1.23373533611470521e-014 params=-0.1156346324045534/-0.5338602862636189/14237.3200001/53000.13140\ 21613/2048.02048/384.0000049/768.00024/128.0076800000001/768.00768000000\ 01/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000<3>000000000<9>X0a_0dc0h<3>p0w<4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7U\ X6`Z4h_2oa0wc<11>2TG2RE3OC<3>4D3<17>kkammcpoe<3>zwm<6>cYO`UKYQG<3>KA0000\ <43>000<4>000330<11>110110110<3>000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A\ 00<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0C<3>A08004000<25>000 } Newton_frame { ; Time 0.17.06.50 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=-0.507813/-0.00478368/0.9488575/1.0685/180 params=-0.1156346324045534/-0.5338602862636189/14287.3210001/53000.13140\ 61613/2048.02048/384.0000049/768.00024/128.0076800000001/768.00768000000\ 01/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200000<2>455677899ABBBCC<18>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455\ 344122000<25>0bo0cq0es<3>0kz<25>09C08A068<2>022000111<22>jeOlgPniQpjRrlS\ tnT<2>ysX<25>BB7996775<3>000<24>n00p00r00<3>y00<30>200 } Only_one { ; can be the winner ; Time 0.17.15.61 ; Albrecht Niekamp June, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mult243.frm formulaname=multifractal_5 ismand=y function=cos/exp/exp/sin passes=t center-mag=-0.302531/-0.00478368/0.842554/1.0685/180 params=-0.1156346324045534/-0.5338602862636189/19287.3210001/53000.13140\ 81613/2048.02048/384.0000135/768.00056/128.0076800000001/768.00768000000\ 01/1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000<2>110110000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0\ F<3>z0K<6>Z0EV0DR0C<3>A08004000<26>000<4>000<9>X0a_0dc0h<3>p0w<4>_0dX0aU\ 0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<11>2TG2RE3OC<3>4D3<17>kkammcpoe<3>zw\ m<6>cYO`UKYQG<3>KA0000<43>000<4>000330<12>110 } -------------------------start-frm------------------------------------------ FRM:Multifractal_5 { ; Albrecht Niekamp 230603 ;only integers as first input, second input 5 digits to the right ;real(p2) 5digits: shape, outside, in1, in2, in3 ; 0_off 1_mand 2_jul/bees 3_many_mods 4_newtjul +5_reset digit1: +5_warp ; input2 : 2digits_many_mods 5digits_frm2 use : 0_no 1_yes ;imag(p2)(-) 2-4digits : quasinewton input (max 2000) ; 1digit : many_mods multipl. off 1_out 2_in1 3_in2 4_all ; 1digit : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : 4digits(-)_frm1 2digits_frm2 4digits_bees ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in ;real(p4) outside : factor (fn2), border-out ;imag(p4) inside1 : maxiter1, factor1 (fn2) ;real(p5) inside2 : maxiter2, factor2 (fn3) ;imag(p5) inside3 : maxiter3, factor3 (fn4) ; da=real(p2) dd=trunc(da) da=round((da-dd)*10000000)+11111 d=trunc(dd/10000) ex0=d>5 d=d-5*ex0 vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) ex1=d>0 dd=dd-d*1000 rs1=d>5 d=d-5*rs1 v1m=(d==3) v1j=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) ex2=d>0 