November 2005 - Fractint - mailman.xmission.com

newbie question
by john 27 Nov '05

27 Nov '05

Hi: I am new to this. I want to create a skyline pattern of rectangles. I know I need the L System grammar. I am just not sure about the specifics. Below is a crude example of what I am talking about. Any advice on algorithms, names, and driections for solving the problem would be helpful. start with a line ___________ one iteration ___ ___| |___ two iterations _ _ _| |_ _ _| |_| |_| |_ J.

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FOTD 27-11-05 (Curlicues [7])
by Jim Muth 27 Nov '05

27 Nov '05

FOTD -- November 27, 2005 (Rating 7) Fractal visionaries and enthusiasts: Today's different looking image shows the open inside of a Julia set of the Z^(1.1)+C Mandeloid as pictured 109 levels up the hyperspiral. The image consists totally of 'zmag' inside fill, which curiously enough makes an image both chaotic and orderly. I named the image "Curlicues" because of its resemblance to those decorative flourishes added to fancy signatures. The rating of a 7 is perhaps a bit high, but I feel I have not done too much exaggeration. The coloring appears adequate even though only a small part of the 256 available colors were actually used. The image is divided so finely that the few colors blend into an effective illusion of far more colors. The render time of 7-1/2 minutes is within reason, though a bit slow for the hectic pace of today's active world. To speed up things, the completed GIF image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A partly cloudy and slightly milder day Saturday here at Fractal Central was still not warm enough for the fractal cats to be comfortable in the yard. After spending 15 minutes outside, they retreated to pass the afternoon in the comfort of their window shelf. A generous treat of tuna in the evening kept the day from being a total loss. My day was again average. The next FOTD will appear in 24 hours, which is the average time between postings. Until then, take care, and wonder why. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Curlicues { ; time=0:07:25.33--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC center-mag=-0.398904/-0.064900\ 2/1.251213/1/67.5/1.31075705844807544e-014 passes=1 params=1.1/0/109/0/-0.2563/-0.7076/0/0 float=y maxiter=255 inside=zmag periodicity=10 colors=000OKzOKzOKyOKxOKwOKuOKtOKrOKqOKoOFnOAlOAjN\ AgNAeNBcNBaNC`NC_NCZNDXNDWNEVNEUNETNFSMFRMGQMGPMGO\ MHNLGMKFLJEKIDJHCIHBHHAGHAFIAELBFNCFPDFREFSFFTGFVH\ FWHFXHFYHFZHF_GF`GFbGFcGFdFFeFFfFGgEGhEGjEGkEGlDGm\ DGnDGrDGvFGzKGzPGzUGzZGzcGzcGzcIzcHzcGzcFycExaDw_C\ vYBuWBtYAs_9sa8rc7qe6qg5pi4qk2pi4og6ne7md9lcBkbCja\ Ei`Gh_HgZJfXLeVMdTOcRQbPRaOT`MV_KX`LWaLWbLWcLWdLVe\ LVeLVfLVgLVhMUiMUjMUkMUkMTlMTmMTnMToMTpNSqNSqNSrNS\ sNRtNRuNRvNRxOQvNRtNSrNTqMUoMVmMWlLXjLYhLZgK_eK`cK\ aaKb`JcZJdXJeWIfUIgSIhRHiPHjNHkLHlKGmIGnGGoFFpDFqB\ FrAFs8Gt6Gu3Hv5Hu6It7Is8Jr9JqAKqBKpCLoDLnEMmFMlGNl\ INkJOjKOiLPhMPgNQgOQfPReQRdRScSSbUTcTTbTUbSUbSVbRV\ bRWbQWbQXaQXaPYaPYaOZaOZaN_aN_aN``M``Ma`La`Lb`Kb`K\ c`Kc_Jc_Jc_Ic_Ic_Hc_Hc_GcZHc_Ic_Ic_Jc_Jc_Kc_Lc_Lc_\ Mc_Mc_Nc_Oc_Oc_Pc_Pc_Qc_Rc_Rc_Sc`Sc`Tc`Uc`Uc`Vc`Vc\ `Wc`Xc`Xc`Yc`Yc`Zc`_c`_c` } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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Re: [Fractint] Re: quaternion product correction (Lee Skinner)
by Russell Walsmith 26 Nov '05

