"Lee H. Skinner" <skinner@thuntek.net> previously wrote:
I would be grateful if SherLok and Hiram would repost their pars with the colors. Otherwise, I can generate the pars as already posted with default.map, but I'm sure they won't look as well as the images on the machines of the original artists!
Certainly, Lee. Thanks for the admonition against posting attachments; I really wasn't aware of it, but I fully understand the rationale: I left my virus-scanner going last night, came back in the morning to find... in spite of my fairly high level of vigilance a malicious spammer had gotten 2 copies of the mydoom.f worm onto my computer disguised as, of all things, a .png file! I notice that the recordcolors representation is _much_ more concise than the .map file too. So, I've included the revised pars later in the body of this message, as well as one additional one that uses the linear Julibrot slicing formula, called "ClubmossMorass" that illustrates the extreme disorder that can found in some of the slices. Also, I mentioned the possibility of doing nonlinear slices the Julibrot Set and then mapping the parameter of variation on those surfaces to the complex plane to view it, but didn't give any examples. Here are two formulae which do that, though I haven't optimized them to be especially intuitive with regard to the subset of the space they're slicing. The first one slices on a spherical surface, while the second one is a slight modification of the first to slice a Lisajous surface: /***********************FRMS BEGIN******************************************/ JulibrotSlice1+1i { ; a nonlinear slice of the Julibrot: ; the surface of the sphere passing through C2 origin ((0+0i),(0+0i)) ; with radius p1 is rotated about the origin by complex angle p2 and ; then offset by (p3,p4) so that its surface passes through the C2 ; position {z0=p3,C=p4}. The parameter of variation represented by ; "pixel" then maps points on the spherical slice to the screen. ; Varying p2 then rotates the sphere around the anchor point (p3,p4) ; while varying p1 expands or contracts the bubble while maintaining ; the anchor point on the bubble. ismand = true r = p1 ; complex radius of sphere which is the slice cosphi = cos(p2) ; sphere will be rotated by p2 sinphi = sin(p2) k = pixel ; complex angular parameter of variation on sphere surface z0 = r*(cos(k)-1), c0 = r*sin(k) z = cosphi * z0 - sinphi * c0 + p3 c = sinphi * z0 + cosphi * c0 + p4 lim = 9 : z = sqr(z) + c |z| <= lim } JulibrotSlice1+2i { ; generalization of JBS1+1i spherical slice into ; a Lisajous surface slice in C2{z0,c} parameterized ; by {cos(k),sin(p5*k)}, ie. p5 contains the harmonic ; multiple. As p1 shrinks pseudotiling should occur. ismand = true r = p1 ; scale factor, not really "radius" anymore cosphi = cos(p2) sinphi = sin(p2) k = pixel ; parameter of variation z0 = r*(cos(k)-1), c0 = r*sin(p5*k) z = cosphi * z0 - sinphi * c0 + p3 c = sinphi * z0 + cosphi * c0 + p4 lim = 9 : z = sqr(z) + c |z| <= lim } /****************************FRMS END***************************************/ Concerning the following pars, JBS1+1i_init (the nearly M-set figure with oversized buds on the 2^n spike) and JBS1+2i_init (the Rorschach-like double blot) are just for starting an exploration into these slices. The pair {"DisconnectDemo","TendrilDisconnect"} illustrates the point I tried to make in my previous post about the breaking of connectedness, in this case very subtly, in the oblique Julibrot slices: the first par shows a large scale