July 2003 - Fractint - mailman.xmission.com

FOTD 27-07-03 (Nothing in Sight [5])
by Jim Muth 27 Jul '03

27 Jul '03

FOTD -- July 27, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal is a different kind of thing. It is so different in fact that I don't know what to call it. It is like nothing I have seen before, and this is why I named it "Nothing in Sight". I realize that this could raise the philosophical puzzle of whether nothing is actually something, but this is not really a puzzle at all. When a fish sees a gas bubble rising to the surface, it does not see an absence of water, it sees a real object that, assuming fish understand gravity, defies gravity. For that fish, nothing has literally become something. And is not a positron nothing more than the lack of a negative charge? In today's fractal, we are once again in the vicinity of the blazing rectangle of the past two FOTD's. But we have rotated a full 90 degrees from the Julia direction and are viewing the scene in the Rectangular direction, where imag(z) and imag(c) are displayed on the screen. The image has been rotated and unrotated, stretched and unstretched, skewed and unskewed so far that I have lost track of its undistorted appearance. Actually, the undistorted image is the distorted view, and the stretching, etc. is necessary to undistort it. The appearance of X-axis symmetry is illusory. A close inspection will reveal subtle differences. The image is more a curiosity than a work of art, and as such can be rated no higher than a rating of an average 5. (With all the average ratings I give my images, I would make a very poor salesperson.) The render time of 5 minutes is within reason. Downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is also quite reasonable. A hot day Saturday brought out the laziness in the fractal cats. Of course, it takes very little to bring out laziness in old cats. When the temperature hit 90F 32C, they hit their beds, and stayed there most of the afternoon. They didn't get active until the sun was gone from the yard, when they took a short stroll to the holly thicket. Today is supposed to be even hotter, though to me it seems to be starting cooler. It remains to be seen how the duo will adjust. I'm going to adjust by doing as little as possible, except in the world of fractals that is. Until next FOTD, take care, and I do not believe that physical aliens from space are visiting earth, but why then does it concern me so much when I see others who do believe we are being visited? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Nothing_in_Sight { ; time=0:05:28.89--SF5 on a P200 reset=2002 type=formula formulafile=julibrot.frm formulaname=SliceJB-new passes=1 center-mag=-0.000\ 01046291457683/+0.02511627776549527/1353.851/0.065\ 63/89.9392475138482297/0.0607524861518090667 params=0.5/0.5/0/0.5/2.003/0/-1.7435/0/0.00019/0.0\ 7388 float=y maxiter=1000 inside=bof61 logmap=51 periodicity=10 colors=000GADIAFJAHKAJMALNANPAPQARSBTTBVUBXWBZXC`Z\ Cb_Cd`CfbChcDjeDlfDngDpiErjEtlEvmExnEzoGzpIzpKzqMz\ qOzrQzrSzsUzsWztYzt_wubtueqvhnvklwnjwqhytgywhzwhzw\ hzmczjfzgizdczaYzZTzWNzTHzQCyN6xK1wJ5uI9sHDqGHoFLm\ FOkESiDWgC_eBccBfaAj_9nY8rW7vU7yS9wQAuOBsMCqKDoKEm\ MFkOGjQHhSIfTJdVKbXL`ZMZ`NYbOWcPUeQSgRQiSOkTMlULhS\ MdQM`OMXMMTKMPIMLGMHEMDCM9AM59MF8MO7MX6Me6Mc7La8L`\ 9KZAKXBKWCJUDJTEJRFIPGIOIHMKHKMHJOGHQGGSGEUFCWFBYE\ 9_E7aE6cD4eD3gD6iE8kFBmGDnHGnIImJLlKNkLPjMSiNUhOXg\ PZfQaeRcdSecTd`SdYRdWQdTPcQOcONcLMcILcGKbHNaIP`JSZ\ KVYLXXM_WMaUNdTOgSPiRQlPRoOSqNTtLSwMTvMTvMTvMTvNTv\ NTvNTvNTvNUvOUvOUvOUvOUvPUvPUvPUvPVuRVuQVuUVuQVuXV\ uRVu_VuRWubWuRWueWuSWuhWuSWukYvSXunWuTVtqVtUUttTsU\ SswSsVRrzQrWPrzPqXOqzOqYQpzSpZUozWo_Yoz_n_anzcn`em\ zgmaimzklbmlzopaqnzslcukzwiezhzzfgzdzzcizazz`kzZzz\ YlzWzzUnzTzzRpzQzzODzfzza } frm:SliceJB-new {; by John R. H. Goering, July 1999 pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1), b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), 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)+(p4), z=r+flip(s)+(p5): z=z^(p3)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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RE: Four Dimensional Scene
by harrybissell 26 Jul '03

26 Jul '03

<delurk mode> its an 8 for sure. beautiful piece <relurk mode> H^) harry

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FOTD 26-07-03 (Blazing Rectangle-2 [5])
by Jim Muth 26 Jul '03