26 Nov '05

----- Original Message ----- From: "Lee H. Skinner" <skinner(a)thuntek.net> > Russell, > > >> A_Mantabrot {;Gerald Dobiasovsky's 3D envelope wrapped around > > You turned my PC into an aquarium! > > Lee Lee, Your statement baffled me at first, since I couldn't imagine why anyone would want to populate an aquarium with even one of these pasty-white devilfish. Indeed, the idea seemed rather macabre. But then, as your skill at fashioning color maps came to mind, the light came on... Although the non-grey maps that I'd applied to the 3D T-set hadn't worked well at all, I thought to try one on the 'Mantabrot'. The effect was a complete surprise; I've used dozens of different maps on this object, and virtually every one, in at least a part of its cycle, gives some cool effects. I interpret your comment then to imply that you've come across some nice variations. If so, would you mind sharing some pars? Ciao, Russell

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FOTD 26-11-05 (Picket Fractal [7])
by Jim Muth 26 Nov '05

26 Nov '05

FOTD -- November 26, 2005 (Rating 7) Fractal visionaries and enthusiasts: The JuliaBC formula, which I recently found in a forgotten file, is proving to be one of the most useful. Today it takes us 109 turns up the logarithmic spiral to examine a Julia set of the Z^1.09+C Mandeloid. The unusually small exponent of Z would not be expected to produce much of a fractal. But in the world of fractals, first impressions are not always accurate. The resulting image reminds me of a picket fence, so I named it "Picket Fractal". The image consists of about half inside and half outside stuff. The inside parts have been brought to life by the 'bof61' inside fill, making an image that, at least in my opinion, rates a 7. If I had put a bit more effort into the colors, the image might have rated an 8. Today's image would appear to have symmetry around the origin. This is one of those wrong first impressions I warned about. Check those colors more carefully. They most certainly are not symmetrical. As I said, first impressions of fractals are not always accurate. The render time of under 3 minutes is fairly fast, but not as fast as downloading the already rendered image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Bright sun was spoiled by a temperature that never rose above freezing here at Fractal Central on Friday. The cats displayed their displeasure by showing no interest at all in going outside and getting into a spat over something only they knew about. The tuna only half satisfied them. My day was average, which is not all that bad. The next in the near-endless series of fractals will appear in 24 hours. Until then, take care, and be alert. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Picket_Fractal { ; time=0:02:50.05--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC center-mag=-0.138768/-0.362364\ /0.8458201/1/67.5/3.88578058618804789e-016 passes=1 params=1.09/0/109/0/-0.2563/-0.7076/0/0 float=y maxiter=255 inside=bof61 logmap=14 periodicity=10 colors=0006AL7AM8AN9ANAAOBAPCAPDAQEARFARGASHATIAUJ\ AVJAWJBXJCYJDZJE_JF`JGaJHaJIcJJdJKdJLeJMgJNgIOhIPi\ IQiIQjIRkIRkIRlISmISmHSnHSoHToHTpHTqHUqHUrHUsHVsGV\ tHVuHWuIWvIWwJXwJXxKXyKXyKWxKWxKWxKWxKWxKWxKWwKWwK\ WwKWwKWwKWwJWvJWvJWvJWvJWvJWvJWvJWuJWuJWuJWuJWuJWu\ IWtIWtIWtIWtIWtIWtIWsIWsIWsIWsIWsIWsIWsHWrHWrHWrHW\ rHWrHWrHWqHWqHWqHWqHWqHWqHWqIXrIYrIYrIZrIZrI_rI_rI\ `rI`rJarJarJbrJbrJcrJcrJdrJdrJerKerKfrKfrKgrKgrKhr\ MirOirQjrSjrUkrWkrYlr_lramrcnreorgpriqrkrrmssottqu\ usvvuwwwxxyyyzzzyyywxxuwwsvvquuottmstkruiqugpveovc\ nwamw_lwYkxWjxUiyUiyUhzVgzVgzWfzWezXezXdzYdzYczZbz\ Zbz_az_`z``z`_zaZzaZzbYzbXzcXzcWzdVzdVzeUzeTzfTzfS\ zgRzgRzhQziOzhQzhRzgTzgUzgVzfXzfYzf_ze`zeazeczddzd\ fycgwchvcjubktbmsbnraopaqoarnatm`ulbvk_vjkvhZvgmvf\ ZvejvdYvcmvaYvbrvcYvcmvdYvewveYvfYvgYvgXvhXviXuiXt\ jXskXrkXqlXpmXomWmnWloWko } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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Re: quaternion product correction (JoTz)
by Russell Walsmith 26 Nov '05