view of what looks at that vantage to be an intact M-set with its tendrils connected and with minimal distortion; the second par shows a closeup of the major minibrot on the spike. In contrast, it looks more like the outline of Antarctica than a minibrot, and there are very defined breaks on its subsidiary tendrils, which hook at the break almost as if there were a physical repulsion force involved. Finally, there is the series {"FountainOfWraiths","MutatedFntOWraiths","ThrowingStarSpiral"} The first one is an overview of a Lisajous surface slice illustrating many design themes hybridized in one image: Julialike here, Mandelbrotlike there, disconnected recursively selfsimilarity in one region, a monolithic bulk with a border like torn paper in another, with short transitions between dissimilar themes. I believe this is caused by the often-changing curvature of the surface in the Julibrot space. The second par show what happens to this region when a modest reduction in the imaginary component of one of the parameters is made: overwhelming Mandelbrot character asserts itself and most of the unconnected satellites either reconnect or move closer to the main mass. And yet... the third par of the trio is just a magnification of one of the satellites in the second par-- no changing the params-- even on the Mandelbrotlike slice here is a region with fully Julia set character: Extreme symmetry, recursive self similarity, etc. These pars follow: /********************************PARS BEGIN**********************************/ TumbleweedJBS { ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=julibrot.frm formulaname=julibrotslice0+1i ismand=y center-mag=+0.58460176000000000/+0.37746477100000000/49.04443/0.9997 params=4/0/0/0 cyclerange=0/23 colors=UUU0000w0<14>2n42n42m4<3>3j6c0w<2>www<3>NkQEhI4d9<8>JZLLYMNXO<3>U\ UU<3>AOA5M50K0<9>`hBdjDhmE<3>wwJ<15>uMNtKNtHN<2>tAOs7Pq7P<4>b4Q_3QX3R<3>\ L0SS0S<3>S00<3>SS0<3>0S0<2>0SL<25>LMQLMQMLR<3>QKSSKSSKS<15>LLSLLSKMS<58>\ DHDDHDDHCDHCDHCCGBBGB<2>BGFBGGBFGBDGBCG000<7>0000w00w0 } FireflyDawnJBS { ; Fractint Version 2003 Patchlevel 1 ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=julibrot.frm formulaname=julibrotslice0+1i ismand=y center-mag=-0.02349570395000000/-0.04868921628458539/205.3879/1/-177.500\ 000000000028/3.88578058618804789e-016 params=4.2/-3/0/0 float=y cyclerange=0/23 colors=UUU0000w0<14>2n42n42m4<3>3j6c0w<2>www<3>NkQEhI4d9<8>JZLLYMNXO<3>U\ UU<3>AOA5M50K0<9>`hBdjDhmE<3>wwJ<15>uMNtKNtHN<2>tAOs7Pq7P<4>b4Q_3QX3R<3>\ L0SS0S<3>S00<3>SS0<3>0S0<2>0SL<25>LMQLMQMLR<3>QKSSKSSKS<15>LLSLLSKMS<58>\ DHDDHDDHCDHCDHCCGBBGB<2>BGFBGGBFGBDGBCG000<7>0000w00w0 } WaltzingWizardsJBS { ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=fractint.frm formulaname=julibrotslice0+1i center-mag=-0.07163947820000000/-3.98956388000000000/76.45664/0.9997/-95\ .0131129858647654/1.6954329223432818e-005 params=3.5/-3/4/0 cyclerange=0/23 colors=UUU0000w0<14>2n42n42m4<3>3j6c0w<2>www<3>NkQEhI4d9<8>JZLLYMNXO<3>U\ UU<3>AOA5M50K0<9>`hBdjDhmE<3>wwJ<15>uMNtKNtHN<2>tAOs7Pq7P<4>b4Q_3QX3R<3>\ L0SS0S<3>S00<3>SS0<3>0S0<2>0SL<25>LMQLMQMLR<3>QKSSKSSKS<15>LLSLLSKMS<58>\ DHDDHDDHCDHCDHCCGBBGB<2>BGFBGGBFGBDGBCG000<7>0000w00w0 } PaisleyZipperJBS { ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=fractint.frm formulaname=julibrotslice0+1i center-mag=-0.968336/0.127203/26.01933/1.0003/-85.0154903477167636/-0.00\ 296067121431022734 params=3/0.0312885046005249/1.35/0 cyclerange=0/23 colors=UUU0000w0<14>2n42n42m4<3>3j6c0w<2>www<3>NkQEhI4d9<8>JZLLYMNXO<3>U\ UU<3>AOA5M50K0<9>`hBdjDhmE<3>wwJ<15>uMNtKNtHN<2>tAOs7Pq7P<4>b4Q_3QX3R<3>\ L0SS0S<3>S00<3>SS0<3>0S0<2>0SL<25>LMQLMQMLR<3>QKSSKSSKS<15>LLSLLSKMS<58>\ DHDDHDDHCDHCDHCCGBBGB<2>BGFBGGBFGBDGBCG000<7>0000w00w0 } ClubmossMorassJBS { ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=julibrot.frm formulaname=julibrotslice0+1i ismand=y passes=1 center-mag=-0.83799791350000000/+0.43607524050000000/75.69757/0.9997/-22\ .4825937673992158/-3.10843519833532334 params=3/0.0312885046005249/1.35/-0.12 maxiter=10000 cyclerange=0/23 colors=UUU0000w0<14>2n42n42m4<3>3j6c0w<2>www<3>NkQEhI4d9<8>JZLLYMNXO<3>U\ UU<3>AOA5M50K0<9>`hBdjDhmE<3>wwJ<15>uMNtKNtHN<2>tAOs7Pq7P<4>b4Q_3QX3R<3>\ L0SS0S<3>S00<3>SS0<3>0S0<2>0SL<25>LMQLMQMLR<3>QKSSKSSKS<15>LLSLLSKMS<58>\ DHDDHDDHCDHCDHCCGBBGB<2>BGFBGGBFGBDGBCG000<7>0000w00w0 } StarfishArchipelago { ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=julibrot.frm formulaname=julibrotslice1+1i ismand=y center-mag=-0.93215146650000000/+0.52077522900000000/43.79142/0.9997/90/\ 3.88578058618804789e-016 params=1/0/0/0/0/0/0/0 colors=000<3>8DMBGRDKXFNaHQgKUm<7>PdmQemRgm<2>TkmUmmSko<3>Kcw<3>enwkqwqt\ wwww<4>K00wph<10>wcIwbFw`D<3>wW2<9>NC3JA3F83<3>004<172>001001001<3>000zz\ zzzz } JBS1+1i_init { ; Julibrot Slicer taking spherical slices of (Z0,C) space ; z-screen parms: p1 = complex radius of sphere ; p2 = complex angle of rotation of p_o_v origin on sphere ; (p3,p4) = location in (Z0,C) space of p_o_v origin ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=julibrot.frm formulaname=julibrotslice1+1i ismand=y center-mag=-0.520063/2.35e-006/0.4986678 params=0.78/0/0/0/0/0/0/0 float=y colors=UUU5M50K0<6>Qa8Uc9XfA`hB<3>prHsuIwwJ<9>v_MvYMvWM<3>uMNtKNtHN<2>tA\ Os7Pq7P<4>b4Q_3QX3R<3>L0SS0S<3>S00<3>SS0<3>0S0<2>0SL<24>KMQLMQLMQ<3>PKSQ\ KSSKS<13>MLSMLSLLS<3>KMSKMRKMR<54>DHDDHDDHDDHCDHCDHCCGBBGB<2>BGFBGGBFGBD\ GBCG000<5>0000000000w00w00000w0<13>2o42n42n4<3>3k63j6c0w<2>www<3>NkQEhI4\ d9<4>CaGE`HG_IH_KJZL<5>UUU<3>AOA } JBS1+2i_init { ; Lisajous surface slicing of Julibrot (Z0,C) C2 space ; p1 = scale factor(complex); p2 = complex rotation angle ; (p3,p4) = origin of the parameter of variation on surfac ; e,k. p5 = harmonic factor n in "{cos(k),sin(n*k)}" ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=julibrot.frm formulaname=JulibrotSlice1+2i float=yes corners=-1.702835/2.297165/-1.5/1.5 params=0.8/0/0/0/0/0/0/0/3/0 float=y maxiter=2000 inside=0 colors=000PP0<2>MM00z0<35>0R0<4>0M000z<35>00R<4>00M0zz<35>0RR<4>0MM00000\ 0zzzz0z<35>R0R<4>M0Mz00<35>R00<4>M00zz0<36>QQ0 } DisconnDemo { ; At this scale the structure looks very close to being ; a largely undistorted reflection of the M-set. But , ; examination of the tendril topology around the major ; minibrot shows divergent morphology at microscale only. ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=julibrot.frm formulaname=julibrotslice1+1i center-mag=-18.8537/0.0402218/13.20172 params=0.78/18/0/0/0/0/0/0 float=y colors=UUU00KE`H<3>LYMNXOPWQ<2>UUU<3>AOA5M50K0<6>Qa8Uc9XfA`hB<3>prHsuIww\ J<9>v_MvYMvWM<3>uMNtKNtHN<2>tAOs7Pq7P<4>b4Q_3QX3R<3>L0SS0S<3>S00<3>SS0<3\
0S0<2>0SL<24>KMQLMQLMQ<3>PKSQKSSKS<13>MLSMLSLLS<3>KMSKMRKMR<54>DHDDHDDH\ DDHCDHCDHCCGBBGB<2>BGFBGGBFGBDGBCG000<5>0000000000w00w00000w0<13>2o42n42\ n4<3>3k63j6c0w<2>www<5>4d9<3>BaE }