26 Jul '03

FOTD -- July 26, 2003 (Rating 5) Fractal visionaries and enthusiasts: In today's image we take another look at the rectangle that caught fire in yesterday's image. That rectangle, which is located in the Z^2.003+C Julia set with a C-value of -1.7435, at the Z-coordinates of 0.00019,0.07388 and at a magnitude of 100, is one of the most curious things I have yet discovered in the world of fractals. When viewed as a Julia set, it is as perfect a rectangle as one will find in any random fractal. But the slightest deviation from the Julia orientation has a devastating effect on it. A rotational deviation of as much as 1 degree totally destroys the perfection of the rectangular shape and produces a curvilinear quadrilateral such as we have in today's image. Changing the imaginary part of the C-value even the slightest distance from zero has an even more devastating effect. The entire rectangle rapidly falls apart into fractal debris and vanishes into the fractal ether. Since today's image is another sequel, I have named it "Blazing Rectangle-2". As an FOTD, it rates an average 5, but hey, the average FOTD is nothing to be sneezed at. And the render time of 5 minutes is fast enough to make the attached parameter file a near-joy to run. Those who prefer the acquisition of their fractals to be total ecstasy may download the completed GIF image file from one of the two FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday, with its brilliant sun and temperature of 86F 30C, turned out to be one of those rare perfect summer days here at Fractal Central. The fractal cats were in one or their rare near-perfect moods as they passed the afternoon in the yard. My mood was a bit less than perfect as the work piled up faster than I could accomplish it. Today's weather is promising to be less than perfect, but still quite pleasant. If I can finish the modicum of work by noon, I'll have a pleasant enough day. And I'm certain to find an interesting fractal before the day ends. To see that interes- ting fractal, check back here in 24 hours. Until then, take care, and is truth a fractal? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ BlazingRectangle-2 { ; time=0:04:59.97--SF5 on a P200 reset=2002 type=formula formulafile=julibrot.frm formulaname=SliceJB-new passes=1 center-mag=+0.004\ 99268009490636/-0.00325779513771971/76.89922 params=0.5076/0.5037/0.49256/0.49876/2.003/0/-1.74\ 35/0/0.00019/0.07388 float=y maxiter=1000 inside=bof61 logmap=51 periodicity=10 colors=000GADIAFJAHKAJMALNANPAPQARSBTTBVUBXWBZXC`Z\ Cb_Cd`CfbChcDjeDlfDngDpiErjEtlEvmExnEzoGzpIzpKzqMz\ qOzrQzrSzsUzsWztYzt_wubtueqvhnvklwnjwqhytgywhzwhzw\ hzmczjfzgizdczaYzZTzWNzTHzQCyN6xK1wJ5uI9sHDqGHoFLm\ FOkESiDWgC_eBccBfaAj_9nY8rW7vU7yS9wQAuOBsMCqKDoKEm\ MFkOGjQHhSIfTJdVKbXL`ZMZ`NYbOWcPUeQSgRQiSOkTMlULhS\ MdQM`OMXMMTKMPIMLGMHEMDCM9AM59MF8MO7MX6Me6Mc7La8L`\ 9KZAKXBKWCJUDJTEJRFIPGIOIHMKHKMHJOGHQGGSGEUFCWFBYE\ 9_E7aE6cD4eD3gD6iE8kFBmGDnHGnIImJLlKNkLPjMSiNUhOXg\ PZfQaeRcdSecTd`SdYRdWQdTPcQOcONcLMcILcGKbHNaIP`JSZ\ KVYLXXM_WMaUNdTOgSPiRQlPRoOSqNTtLSwMTvMTvMTvMTvNTv\ NTvNTvNTvNUvOUvOUvOUvOUvPUvPUvPUvPVuRVuQVuUVuQVuXV\ uRVu_VuRWubWuRWueWuSWuhWuSWukYvSXunWuTVtqVtUUttTsU\ SswSsVRrzQrWPrzPqXOqzOqYQpzSpZUozWo_Yoz_n_anzcn`em\ zgmaimzklbmlzopaqnzslcukzwiezhzzfgzdzzcizazz`kzZzz\ YlzWzzUnzTzzRpzQzzODzfzza } frm:SliceJB-new {; by John R. H. Goering, July 1999 pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1), b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), 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)+(p4), z=r+flip(s)+(p5): z=z^(p3)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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Multifractal_7
by Albrecht.Niekamp＠t-online.de 26 Jul '03