26 Nov '05

Yo JoTz, That "shadow Mandelbrot" is among the interesting effects in this video. Maybe even a theme in its own right. Clearly, there are many considerations in finding the optimal parameters for an animation of these kinds of sets. It seems promising though. I redesigned the T-C formula with the objective of trying to keep the size of the set from changing too much throughout the transitions, and it seems to have helped a bit. It also brought about some new effects on either side of the interval real(p3) = [1,0]. Maybe, for the fun of it, you'll give this version a little spin... ---------------------par file---------------------- Tmorph { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=fromfile formulaname=T_C_morph passes=3 center-mag=-0.343038/-0.186895/0.4524726 params=0/0/-1.5/1.5/3/0/0/4/150/253 float=y maxiter=2000000000 outside=summ periodicity=0 colors=(a)grey.map } ---------------------frm file---------------------- frm:T_C_morph {;periodicity=no, outside=summ ;maxit > p5real*(p5imag+1) ;-------------------------------------------- ;p1real: Rotation about x-axis (1st rotation) ;p1imag: Rotation about y-axis (2nd rotation) ;p2real: Far clipping plane ;p2imag: Near clipping plane ;p3real: Constant coefficient ;p3imag: ;p4real: z1(0) ;p4imag: Bailout ;p5real: Maxiter per slice ;p5imag: Number of slices - 1 ;-------------------------------------------- ; bailout = imag(p4), tiefnum = imag(p5) delta = (real(p2)-imag(p2))/tiefnum tmp = pi/180 rotXax = exp(flip(real(p1)*tmp)), rotYax = exp(flip(imag(p1)*tmp)) ; HPixXY = rotYax VPixZ = real(rotXax) VPixXY = flip(conj(rotYax)) NXY = VPixZ*VPixXY NZ = imag(conj(rotXax)) VPixXY = -NZ*VPixXY ; tmp = NXY*imag(p2) + HPixXY*real(pixel) + VPixXY*imag(pixel) cx = cx0 = real(tmp), cy = cy0 = imag(tmp) cz = cz0 = NZ*imag(p2) + VPixZ*imag(pixel) ;HPixZ -> 0 tmp = NXY*delta, dcx = real(tmp), dcy = imag(tmp) dcz = NZ*delta x1 = 0, y1 = 0, z1 = real(p4) d1 = sqrt(real(p3)), d2 = sqrt(1-real(p3)) d3 = d1 + d2 j = m = i = 0: a = sqr(x1) + 2*y1*z1 b = sqr(z1) + 2*x1*y1 c = sqr(y1) + 2*x1*z1 x1 = d1*a + d2*c + cx y1 = d3*b + cy, z1 = d2*a + d1*c + cz IF (bailout >= (sqr(x1)+sqr(y1)+sqr(z1))) i = i + 1 ELSE i = 0 m = m + 1 cx = cx0 = cx0 + dcx cy = cy0 = cy0 + dcy cz = cz0 = cz0 + dcz x1 = 0, y1 = 0, z1 = real(p4) ENDIF z = m - j j = j + 1 tiefnum >= m && p5 >= i } ---------------------end file---------------------- ----- Original Message ----- From: JackOfTradeZ <JackOfTradeZ(a)comcast.net> To: fractint(a)mailman.xmission.com Subject: [Fractint] Re: quaternion product correction (Russell Walsmith) Date: Thu, 24 Nov 2005 09:44:55 -0700 > > 11/24/2005 > > The Gerald Dobiasovsky / Russ Walsmith (morph + pirouette) viddie; 3D > grayscale, is posted: > > http://www.fractal-animation.net/morph_x.zip > > 640x480 AVI, 30 sec, 4.4 MEG > > A shadow mandelbrot creeps across the main form momentarily - loox like a > tarantula / evil ghost. > I'll let someone else try to explain what's up with that. > This is the "weird thing" I mentioned, I didn't recognize what it was at > first. > > > HaPPy HoLiDaZe ! > > JoTz > > > > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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FOTD 25-11-05 (All Inside Stuff [6])
by Jim Muth 25 Nov '05