TendrilDisconnect { ; Demonstration of the disconnection of minibrot tendril ; structure when doing a curved slice of the Julibrot even ; when at large scale the structure looks mundane. This is ; the largest minibrot on the spike.LgScale="DisconnDemo" ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=julibrot.frm formulaname=julibrotslice1+1i center-mag=-18.85374671818577000/+0.09726135651887585/867.2483 params=0.78/18/0/0/0/0/0/0 float=y colors=UUU00KE`H<3>LYMNXOPWQ<2>UUU<3>AOA5M50K0<6>Qa8Uc9XfA`hB<3>prHsuIww\ J<9>v_MvYMvWM<3>uMNtKNtHN<2>tAOs7Pq7P<4>b4Q_3QX3R<3>L0SS0S<3>S00<3>SS0<3\
0S0<2>0SL<24>KMQLMQLMQ<3>PKSQKSSKS<13>MLSMLSLLS<3>KMSKMRKMR<54>DHDDHDDH\ DDHCDHCDHCCGBBGB<2>BGFBGGBFGBDGBCG000<5>0000000000w00w00000w0<13>2o42n42\ n4<3>3k63j6c0w<2>www<5>4d9<3>BaE }
FountainOfWraiths { ; Extreme disorder seems to be engendered in some of the ; Julibrot slices, far more than in the tangent intersecti ; ing Julia or M-brot-parallel slice. There is high grain ; iness in the "fountain" and no dominant ordering princip ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=julibrot.frm formulaname=JulibrotSlice1+2i center-mag=5.65151/0.801464/18.45106/1/15.0000000000004228/-1.5228096561\ 5148034e-013 params=2/-0.4/1/0/0/0/0/0/1.1/-0.206 float=y maxiter=10000 colors=000U0c0e0<3>eL0eeeLLL<4>ssLzzLzzz000555<3>HHHKKKOOO<3>ccchhhmmmss\ szzzxzw<3>xjUxfNxbFxZ8wU0<5>UiVPl_Koe<3>0zz<2>0Gz<3>rVzzVz<3>zVV<3>zzV<3\
VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0S<3>S00<3\ SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKKS<2>QKSSK\ SSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3>G00<3>GG\ 0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G8<2>8GE8G\ G8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBGGBFGBDGBC\ G000<6>000 }
MutatedFntOWraiths { ; By slightly lessening the magnitude of the imag comp of ; the harmonic used to generate the viewing slice, the ima ; ge becomes much more Mandelbrot-like; many of the former ; ly unconnected structures reconnect or move closer. ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=julibrot.frm formulaname=JulibrotSlice1+2i center-mag=5.73804/0.347052/3.105436/1/15.0000000000008864/-2.9222457786\ 9149016e-013 params=2/-0.4/1/0/0/0/0/0/1.1/-0.1 float=y maxiter=10000 colors=000U0c0e0<3>eL0eeeLLL<4>ssLzzLzzz000555<3>HHHKKKOOO<3>ccchhhmmmss\ szzzxzw<3>xjUxfNxbFxZ8wU0<5>UiVPl_Koe<3>0zz<2>0Gz<3>rVzzVz<3>zVV<3>zzV<3\
VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0S<3>S00<3\ SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKKS<2>QKSSK\ SSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3>G00<3>GG\ 0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G8<2>8GE8G\ G8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBGGBFGBDGBC\ G000<6>000 }
ThrowingStarSpiral { ; Magnified region of the mutated "Fountain of Wraiths", ; a highly ordered spiral with almost complete Julia chara ; cter, showing none of the chaotic design order of the ; original FoW. ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=julibrot.frm formulaname=JulibrotSlice1+2i center-mag=+6.03156641179530300/+0.25961594375856050/456.356/1/-12.50000\ 00000212896/1.78242143267226538e-011 params=2/-0.4/1/0/0/0/0/0/1.1/-0.1 float=y maxiter=1000000 colors=000U0c0e0<3>eL0eeeLLL<4>ssLzzLzzz000555<3>HHHKKKOOO<3>ccchhhmmmss\ szzzxzw<3>xjUxfNxbFxZ8wU0<5>UiVPl_Koe<3>0zz<2>0Gz<3>rVzzVz<3>zVV<3>zzV<3\
VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0S<3>S00<3\ SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKKS<2>QKSSK\ SSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3>G00<3>GG\ 0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G8<2>8GE8G\ G8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBGGBFGBDGBC\ G000<6>000 }
/****************************************PARS END*******************************************/