26 Jul '03

Hi, the new multifractal edition now has 8 formulas to choose, a phoenix type is now available and a spider type. The maximum now has been reached concerning the structure of the formula and the possible amount of inputs. Another fundamental improvement is that the "warp-effect" now is used in two different ways: If reset is checked "z" is set to the basic value and the effect, if enabled, is applied to the input. If reset is not checked the effect, if enabled, is applied to "z" which generates a different image, of course. This means a whole lot of new possibilities and is especially useful in case of sensitive inputs such as Julia, Spider, Phoenix. So there are four different ways to control each in/out part of the image, with or without reset and with or without thw warp-effect, which by itself can be modified in many ways. Fractal greetings, Al --------------------------------start-frm---------------------- FRM:Multifractal_7 { ; Albrecht Niekamp 240703 ;p1 (spider)julia-seed ;real(p2) 5digits: frm-use: shape, outside, inside1, inside2, inside3 ; 0_off 1_secant/mand 2_bees/jul 3_m_mods/phoen 4_newt/spider +5_reset ; input2 : 2digits_many-mods 2digits_phoenix 2digits_spider ; 5digits_secondary frm use : 0_no 1_yes +5_warp ;imag(p2)(-) 2-4digits : quasinewton input (max 2000) ; 1digit : no many_mods multipl. 1_out 2_in1 3_in2 4_all ; 1digit : iter-reset 1_out 2_in1 3_in2 4_all ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) many_mods bailout, bailout ;imag(p3) shape : factor (fn1), outside : border-in (5digits+fract) ;real(p4) outside : factor (fn2), border-out (5digits+fract) ;imag(p4) inside1 : maxiter1, 5digits_factor1 (fn2) ;real(p5) inside2 : maxiter2, 5digits_factor2 (fn3) ;imag(p5) inside3 : maxiter3, 5digits_factor3 (fn4) ;fn(1) is shared by many_mods, bees da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 d=trunc(dd/10000) t=d>5 dd=dd-d*10000 d=d-5*t d3=(d==2)+(d==4) d4=(d3==0) vb=(d==3)+(d==4) 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) ; 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 ab=(d==2)+(d==7) da=da-d*10000 d=trunc(da/1000) w1=d>4 ab1=(d==2)+(d==7) da=da-d*1000 d=trunc(da/100) w2=d>4 ab2=(d==2)+(d==7) da=da-d*100 d=trunc(da/10) w3=d>4 ab3=(d==2)+(d==7) d=round(da-d*10) w4=d>4 ab4=(d==2)+(d==7) tt=ex0+ex1+ex2+ex3+ex4 ; 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 ; mo=vb>ab mo1=v1m>ab1 mo2=v2m>ab2 mo3=v3m>ab3 mo4=v4m>ab4 ; sc=((ab+vb)==0) sc1=((ab1+v1m)==0) sc2=((ab2+v2m)==0) sc3=((ab3+v3m)==0) sc4=((ab4+v4m)==0) ; px=((ab+vb)==2) px1=((ab1+v1m)==2) px2=((ab2+v2m)==2) px3=((ab3+v3m)==2) px4=((ab4+v4m)==2) ; if (d4) z=0 if (vb) if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel endif else c=pixel z=pixel*sc endif else c=p1 z=pixel endif t=0 u=d3 bo=z p=pp z0=p7 zold=(0.0,0.0) cb=p9 : If (tt) t=t+1 if ((ex0) && bo>b0) u=2*(fn1(t/sfac)) if (d4) z=z*u if (mo) c=0.4*log(sqr(pixel^mm)) ba=mb else c=pixel endif else z=pixel cb=p9*u c=p1*u p=pp*u endif ex0=0 tt=tt-1 elseif ((ex1) && bo>b1 && bo<b2) if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif rs=rs1 ab=ab1 if (dd1) if (rs) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif vb=v1j d3=1 else d3=0 if (rs) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v1m if (mo1) 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) if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif rs=rs2 ab=ab2 if (dd2) if (rs) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v2j d3=1 else d3=0 if (rs) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v2m if (mo2) 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) if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif ab=ab3 rs=rs3 if (dd3) if (rs) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v3j d3=1 else d3=0 if (rs) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) 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) if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif ab=ab4 rs=rs4 if (dd4) if (rs) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v4j d3=1 else d3=0 if (rs) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v4m if (mo4) 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) 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) zt=z*z+ph-0.5*zold ;Phoenix Mike Wareman zold=z z=zt else z2=fn1(z)+c ;Many_mods Linda Allison q=cos(z2) z=c*(1-q)/(1+q) 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) z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 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 } -------------------------------------------start-par--------------------- downmix { ; inside spider-newton-phoenix ; Albrecht Niekamp July, 03 ; ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=cos/exp/exp/exp passes=t center-mag=0.453671/1.33227e-015/1.323725/1/-90/3.88578058618804789e-016 params=-0.02237006744590594/-0.07473982970671712/10498.32595010101/5000.\ 0608020602/2048.04084/384.0000045/384.00024/256.0076800000001/512.007680\ 0000001/768.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200677<21>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0d\ q0es<3>0kz<25>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>00\ 0<24>n00p00r00<3>y00<25>B00900700<3>000<2>455 } spinewphoesec { ; Albrecht Niekamp July, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=cos/exp/exp/sin passes=t center-mag=-8.88178e-016/-8.88178e-016/1.041667/1/-90/3.8857805861880478\ 9e-016 params=-0.02237006744590594/-0.07473982970671712/40986.3259501001/5000.0\ 608020602/2048.04094/384.0000045/384.00024/256.00768/768.0076800000001/1\ 024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200677<21>hiijkkkll<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0d\ q0es<3>0kz<25>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3>00\ 0<24>n00p00r00<3>y00<25>B00900700<3>000<2>455 } Secantflyer { ; Albrecht Niekamp July, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=cos/exp/exp/sin passes=t center-mag=0.312805/0/0.6666667 params=-0.02237006744590594/-0.07473982970671712/31997.32595010605/5000.\ 0608020602/2048.04094/384.0000045/384.00024/256.00768/768.0076800000001/\ 1024.00768 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=2000gt<22>09C08A068<2>022000111<24>niQpjRrlS<3>ysX<25>BB7996775<3\ >000<24>n00p00r00<3>y00<25>B00900700<3>000<2>455677899ABBBCC<18>hiijkkkl\ l<3>rss<21>HIIFGGEFF<3>677455344122000<25>0bo0dq0es<3>0kz0jx0hv } Double_image { ; Time 0.19.43.53 ; Albrecht Niekamp July, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t center-mag=0.426332/6.66134e-016/1.344086/1/-90/-1.23373533611470521e-01\ 4 params=-0.02237006744590594/-0.07473982970671712/10482.64595310601/5040.\ 0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\ 12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000bo<19>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslS\ unT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23\ >eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<4>\ 0dq } Layers { ; of the onion ; Albrecht Niekamp July, 03 ; Time 1.33.03.85 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t center-mag=0.972387/-0.248155/26.88172/1/-90/-1.23373533611470521e-014 params=-0.02237006744590594/-0.07473982970671712/10482.64595110606/5040.\ 0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\ 12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=2000bo<19>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslS\ unT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23\ >eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<4>\ 0dq } Hanging_gardens { ; of Semiramis ; Albrecht Niekamp July, 03 ; Time 0.48.12.55 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t center-mag=+0.36133792768156270/-0.64229253619003070/116197.8/1/-90/3.88\ 578058618804789e-016 params=-0.02237006744590594/-0.07473982970671712/10482.64595110606/5040.\ 0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\ 12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000JQ<12>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3\ >e`LgbMidN<3>qjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25\ >C00A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<10\ >0IO } mm_meets_spider { ; Time 0.36.26.15 ; Albrecht Niekamp July, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t center-mag=+0.36139649738980650/-0.64231765276418100/11619.78/1/-90/-1.2\ 3373533611470521e-014 params=-0.02237006744590594/-0.07473982970671712/10482.64595110656/5040.\ 0608020602/82048.02048000001/384.0000045/384.00024/128.00768/184.00768/5\ 12.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200555<20>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0b\ o0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslS\ unT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000222\ 444 } Ying&Yang { ; Time 0.19.14.27 ; Albrecht Niekamp July, 03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/cosxx/cos/sin passes=t center-mag=+0.38684901922323730/-0.63969404719008790/37.1833/1/-90/-1.23\ 373533611470521e-014 params=-0.02237006744590594/-0.07473982970671712/10437.32595910656/5000.\ 0608020602/82048.02048000001/384.0000045/384.00024/128.00768/190.0076800\ 000001/384.0076800000001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200pppqqqsss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08\ A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslSunT<2>zsX<25>CB7A96875\ <3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>eeegggiiijjjlllnnn } The_Brain { ; Time 0.02.53.45 ; Albrecht Niekamp July, 03 ; Shape Phoenix ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_7 function=sin/sin/exp/sin passes=t center-mag=0/0/0.6666667 params=-0.02237006744590594/-0.07473982970671712/32946.32595710155/5000.\ 0608020602/2048.04094/384.0001645/384.00048/128.00768/384.0076800000001/\ 512.0076800000001 float=y maxiter=2048 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200033021000<4>984BA5DC6FE7HF8JH9<13>jeNlgOniPpjQrlRtnS<2>ysW<25>\ BB6995774553442220000<24>n00p00r00<3>y00<25>B00900700<3>000221<4>9A9BCBD\ EDFGFGHG<15>hihjkjklk<3>rsr<21>HIHFGFEFE<3>676454343121000<25>0bn0dp0er<\ 3>0ky<28>055 } ---------------------------------------------------------------------------- ----end-----------------------