25 Nov '05

FOTD -- November 25, 2005 (Rating 6) Fractal visionaries and enthusiasts: Yesterday's discussion was short because I inadvertently deleted the regular discussion and wrote over its disk space before I realized the file was gone. That's two discussions I've lost this month. 'Wordperfect5.1', the DOS program I use, does not have a waste basket. The lost discussion was about oddities of the fourth dimension and the three-dimensional slices of the Z^2+C Julibrot. One of these days I'll re-write it, but today we have more immediate things to discuss. Today's image is part of the inside of a Julia set of the Z^1.15+C Mandeloid as it appears 55 levels down the spiral. It consists almost totally of inside stuff made visible by the 'atan' inside fill, and is one of the most unusual all-inside images I have seen. The eight leaf-like features surrounding the hole at the center at first appear symmetrical, but first impressions are sometimes deceiving. In addition to being colored differently, each leaf has a slightly different shape and a different inside pattern. I named the image "All Inside Stuff" as a mere description. I rated it a 6 because I feel it is at least slightly above average. The render time of the parameter file, just under 8 minutes, borders on slowness. A notably faster way to see the image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and download the finished image from there. A light snow fell overnight Wednesday here at Fractal Central, but the 1/2 inch (1cm) melted away as soon as the sun rose. Unfortunately the grass remained too wet for the sensitive paws of the fractal duo, who once again passed the day on the shelf by the window. My day was occupied by the Thanksgiving goings on. The next FOTD will appear as scheduled in 24 hours or so at this same place. Until then, take care, and when you row your boat, remember that life is but a dream Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= All_Inside_Stuff { ; time=0:07:41.15--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC passes=1 center-mag=0.198246/-0.362094/1.593045 params=1.15/0/-55/0/0.547/-0.465/0/0 float=y maxiter=255 inside=atan periodicity=10 colors=333uLMumOmMMB48nMMkOMiROeUMcVLZVGUXCRZCXNCc\ IFkHHrJJuLL`DDKNOHljLuuLuPKtY_abnUpuruE5CG69I77K77\ M88O99Q99RAARAAUBBVBBVBBXCCZCCZCC`DDbEEbEE77K77I55\ E44B337225111111111111111DDb422542763994BD5DE5FI7G\ K7IO9LRAMUBPXCRZDUbGVcHYgI`kL`lLcpNdrPguQhuSjuSjuS\ luTmuTmuTggNjuSiuQhuQfuOeuOeuNduNbuLauL`uLZtKXrJXp\ JVnIUnISlHQkHOiGMgGMgGLeFJcFHbEG`DEZCEZCCXCBVBBUBA\ RAARAntKMMMLLuLLuKKtMJkSPcVVVZZYgeSqubptWnkOneIn_I\ nVI4986GCJMJbWQui`ufYucVubSuZOugbuWLuYNua`eRbubuut\ uukuuburWuoOuiJpYLucLueHliGbnIXuNRuPLuLLuRLuYLueLr\ kNotTludnuWpuQtuLkfLurLuuLuuLlllgggc_a`MUtKWRAK337\ 74BO9GgGPuL_uLUpJQgGJXCCO99E555223735E58M8BUCEbHGi\ NJpSLucLuWGgKCXCBUBCRAOQ9gSGuWLuYLuVLuTLuRLuNLuMLu\ LLuLLrJJUBB522uLUrPMXPCZHCMK8HVBFeFLuLInID`D8M8373\ 424111737VBNpWeumpuVtlLucLuuuurrufhkVZ`KURG96CCXAA\ RD8MF6GM8GUBI`DJeFKlHKtKM } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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Re: quaternion product correction (Russell Walsmith)
by JackOfTradeZ 24 Nov '05