dd=dd-d*100 rs2=d>5 d=d-5*rs2 v2m=(d==3) v2j=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) ex3=d>0 dd=dd-d*10 rs3=d>5 d=d-5*rs3 v3m=(d==3) v3j=(d==4) dd3=(d==2)+(d==4) ex4=dd>0 rs4=dd>5 dd=dd-rs4*5 v4m=(dd==3) v4j=(dd==4) dd4=(dd==2)+(dd==4) tt=ex0+ex1+ex2+ex3+ex4 ; mm=trunc(da/100000) da=da-mm*100000 d=trunc(da/10000) ab=(d==2) da=da-d*10000 d=trunc(da/1000) ab1=(d==2) da=da-d*1000 d=trunc(da/100) ab2=(d==2) da=da-d*100 d=trunc(da/10) ab3=(d==2) da=da-d*10 ab4=(da==2) ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*10000000000) pp=trunc(dd/100)/10 dd=dd-1000*pp da=trunc(dd/10) so1=((da==1)+(da==4)==0) so2=((da==2)+(da==4)==0) so3=((da==3)+(da==4)==0) dd=dd-10*da ir1=(dd==1)+(dd==4) ir2=(dd==2)+(dd==4) ir3=(dd==3)+(dd==4) ; 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 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=real(p3) mb=trunc(d) ba=(d-mb)*100000 ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) fac1=(d-mi1)*100000 ; d=real(p5) mi2=trunc(d) fac2=(d-mi2)*100000 ; d=imag(p5) mi3=trunc(d) fac3=(d-mi3)*100000 ; bg=((ab+vb)==0) bg1=((ab1+v1j)==0) bg2=((ab2+v2j)==0) bg3=((ab3+v3j)==0) bg4=((ab4+v4j)==0) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else if (bg) c=p9 else c=p1 endif z=pixel endif t=0 d3=(ismand==0) u=d3 bo=z p=pp : If (tt) t=t+1 if ((ex0) && bo>b0) u=2*(fn1(t/sfac)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel if (bg) c=p9*u else c=p1*u p=pp+u endif endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) u=2*(fn2(t/ofac)) rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel endif vb=v1j d3=1 if (bg1) c=p9*u else c=p1*u p=pp+u endif else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1m if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir1) t=0 endif ex1=0 tt=tt-1 elseif ((ex2) && t>mi1) u=2*(fn2(t/fac1)) rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel endif vb=v2j if (bg2) c=p9*u else c=p1*u p=pp+u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v2m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir2) t=0 endif ex2=0 tt=tt-1 elseif ((ex3) && t>mi2) u=2*(fn3(t/fac2)) ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel endif vb=v3j if (bg3) c=p9*u else c=p1*u p=pp+u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3m if (vb) if (so3) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif if (ir3) t=0 endif ex3=0 tt=tt-1 elseif ((ex4) && t>mi3) u=2*(fn4(t/fac3)) ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel endif vb=v4j if (bg4) c=p9*u else c=p1*u p=pp+u endif d3=1 else d3=0 z=z*u c=z if (rs) z=0 endif vb=v4m if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) ba=mb endif endif ex4=0 tt=tt-1 endif endif if (vb) if (d3) n=z^p-1 d=p*z*z z=z-n/d else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z1=fn1(z)-c ;Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p0 endif bo=|z| bo<=ba } ----------------------------------end-------------------------------------