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FOTD 25-07-03 (Blazing Rectangle [6])
by Jim Muth 25 Jul '03

25 Jul '03

FOTD -- July 25, 2003 (Rating 6) Fractal visionaries and enthusiasts: After discovering that the fourth spatial dimension was in my back pocket, I went searching. Maybe I searched in the wrong pair of pants, but I suspect that the extra dimension slipped off into hyperspace while I was not looking, and has escaped for good. What a disappointment -- having a visualization of the fourth dimension so close and then losing it. I guess I'll never see a hypersphere in the condition of double rotation, or a pseudosphere in its infinite entirety. Today's image appears to be rotating. It is a slightly enlarged and distorted view of a small part of yesterday's image, on which I have used a more flexible Fractint generating formula so that I would have more angles to examine. The angle of today's slice is once again very close to, but not exactly, the Julia direction. That slight rotation explains the "Blazing Rectangle" name. The feature in the center of today's image has a roughly rectangular shape, but it is not rectangular enough to justify the word 'rectangle'. Where then is the rectangle? The rectangle is actually very close, but it is hiding. To see the near-perfect rectangle, change both parts of the p1 and the p2 parameters to exactly 0.5 and re-render the image. It takes only a minute or two. Now the rectangle is visible, revealed in all its near-perfect glory at the center of the frame. Actually, I easily might have used the pure Julia version of today's scene as the FOTD of the day, but the distorted version has more action, and the pure Julia version doesn't appear to be blazing. I rated the image at a 6, which equals a bit above average. After searching carefully, I could find little that has not been seen before. (Originality in doing old things rates high with me.) The render time of 2 minutes is unusually short, due mostly to the low magnitude of only 44. Those who download their FOTD images will find today's posted as usual to Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A perfect day on Thursday, with a temperature of 81F 27C, produced perfect cats. Tippy was a bit too perfect when he viciously attacked my ankle like he used to do long ago when he was still a kitten and wanted to be played with. To see if he was feeling playful, I took the feather on a string from its shelf, where it had rested untouched for several years, and to my surprise, Tippy actually leaped around chasing it. Thomas watched the activity with interest, but weighing over 17 pounds, declined to participate. At the end of the day, both Tippy and Thomas were exhausted, and needed no additional treat before settling down for the night. Today looks like it will be a repeat. I'll make a full report in tomorrow's FOTD, which will appear in 24 or so hours. Until then, take care, and what do you call someone who wastes his time talking about stuff he does not believe in? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Blazing_Rectangle { ; time=0:02:19.51--SF5 on a P200 reset=2002 type=formula formulafile=julibrot.frm formulaname=SliceJB-new center-mag=-0.0021281/-0.1\ 47743/44.02148/1/140/5.12714870559705105e-014 params=0.5013/0.5007/0.5016/0.5012/2.003/0/-1.7435\ /0/0.00019/0.07388 float=y maxiter=2000 passes=1 inside=bof61 logmap=34 periodicity=10 colors=000zFzzFzzFzyFzxFzvFzuFzsFzrFzpFzoFzmFzlFzj\ FziFzgFzdFzaFz_FyXFxTFvQFuOFsLFrIFpFFoCFm9Fl6Fi3Ff\ 0Fc0F`0FY0FV0FS0DP0CM4AJC9IJDCQJMXOGcSCjY6ra1yf0zj\ 0zl0zm0zm0zo0zp0yp0xr0xs0vs0vu0uv0uv0sx0ry0ry0pz0p\ z1oz1mz3mz3lz3lz4jz4jz4gz9dxDasG_oLXjOTfSQaVOY_MTa\ JOfGJjDFmAAr76u41y10z00z00z10z40z70zA0xD0uG0rJ0oM0\ lP0iS1fV3cY3``4Yc6Vf7Si9PlAMoALpGPrMSsSVuY_vcaxidy\ ogzulzzozzrzzuuzrjzoazlSziIzf9xc0v`0u_0xa9ycJzdSzf\ `zgjziszjzzlyzjvziuygrvgosfmpdjmdgjcfgacd````_Y_XV\ YTSYSPXPMVMJTLGTIDSFAQD7QTJLgVGxfCzp7zsCzuFyvJuxMp\ yQmzTizXdz``zcXzgSzjPzmOzoMzpLzrJxsIuuGsvFpxDmyCjz\ Agz9dz7cz6`z4Yz3Vz1Sz0Qz3Oz4Mz6Jz9IvAGsCDpDClG9iI7\ fJ6aL3_O1XP0SQ0PS0MQ0OP0OM0PGSOCPJ9MG6JD1G90D60A30\ 7004001003334CA6MJ7VS9d_AmgCxoCzmAzl9uj7oi6ig4cf4_\ d3Tc1Oa0I`0C`07_1F_3M_4S_7_xoMzmPzjQziTzgXzf_zd`za\ _z_YxXXuTXpQVmPTiMTfJScGQ } frm:SliceJB-new {; by John R. H. Goering, July 1999 pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1), b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), 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)+(p4), z=r+flip(s)+(p5): z=z^(p3)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 24-07-03 (Four-Dimensional Scene [?])
by Russell Walsmith 24 Jul '03