2 1

FOTD 30-06-03 (Washboard [6])
by Jim Muth 30 Jun '03

30 Jun '03

FOTD -- June 30, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's trip into Fractal Land takes us to the parent fractal created by subtracting Z^(1.1) from Z^(-1.1) and adding (1/C). This parent fractal should more properly be called the parent fractals because the entire parent consists of two similar sized Mandeloids sitting side by side. The Mandeloid on the right is fairly intact, with all its bays and valleys, while the one on the left is only half there. Its main bay, along with other accessories, is missing. Today's image is located in the East Valley area of the intact Mandeloid on the right. I named the image "Washboard" when I noticed the square ribbed effect around the central midget. This ribbed effect is due entirely to the unavoidable discontinuities in the image. It is a good example of discontinuities leading to a positive result. And BTW, a washboard is an object that was used to wash clothes before we had washing machines. The image rates a 6, which is just the slightest above the average of all my fractals. If I had compared it to only the FOTD fractals, it would rate around a 4. I really should broaden my rating system, since nearly every FOTD image rates between a 4 and a 7. But doing so would distort the record. Perhaps I'll shift to a 0-to-100 scale and rate my images as though they were a school test. We'll see what I think about the idea. With a render time of 5 minutes, (and a rinse time of 3 minutes) the washboard cycle is a fast one. Downloading the completed image from one of the FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is even faster. Except for being a bit too warm for comfort, Sunday was a near perfect day here at Fractal Central, especially for cats. The rain held off, and the warm sun, gentle breezes and temperature of 88F 31C gave them a most enjoyable day in the yard. Of course, at their age, enjoyment for cats means sleeping as much as possible. Today is promising to be a repeat. With a little bit of luck, the duo will have another great day. And with a bit more luck I'll finish the day's work by noon, leaving lots of time to find the next FOTD. Until that next FOTD appears, take care, and the meaning of life could be encoded in a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Washboard { ; time=0:05:10.88--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.01267188732830007/-0.352921833830621\ 70/3.316742e+009/1/107.5/0.000111833820926623972 params=-1/1.1/1/-1.1/0/0 float=y maxiter=1000 inside=0 logmap=95 periodicity=10 colors=000WhwW_uWQsWFoW6nW0lW0jW0hW0eW0aU0YS0UQ0QP\ 1PN6LL9HJDDHH9FL8DSBD_FBeHBlL9nN9xQ8sU8zW6z_6zaLz_\ Yx_zlYz_YzPYzaoznzwzziwzeszcqzQnzFlz3hz0fz0cz0az0Y\ z0Wz0Sz0Qx0Ns0Ln0NQ0N008D00eH0zN0zS0zW0za0zf1zj6zo\ 9zsDzl9zf6z_1zU0zN0zH0z90z30z00W000z6zw0zcFlJf6NaF\ QYNSUUWQaYNhaHocDwf9zh6zl1zn0zc3zS8zHBo6Fe0JU0H_0F\ c0Dh0Dl0Bq09u09x08z06z03z03z01z00z00z09z0Hz0Pz0Yz0\ ew0lo0uj0zc0zY0zU0zS0zQ0zP0zNDjWfUejeSnoHqz6uz0xz0\ Pz00z00o00c00Q80DF00N00U30SB9SHLSPWSWeSaoShzSozSuz\ SnzLhzDcz6Wx0Qs0Ln0Fj0Hl0Hl0Hn0Jn0Jo0Jo0Lq0Lq0Ls0N\ s0Nu1Nu3Pw6Pw8Px9PxBUzFYzHczJfzNlzPozQszSDqjSFWe0J\ U0DLB8BS30j00z00z00z00z10z90zF0zN0zS0w_0ue0ql0oq0n\ o0lo6njDoeLq_SsU_sPfuJnwDux8zz1zz0zx6zzFzzNzzWzzcz\ zlzzszzzzzzzzzzzzzzzzzzqzzzzzzzczzFzz00zz0zz0zz0zz\ 0zz0zz0zz0zx0zq0zl0zf0za0zW0zQ0zL0zF0z90z30z0Yze_z\ caz_azYDzs0zz0zzzzzzzzzzx } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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RE: [Fractint] FOTD 29-06-03 (Time Lash [5])
by Jim Muth 29 Jun '03

29 Jun '03

At 11:34 AM 6/29/03 -0400, Thaddaeus Parker wrote: >Jim: > >For all the time that I have been on the list I >have not once seen an FOTD below a 4. Is it similar >to our national threat level, where we will never >see a green or a red level? Curiosity is just >killing me at this point. There are so few FOTD's with a rating below a 4 because I discard these images and never use them. In the rather distant past, I have posted a few FOTD's with a rating as low as 2, and a number of images with a rating of 3. When I rate an FOTD image, I compare it to all my fractals, including those that never make FOTD. I would be more correct if I compared my FOTD images with only the other images that actually made FOTD's. BTW, you also have never seen a rating of 10. Jim M.

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FOTD 29-06-03 (Time Lash [5])
by Jim Muth 29 Jun '03