24 Jul '03

The "4-D" fractal definitely transcends any rating schema, as it is much more than the sum of its pixels; it provokes the mind into all sorts of haunting imagery. A 'metaphysical' definition of art that I am fond of is "That which uses those things in the realm of illusion to point beyond the illusion" and that's a quality I discern here... good one... Russell -- --------- Original Message --------- DATE: Thu, 24 Jul 2003 09:47:00 From: Jim Muth <jamth(a)mindspring.com> To: fractint(a)mailman.xmission.com Cc: philofractal(a)lists.fractalus.com > >FOTD -- July 24, 2003 (Rating ?) > >Fractal visionaries and enthusiasts: > >How does one answer the question, "Where is the fourth spatial >dimension?" This, in my opinion, is one of the most puzzling >questions that has ever been asked. We know where it would be >if it existed, but it cannot exist. There is no room for it. >Three-dimensional space is all there is. Yet it does exist. >Using numbers, we can take apart and examine 4-D hyperspace as >rigorously as we examine three-dimensional space. I suspect >that the inability to perceive 4-D space is a limitation of our >awareness, and that the fourth dimension is there all around us, >if only we had eyes to see. How to open our eyes and adjust our >numbers is anyone's guess. > >Today's image is a scene in the Z^2.003+C Julibrot. Julibrots >are four-dimensional things that, sliced in one direction give >Julia sets and, sliced in another direction, give perturbed >Mandelbrot sets. Of course, being hypersolid, the 4-D Julibrot >can also be sliced in oblique directions between the Julia and >Mandelbrot directions. > >Today's scene is sliced in a direction only one degree from the >Julia direction, but that single degree makes a world of differ- >ence. (To see the pure Julia set, change imag(p1) from 89 to >90.) The Z^2.003+C Mandeloid is shaped almost exactly like the >classic Mandelbrot set, whose formula is Z^2+C, the major change >being along the negative stem, which has split into an infinity >of curving, infinitely-divided filaments. The large midget at >-1.75 has also started to split, and today's scene is located in >the East Valley of this midget, which has broadened into a much- >divided wedge-shaped thing. > >I have given the image the name "Four-Dimensional Scene", which >is a fair description. But I am undecided on the worth of the >picture, which comprises all there is of the fractal. Sometimes >I think it is worth an 8, then I view it again and see an image >worth only a 4. The image will likely go unrated. > >The modest render time of X minutes can be avoided by download- >ing the finished GIF image from: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > >or from: > > <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> > >Though it was quite humid, the temperature rose no higher than >84F 29C and no rain fell here at Fractal Central on Wednesday, >giving the dynamic fractal cats a most pleasurable day. The >good weather also helped conserve the stressed tuna population, >since no treat was necessary. > >Today is promising to be a slightly less humid repeat. I expect >a repeat from the fractal cats. More good news is that the work >shelf is filling up. And the best news of all is that I shall >return in 24 hours with another glorious fractal. Until then, >take care, and when I started the FOTD on the Fractal-Art list >in April of 1997, I expected to keep it going maybe a week or >two. > > >Jim Muth >jamth(a)mindspring.com >jimmuth(a)aol.com > > >START 20.0 PAR-FORMULA FILE================================ > >4-DimensionalScene { ; time-0:06:55.34--SF5 on a p200 > reset=2002 type=formula formulafile=allinone.frm > formulaname=multirot-XY-ZW-new function=ident/flip > center-mag=-0.0156752/-0.0738926/7.021696/1/-90/3.\ > 88578058618804789e-016 params=90/89/2.003/0/0.0001\ > 9/0.07388/-1.7435/0 float=y maxiter=8000 inside=0 > passes=1 logmap=yes periodicity=10 > colors=0000000000000000200400600830A60C90EC0GF0II4\ > KL6MOAOREQUGSXJU_LWbPYeT_hVakZcnbeqdgtgiwhjzikzjmz\ > kmzlmzmmznmzomzpmzqozrqzssztuvuvnvogugTkbEbV0XR0VP\ > 0VN0TN0TL0RJ0RJ0PH0PG0PG0RL2RP8RVERZJRbPRgVRk`RqdU\ > uicxomzurzzzzzvzzrzzmzzhzzfzoosbxiPz`CzT0ob4Rk82uC\ > 0zE0zG0xH0vJ0sL0qN0oP0mR4iR6gTAeVEdXG`ZJZ`NXbbGRPV\ > bCim0xv0zz0zz0zz0zz0oz0dz0Ru0Eq00m00i40g`6ez0mzEeq\ > R`ddVPqNCzH0z00zC8zLJzXTzebzoezigxeigbkRZk2NmAVoH`\ > qPesXkudqvkvxszzzzzzzxuzvqzukzsezqbzoXxoRvmNukHuiC\ > sg8qe2od0md0md0qd8udGxdNzdVzdbz``zXZzTXxPXuLVqJToG\ > RkCRg8Pe4Nb0Na2N`H40RE0`N6iXCseJzoPzxXdbzdbzdbzdbz\ > dbzdbzdbzdczcczcczcczcczcczcczcczcczcczcczcczcczcc\ > zcczcczhc0mc0rc0vc0zV0zT2zP8zLEzJHzGNcczz8Zz6dz2iz\ > 0oz0s20z40z60z60z86zAAzAEzCJzENvERuGZsGdqHioHomJuk\ > JziLzgLzeNzdNzbPz`Pz`NzdNzeNzgNziNzkNzoNzqNzsNzuNz\ > vGsqAmm4gi0be0X`0RX0LT0GP } > >frm:multirot-XY-ZW-new {; draws 6 planes and rotations >;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J >;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J >a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, >z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, >c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: >z=z^(p2)+c, >|z| <= 36 } > >END 20.0 PAR-FORMULA FILE================================== > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