29 Jun '03

FOTD -- June 29, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image was created by the MandelbrotMix3 formula. This formula mixes together and iterates four different powers of Z. But it has a down side. It does not automatically initialize Z to a critical point of the formula. That task must be done by hand, and the resulting value entered as real(p5), which is the reason I use the formula so rarely. Formulas such as those calculated by the M-Mix3 formula have several critical points, which are points where the function is stationary and midgets thrive, so several different fractal images can be obtained from the same formula when the critical points are calculated by hand. This is one of the good points. But big disadvantages are that calculating critical points is boring work and the resulting fractals are not that much better than those created by the MandelbrotMix4 formula. Today's parent fractal for example mixes various portions of Z^(10), Z, (1/Z), and Z^(2). The resulting image, which resembles a flying saucer or Marvin the Martian wearing an army helmet, could just as easily been created by the MandelbrotMix4 formula. The unusually precise value of real(p5) is one of the critical points of the formula, which I calculated and entered by hand. The parent fractal has X-axis symmetry, with a tiny East Valley just where it should be, and many other valleys that also probably hold worthwhile images. Today's scene is an unusually shallow one located in this East Valley. Today's image rates an average 5, largely because of its spectacularly brilliant colors, which I tweaked in a graphics program. Those who run the parameter file need not be concerned about missing the enhanced colors. The colors are fully encoded in the parameter file. The name of the image, "Time Lash", was chosen while I was watching a 'Doctor Who' episode of that name on TV late Saturday night. The render time of 1/10 second over 10 minutes on my machine, which is nearing the fossil stage, can be cut at least in half on newer units. And as always, the completed GIF image can be downloaded for convenience from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though lots of clouds hung around here at Fractal Central on Saturday, they were thin enough to let the temperature reach 82F 28C -- near perfect cat conditions. Enjoying the conditions to the fullest, the dynamic pair had a peaceful day in the yard. The pushy cat from two doors down the hill stayed where he belongs for a change, so their peace was uninterrupted. Today is starting sunny, and the temperature is still near ideal, but showers are possible. It remains to be seen how the cats' day will go. I'm going to spend the day doing as little as possible. If I get ambitious, I might resume work on the FOTD CD, which has been nearly but not quite ready for several months. I'll probably end up releasing the CD in imperfect form, but I'm not quite ready to give up hope of perfection yet. Until next FOTD, take care, and stay in there with the big-time thinkers. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Time_Lash { ; time=0:10:00.10--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=+1.506891153995481/-0.00013746456513907\ /205962.1/1/-172.5/2.01858393888976195e-009 params=0.001/10/1/1/1/-1/0.1/2/-1.403897684563/0 float=y maxiter=4200 inside=0 periodicity=10 colors=000z0zz0zz0zv0zP0z0lz0zz0zz0zz0zz0zz0zz0zz0\ zz2zz6zzBzvGzhKzZPzPUzBZz2cz0hz0vz0zz0zz0zz0zz0zz0\ zz0zz2zz6qzBhzGZzKPzPBqU2cZ0Pc0Bh02l00q00v00z00z6K\ 6zz0zz0zz0zz0zz0zz0zz0zq0lc0cK0P60G0220G00P00c00l0\ Xz0Wx0Vw0Uv0Tu0St0Rs0Qs00s00s00t00t00u00u20w20w60z\ B0zB0zG0zG0zG0zG0zP0qU0Zc0Gh20lB0vK0zU0zc0vZ0lU0cU\ 0ZP0PP0GK0BK02G00G00B00B00600200200000000000000000\ 000000000Z0zzPzzzzzzzzvzzhzvUzZGzG2h00P00600000000\ 00000000000000000000000000000000000000000000000000\ 000000000000000600B00K00P00Z60cG0hK0qU2vc2zl6zvBzz\ BzzGzzKzzKzzPzzUzzUzzZzzczzczzhzzhzzhzzlzzlzzlzzqz\ zqzzqzzvzzvzzvzzzzzzzzzzzzzzzzzzzzzzvUzK0z00z00P00\ 0000zz2zz6zzBzzGqzKlzKczPZzUPvZKqcBhc6ch0Zl0Pq0Kv0\ Gv06z02z00z00z02z2BqUKhqPczZUzhKzlGzP6z62z00z00z00\ z00z00z00z00z00z00z02z06z0Bz0Gz0Kz0Pz0Zz0cz0hz0lv0\ qv0vq0zl0zl0zh0zGUzU2zl0z } 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 } END 20.0 PAR-FORMULA FILE==================================

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EMACS
by Programmer Dude 29 Jun '03