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Re: [Fractint] FOTD 24-07-03 (Four-Dimensional Scene [?])
by Fr. Jim Lacasse 24 Jul '03

24 Jul '03

Jim I would rate today as a 6 or 6.5. I see the openings as the entrance to something, not sure what. Jim LaCasse >>> jamth(a)mindspring.com 07/24/03 06:47AM >>> FOTD -- July 24, 2003 (Rating ?) Fractal visionaries and enthusiasts: How does one answer the question, "Where is the fourth spatial dimension?" This, in my opinion, is one of the most puzzling questions that has ever been asked. We know where it would be if it existed, but it cannot exist. There is no room for it. Three-dimensional space is all there is. Yet it does exist. Using numbers, we can take apart and examine 4-D hyperspace as rigorously as we examine three-dimensional space. I suspect that the inability to perceive 4-D space is a limitation of our awareness, and that the fourth dimension is there all around us, if only we had eyes to see. How to open our eyes and adjust our numbers is anyone's guess. Today's image is a scene in the Z^2.003+C Julibrot. Julibrots are four-dimensional things that, sliced in one direction give Julia sets and, sliced in another direction, give perturbed Mandelbrot sets. Of course, being hypersolid, the 4-D Julibrot can also be sliced in oblique directions between the Julia and Mandelbrot directions. Today's scene is sliced in a direction only one degree from the Julia direction, but that single degree makes a world of differ- ence. (To see the pure Julia set, change imag(p1) from 89 to 90.) The Z^2.003+C Mandeloid is shaped almost exactly like the classic Mandelbrot set, whose formula is Z^2+C, the major change being along the negative stem, which has split into an infinity of curving, infinitely-divided filaments. The large midget at -1.75 has also started to split, and today's scene is located in the East Valley of this midget, which has broadened into a much- divided wedge-shaped thing. I have given the image the name "Four-Dimensional Scene", which is a fair description. But I am undecided on the worth of the picture, which comprises all there is of the fractal. Sometimes I think it is worth an 8, then I view it again and see an image worth only a 4. The image will likely go unrated. The modest render time of X minutes can be avoided by download- ing the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though it was quite humid, the temperature rose no higher than 84F 29C and no rain fell here at Fractal Central on Wednesday, giving the dynamic fractal cats a most pleasurable day. The good weather also helped conserve the stressed tuna population, since no treat was necessary. Today is promising to be a slightly less humid repeat. I expect a repeat from the fractal cats. More good news is that the work shelf is filling up. And the best news of all is that I shall return in 24 hours with another glorious fractal. Until then, take care, and when I started the FOTD on the Fractal-Art list in April of 1997, I expected to keep it going maybe a week or two. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ 4-DimensionalScene { ; time-0:06:55.34--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip center-mag=-0.0156752/-0.0738926/7.021696/1/-90/3.\ 88578058618804789e-016 params=90/89/2.003/0/0.0001\ 9/0.07388/-1.7435/0 float=y maxiter=8000 inside=0 passes=1 logmap=yes periodicity=10 colors=0000000000000000200400600830A60C90EC0GF0II4\ KL6MOAOREQUGSXJU_LWbPYeT_hVakZcnbeqdgtgiwhjzikzjmz\ kmzlmzmmznmzomzpmzqozrqzssztuvuvnvogugTkbEbV0XR0VP\ 0VN0TN0TL0RJ0RJ0PH0PG0PG0RL2RP8RVERZJRbPRgVRk`RqdU\ uicxomzurzzzzzvzzrzzmzzhzzfzoosbxiPz`CzT0ob4Rk82uC\ 0zE0zG0xH0vJ0sL0qN0oP0mR4iR6gTAeVEdXG`ZJZ`NXbbGRPV\ bCim0xv0zz0zz0zz0zz0oz0dz0Ru0Eq00m00i40g`6ez0mzEeq\ R`ddVPqNCzH0z00zC8zLJzXTzebzoezigxeigbkRZk2NmAVoH`\ qPesXkudqvkvxszzzzzzzxuzvqzukzsezqbzoXxoRvmNukHuiC\ sg8qe2od0md0md0qd8udGxdNzdVzdbz``zXZzTXxPXuLVqJToG\ RkCRg8Pe4Nb0Na2N`H40RE0`N6iXCseJzoPzxXdbzdbzdbzdbz\ dbzdbzdbzdczcczcczcczcczcczcczcczcczcczcczcczcczcc\ zcczcczhc0mc0rc0vc0zV0zT2zP8zLEzJHzGNcczz8Zz6dz2iz\ 0oz0s20z40z60z60z86zAAzAEzCJzENvERuGZsGdqHioHomJuk\ JziLzgLzeNzdNzbPz`Pz`NzdNzeNzgNziNzkNzoNzqNzsNzuNz\ vGsqAmm4gi0be0X`0RX0LT0GP } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE================================== _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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FOTD 24-07-03 (Four-Dimensional Scene [?])
by Jim Muth 24 Jul '03

24 Jul '03

FOTD -- July 24, 2003 (Rating ?) Fractal visionaries and enthusiasts: How does one answer the question, "Where is the fourth spatial dimension?" This, in my opinion, is one of the most puzzling questions that has ever been asked. We know where it would be if it existed, but it cannot exist. There is no room for it. Three-dimensional space is all there is. Yet it does exist. Using numbers, we can take apart and examine 4-D hyperspace as rigorously as we examine three-dimensional space. I suspect that the inability to perceive 4-D space is a limitation of our awareness, and that the fourth dimension is there all around us, if only we had eyes to see. How to open our eyes and adjust our numbers is anyone's guess. Today's image is a scene in the Z^2.003+C Julibrot. Julibrots are four-dimensional things that, sliced in one direction give Julia sets and, sliced in another direction, give perturbed Mandelbrot sets. Of course, being hypersolid, the 4-D Julibrot can also be sliced in oblique directions between the Julia and Mandelbrot directions. Today's scene is sliced in a direction only one degree from the Julia direction, but that single degree makes a world of differ- ence. (To see the pure Julia set, change imag(p1) from 89 to 90.) The Z^2.003+C Mandeloid is shaped almost exactly like the classic Mandelbrot set, whose formula is Z^2+C, the major change being along the negative stem, which has split into an infinity of curving, infinitely-divided filaments. The large midget at -1.75 has also started to split, and today's scene is located in the East Valley of this midget, which has broadened into a much- divided wedge-shaped thing. I have given the image the name "Four-Dimensional Scene", which is a fair description. But I am undecided on the worth of the picture, which comprises all there is of the fractal. Sometimes I think it is worth an 8, then I view it again and see an image worth only a 4. The image will likely go unrated. The modest render time of X minutes can be avoided by download- ing the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Though it was quite humid, the temperature rose no higher than 84F 29C and no rain fell here at Fractal Central on Wednesday, giving the dynamic fractal cats a most pleasurable day. The good weather also helped conserve the stressed tuna population, since no treat was necessary. Today is promising to be a slightly less humid repeat. I expect a repeat from the fractal cats. More good news is that the work shelf is filling up. And the best news of all is that I shall return in 24 hours with another glorious fractal. Until then, take care, and when I started the FOTD on the Fractal-Art list in April of 1997, I expected to keep it going maybe a week or two. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ 4-DimensionalScene { ; time-0:06:55.34--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip center-mag=-0.0156752/-0.0738926/7.021696/1/-90/3.\ 88578058618804789e-016 params=90/89/2.003/0/0.0001\ 9/0.07388/-1.7435/0 float=y maxiter=8000 inside=0 passes=1 logmap=yes periodicity=10 colors=0000000000000000200400600830A60C90EC0GF0II4\ KL6MOAOREQUGSXJU_LWbPYeT_hVakZcnbeqdgtgiwhjzikzjmz\ kmzlmzmmznmzomzpmzqozrqzssztuvuvnvogugTkbEbV0XR0VP\ 0VN0TN0TL0RJ0RJ0PH0PG0PG0RL2RP8RVERZJRbPRgVRk`RqdU\ uicxomzurzzzzzvzzrzzmzzhzzfzoosbxiPz`CzT0ob4Rk82uC\ 0zE0zG0xH0vJ0sL0qN0oP0mR4iR6gTAeVEdXG`ZJZ`NXbbGRPV\ bCim0xv0zz0zz0zz0zz0oz0dz0Ru0Eq00m00i40g`6ez0mzEeq\ R`ddVPqNCzH0z00zC8zLJzXTzebzoezigxeigbkRZk2NmAVoH`\ qPesXkudqvkvxszzzzzzzxuzvqzukzsezqbzoXxoRvmNukHuiC\ sg8qe2od0md0md0qd8udGxdNzdVzdbz``zXZzTXxPXuLVqJToG\ RkCRg8Pe4Nb0Na2N`H40RE0`N6iXCseJzoPzxXdbzdbzdbzdbz\ dbzdbzdbzdczcczcczcczcczcczcczcczcczcczcczcczcczcc\ zcczcczhc0mc0rc0vc0zV0zT2zP8zLEzJHzGNcczz8Zz6dz2iz\ 0oz0s20z40z60z60z86zAAzAEzCJzENvERuGZsGdqHioHomJuk\ JziLzgLzeNzdNzbPz`Pz`NzdNzeNzgNziNzkNzoNzqNzsNzuNz\ vGsqAmm4gi0be0X`0RX0LT0GP } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 23-07-03 (Activity-2 [7])
by Jim Muth 23 Jul '03

23 Jul '03

FOTD -- July 23, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's FOTD takes us to a world very similar to the world of yesterday's image. This explains the name "Activity-2". The parent fractal is another distorted Mandel-thing with a single large bay and a multitude of tiny budlets. Today's scene is located in the filament of a star connected to a high-order budlet on the northeastern shore of the large bay. The generating formula subtracts 1.2 parts of (1/Z) from Z^(1.2) and adds (1/C). Once again I rendered the image with the outside set to the 'atan' option. In fractals as in movies, the sequel is rarely as good as the original, so today's image rates only a 7, which is still a fine rating, but not quite up to yesterday's rating of 8. The render time I wrote for today's image is a rough average. For some reason, the image never seems to render at the same speed twice. The time has been as short as 6:50 and as long as 8:30. But the exact time required for rendering is unimportant, for the completed image may be downloaded 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> A light shower fell just after noon on Tuesday here at Fractal Central. It left the grass just wet enough to spoil the fractal cats' outing in the yard. When the rain was not falling, the sky was partly cloudy. The temperature of 88F 31C felt more like 98 (37) due to the high humidity. A heavy thunder-shower moved in after dark, but by then it made no difference. The cats' day had already been spoiled. Today is forecast to be a repeat. No problem however. The cupboard is filled with tuna. But my work shelf is still quite empty. In the unlikely event that this empty-shelf syndrome continues, it could develop into a problem that tuna cannot solve. In any case, I'll return in 24 hours with the next fractal. Until then, take care, but don't forget to have fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Activity-2 { ; time=0:07:30.00--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.70588265541529430/+0.874913710082279\ 70/7.816022e+010/1/72.5/-0.000115336616405538328 params=1/1.2/-1.2/-1/0/0 float=y maxiter=1200 inside=0 outside=atan periodicity=10 colors=000zmnzmmzmkzmjzmhzmgzmezkdyibygaye_ycZxaXx\ _WxYUxWTySRyOQyKOyHNyFLyDKyCIyAHy8Fy7Ex8Fw8Fv8Fv8G\ u8Gt8Gt9Hs9Hr9Hq9Iq9Ip9IoAJoAJnAJmAKmAKlAKkBLjBLjB\ LiBMhBMhBMgCNfCNfCNeCOdCOcCOcDPbDPaDPaDQ`DQ_DQZERZ\ ERYERXESXESWESVFTVFTUFTTFUSFUSFURGVQGVQGVPGWOGWPFV\ OGWOHXOIXOIYOJYOKZOL_OL_NM`NN`NNaNOaNPbNQcNQcNRdNS\ eMSgMTiMUkMVmMVoMWqMXrMYsLYtL_uLavLcwLexLgyLizLjzL\ kzKlzKmzKnzKozKpzKqyKrxKswNtvMuuLwtKusJsrIqqHopGmo\ FknEimDglDekCcjBaiA_h9Yg8Wf7Ue6Sd5Qc4Ob3Ma1K`3Ia4G\ a6Eb7Cb9CcADcCEdDFdFG0000IH0000LJ0000NL0PM0000SO0T\ PiVQiWQjYRjZSk`TkaUkcVldWleXmgYmhZnwZzw_zm`onaopbp\ qcpsdqteqvfrwgrxgrwhqwhqwhpvhpvhovhoviouinuinuimui\ mtimtjltjltjksjksjksjjskjrkirkirkhrkhqkhqlgqlgplfp\ lfplfpleomeomdomdomdnmcnmcnnbnnbmnamnamnamn`lo`lo_\ lo_lo_koZkoZkpYjpYjpYjpXjpXipWiqWiqViqVhqVhqUhqUhr\ TgrTgrTgrSgrSfrRfsRfsRfsQ } 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 22-07-03 (Lots of Activity [8])
by Jim Muth 22 Jul '03