29 Jun '03

David Jones wrote: > Methinks when I replace my current CorelLinux > installation with a more moden Linux, I should try out > Emacs ... Wouldn't surprise me if both EMACS and vi came with linux. I know vi comes with most unices. Learning either is a major time investment. A technique that has worked for me is to try to learn one new thing each time I use it ("it" being vi in my case). The EMACS/vi thing reminds me a little of the old Word/WordPerfect religious war.... ;-) -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

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[Fractint] Re: Fractals Relate to Expansion-Contraction of the Universe
by JackOTradez 28 Jun '03

28 Jun '03

"All the Universe's a Fractal, and all the men and women merely pixels . . .. ... ..... ........ " "New Scientist" 21 August 1999. Stay Amazed JoTz

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FOTD 28-06-03 (A Merry Land [4])
by Jim Muth 28 Jun '03

28 Jun '03

FOTD -- June 28, 2003 (Rating 4) Fractal visionaries and enthusiasts: Today's image rates only a 4. This sub-standard rating is justified because the image has a flaw known in the world of visual art as muddiness. Muddiness results when colors with too great a difference in brightness are mixed together. Today's image has exactly this flaw, which earns it the 4. Some of the muddiness can be eliminated by changing the inside color from a flat black 00 00 00 to something like a grey 40 40 40. But nothing can save a fractal picture like today's, which is flawed from the start by too much detail. I named the picture "A Merry Land". The name has nothing to do with the fact that Fractal Central happens to be located in the state of Maryland. I gave it the name because, despite the muddiness, there is a kind of merriness in the picture. The generating formula takes the tiniest bit of Z^100 and adds Z^(-2) to it. Even though the portion of Z^100 is only 1/10^32, this tiny bit overwhelms the Z^(-2) and creates an oversized lopsided hole filled with a triangle. Today's scene is located near the tip of the western arm of the triangle. Like yesterday's image, today's is slow. It takes over one hour to render on my machine. The best way to see the image is to wait an hour or so for Paul and Scott to render it, and avoid the hassle of rendering it yourself by downloading the completed GIF image from one of the FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The sun and temperature of 90F 32C on Friday here at Fractal Central was just what the dynamic fractal cats needed to put them in a good mood. They spent the afternoon romping in the yard and lounging on the porch. At one point the cat from two doors down the hill appeared, lurking behind the holly trees. Luckily, I was there to restrain Tippy, who was ready to start a fight. The day ended peacefully, with a pair of exhausted but hungry cats ready to eat and sleep. Today is starting cloudy and cooler. I've got enough work to keep me busy an hour or so, and there is always the grass to trim. It looks like it will be another normal day here at F.C. The next FOTD will appear in 24 hours. Until then, take care and life could be a never-ending fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Merry_Land { ; time=1:21:18.60--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.67128436773857100/-0.029296149029013\ 39/5.503277e+009/1/116.9017790300461/1.20521654432\ 482617 params=1e-032/100/1/-2/0/0 float=y maxiter=7200 bailout=5 inside=0 periodicity=10 colors=000bQ`cP`dOaM1pWChdNamYVwhPvgOvfOueNudNucNt\ cMtbMtaMs`Ls_LrZKrZKrYKqXJqWJqVJpUIpUIpTIoSHoRHnQG\ nPGnPGmOFmNFmMFlLElKElKEkJDkIDjHCjGCjFCiFBiEBiDBhC\ AhBAj86iA8hBAhCCgEEfFGfGIeIKdJMdKOcMQbNSbOUaQWaRY`\ S__Ua_VcZWeYYgYZiX_kWamWboVcqUetVdsWdrWdrXdqXdqYdp\ YdoZdoZdn_cn`cm`claclackbckbcjcciccidbhebhebgfbffb\ fgbegbehbdhbciacjabjabkaaka`la`la_ma_maZn`Yo`Yo`Xp\ `Xp`Wq`Vq`Vr`UvZVr`UoaTlbTidSfeScfR`hRYiQVjQSlPPmP\ MnOJpOGqNCsMDrNDqNDqNDpNEpNEoNEoNEnNFmOFmOFlOFlOGk\ OGkOGjOGiOHiOHhPHhPHgPIgPIfPIfPIePJdPJdQJcQJcQKbQK\ bQKaQK`QL`QL_QL_RLZRMZRMYRMXRMXRNWRNWRNVRNVSOUSOUS\ OTSOSSPSSPRSPRSPQTQQTQPTQOTQOTRNTRNTRMTRMTSLUSKUSK\ USJUTJUTIUTIUTHURHVTHUUHTVHTWHSYHSZHRWRXUUVSXUQ_TO\ bRMeQJhPHkNFnMDqLBtJ9wI7yH8wI9vJAuJBtKCsKDrLEqLFpM\ GoNHnNImOJlOJkPKjPLiQMhRNgROfSPdSQcTRbTSaUT`VU_VUZ\ WVYWWXXXWXYVYZUZ_TZ`S_aR_ } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 27-06-03 (Deep in Scepter Valley [4])
by Jim Muth 27 Jun '03

27 Jun '03

FOTD -- June 27, 2003 (Rating 4) Fractal visionaries and enthusiasts: Due to an unexpected rush job, today's FOTD is late. Since I had almost no time to find a proper FOTD image, I returned to that old warhorse, the Mandelbrot set and found a scene deep in Scepter Valley. During the 3-1/2 hours the scene was rendering, I accomplished other things. When the image was finished, I named it "Deep in Scepter Valley". I gave almost no attention to coloring the image, which limits it to a rating of a 4 -- a little below average. The average fractalist will have little desire to spend 3-1/2 hours waiting for a below-average scene to finish. I recommend visiting one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> and downloading the completed image from there. I sent Paul and Scott the finished image several hours ago, so it should be posted shortly. The temperature reached 97F 36C here at Fractal Central on Thursday. This was too hot for the sensitive duo, who passed the afternoon under the cool air vent. Their moods were surprisingly good for a day that was so hot. No tuna was needed. Today will once again be hot, but not as hot as yesterday. I expect the duo to have another good day. My day will turn good when I wrap up the unexpected pile of work that came in last evening. The next FOTD will appear on schedule in less that 24 hours. Until then, take care, and be practical. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= DeepInScepterVally { ; time=3:24:13.78--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-1.2537\ 967393837293717/0.02363815462420420844/1.061236e+015 params=0/0 float=y maxiter=12000 bailout=5 inside=0 logmap=2534 periodicity=10 colors=000HabC``GabJadNbfQbhUcjXckVZmTVnRRoQNpPMrP\ MuOLwOLyPUnPbdQkVQsLXoNbkOhgPncQt_RrXQpVQnTQV4OmQQ\ kOQiMPgKPfHPdFPbDP`BO_8OY6OW4O3jM5fN7cN9`NBYNDUNFR\ NHONJLOLIONEOPBOR8OT5OMbNNZOOWOPTOPQOQNORKOt9fy4gw\ 8huBitEjrHkqKloOmnRnlUokXpi_qhbqjankaklahmafnacoa`\ q`Yr`Ws`Tt`Qu`Nv`LmeTei`YngQroEyxIvvLttPrsSoqWmpZk\ naim_klZmkYokXqjWsjVuiTylUviVtgWreWpcXn`YlZZiXZgV_\ eS`cQaaO_aJa_MbYPcWSeVVfTYgR`hPcjOfkMilKlmIooHrpFu\ qDxrCzlHxgLwaQvXUtRZsMbrLapKaoJ`nI`lH`kG_jF_hEZgDZ\ fCZdBYcAYb7_d9YaBX_DVYFUWHSUIRSKPQMOOONLQLJRKHTIFV\ HDXFBZE9X76_D7bI7eN7hS7kX7mZ4na7ncAofDohGpkJuoOpmM\ llLhkJdiI`hHWgFSeEOdCKcB8c1GbAObJWbSca`kaisarzazs`\ sl_lf_f_Z_UYUNYNHXHAWA1Z04W46T88RCBOGDLJFJNIGRKDVM\ BYyK`HCHIGQJKYKOeLSmKYwMVuOStPPsRMrTJpUGoWDnYAmZ7l\ YAjYCiYFhYHgYKfYMeYPdXRbXUaXW`XZ_X`ZXcYXeXVdYUdYTd\ ZRcZQc_Pc_Nb`Mb`LbaJaaIab } END PARAMETER FILE=========================================

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