22 Jul '03

FOTD -- July 22, 2003 (Rating 8) Fractal visionaries and enthusiasts: A day that starts with only 37 spam e-mails and a nearly empty work-shelf can't be all bad. Unfortunately, the 37 spams are a fluke, and fortunately, the nearly empty work shelf is a fluke also. I could eliminate the spam, at least for a while, by changing my e-mail address, but all those 'hi ya!', 'remember me!' and 'mdqwk zutpdxloj' subject lines have become almost like old friends waiting to greet me and then be deleted when I open my e-mail box every morning. Today's bustling image is also filled with activity. In fact, it is so active that it appears almost hectic. Because of its activity, I have given it the not very poetic name "Lots of Activity". The parent fractal was created by subtracting 0.8 parts of Z^(-1.2) from one part of Z^(1.1) before adding (1/C). It is a twisted Mandeloid consisting of a single large main bay edged with unusually small buds, which are so similar in size that the main period-2 bud is nearly impossible to find without checking. Avoiding the impossible, I checked. Today's scene is located very near the tip of the filament extending from the 'main' bud. The hectic effect has been achieved by rendering the scene with the 'outside' coloring option set to 'atan'. The normal 'iter' outside setting also creates an interesting scene, as do several other options, but the 'atan' option gives the best results, at least with today's image. I have had a run of below-average images lately, so maybe I have over-rated today's. But when I saw the result of the 'atan' option, I was so surprised that I gave the image a rating of a much-above-average 8. The recent render times seem to be in inverse co-relation to the quality of the finished images. Today's image, which renders in only 5 minutes, continues that trend. And if rendering fractals is not your 'cup of tea', the completed GIF image may be down- loaded from the FOTD web sites, which are located at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather was better than had been expected here at Fractal central on Monday. True, it was oppressively muggy and the temperature reached 91F 33C, but the forecasted rain failed to arrive, permitting the fractal cats an extended romp in the grass. By the time their fun ended, the duo were so tired that they settled to sleep without their customary evening treats. Rain is once again forecast for today, and once again I see great patches of blue sky overhead. A forecast of rain and actual rain are two entirely unrelated things, so I'll believe the forecast of rain when I see actual water falling from the sky. If my cynicism is correct, and it usually is, the cats will have another fun day. And with another slow work day coming, today is sure to be a fun day for me. Until next FOTD, take care and be alert for the rain. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Lots_of_Activity { ; time=0:05:11.15--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.05422309850998541/+0.601340703105692\ 80/3.458086e+010/1/-165/0.0022281871845546905 params=1/1.1/-0.8/-1.2/0/0 float=y maxiter=1200 inside=0 outside=atan periodicity=10 colors=000IUFIUHIUJIULJUNJUPJUQJUSJUUJUWKVYKV_KVaK\ VbKVdLVfLVhLVjLVlLVnLVoNYlO_iPafRdcSfaThZVkWWmTXoR\ ZrO_tLcvIhw5myCrxGwwJzvMzuQztTwsWrrZmqbjpekohlnlmm\ onlrrswpovolumhuletjbtiZsgWsfTrePqcMqbIp`Fp_CoY8oX\ 5nX0oW2nV4mV6lU8kT9jTBiSDhSFgRGfQIeQKdPMcPObOPaNR`\ NT_MVZNY`MWZMVYLUWLTVKSTKRSJQQJPPIONINMHMKHLJGJIGI\ GFHFFGDEFCEEADD9DC7CB6CA4B93A60B82BA4BC5BE7BG9CIAC\ KCCMDCOFCQHCSIDUKDWLDYND_PDaQDcSEeTEgVEiXEkYEm_3pf\ 9ocEo`KnYPnVVmT_mQemNjrKkwJmzHorIqjJw_Iz`Ju`Jw`Jr`\ Jo`Jn`Jm`Jl`Jk`Jj`Ji`Jh`Jg`Jf`Je`JdaJcaJbaJaaJ`aJ_\ aJZaJYaJXaJWbJVcJUfJTiJSlJSqHRlJQdKPXLPUMOPNNKOMUQ\ MTRLSSKQTJPUJOVIMXHLYGKZGI_FH`EGaDEcDDdCCeBAfA9g34\ lA8hGBdME`SHYZKUdNQjQMqRGpSIpTJpUKpVMpWNpWOpXPoYRo\ ZSo_To_Uo`WoaXobYocZnc`ndanebnfcngengfnhgnihmjjmkk\ mklmlmmmomnpmoqmnuCUWCUVCUUDUTDUSEUREUPEUOFUNFUMGU\ LGUKGUIHUHHUGIUFIUEHTBIUD } 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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