24 Nov '05

11/24/2005 The Gerald Dobiasovsky / Russ Walsmith (morph + pirouette) viddie; 3D grayscale, is posted: http://www.fractal-animation.net/morph_x.zip 640x480 AVI, 30 sec, 4.4 MEG A shadow mandelbrot creeps across the main form momentarily - loox like a tarantula / evil ghost. I'll let someone else try to explain what's up with that. This is the "weird thing" I mentioned, I didn't recognize what it was at first. HaPPy HoLiDaZe ! JoTz

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FOTD 24-11-05 (Seahorse Carnival [6])
by Jim Muth 24 Nov '05

24 Nov '05

FOTD -- November 24, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's image is an oblique view of Seahorse Valley. It may be seen by running the parameter file or by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The next FOTD is due tomorrow. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Carnival { ; time=0:16:11.03--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 float=y center-mag=-1.28719/-0.16188/28.777 periodicity=10 params=45/90/85/90/-0.75/0/0/0 maxiter=75000 colors=000zz`cSabTbaUc`Vd_WeZXfYYgXZhW_iV`jVakVblV\ cmVdnVemVeoVepVeqWdoXcmYckZbiZag_ae``ca_aa__bZYcYW\ dYUdXSeWQfWOgVMgUKhUIiTGjSEjSDkRDkRDkRDlRDlRDlRDmR\ DmRDmRDnRDnRDnRDoRDoRDoRDoRDpRDpRDpRDqRDqRDqRDrRDr\ RDrRDsRDsRDsRDsRDrQEqQFqQFpPGpPGoPHoPHnOImOJmOJlNK\ lNKkNLkNLjMMjMMiMNhLOhLOgLPgLPfKQfKQeKRdJSdJScJTcJ\ TbIUbIUaIVaIVWMZRQbMUeGYiBalAeoAdrAcqAboAanA`nA_nA\ ZnAYnAXnAWnAVnAUnATnASnBRnCQnDPnEOnFNnGMnHLnIKnJJn\ KInLHmMHlNHkOHjPHiQHhRHgSHfTHeUHcVHbWHaWH`XH_YH_ZH\ ZZHY_HX`HWaHVaHUbHUcHTdHSdHReHQfHPgHOgHOoaDwv3ur4s\ n4rj4pf4oc4m_4lW4jS4hO4gL4eH4dD4b94a64`A3`E3`H3`L2\ _O2_S2_W1_Z1Zb1Ze0Zi0Zl0`i4bf8dcBf`FhZIjWMlTPnQToO\ WnPUnQTnRRmRQmSPmTNmUMlUKlVJlWIlXGkXFkYDkZCkZBh`Ee\ bGcdI`fKZhMWjOUlQRnTOpVMrXJtZHw`EvbCudDrcEobFlaGi`\ Gf_HcZI`YJYXJWWKUVLVUMWTMXSNYROZQP_PP`PSaOUbOXeOZh\ O`kOhnGeqIatLZwNWzPVzRVzS logmap=y } frm:SliceJulibrot2 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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Re: [Fractint] Re: quaternion product correction (Russell Walsmith)
by Russell Walsmith 23 Nov '05

23 Nov '05

----- Original Message ----- From: JackOfTradeZ <JackOfTradeZ(a)comcast.net> To: fractint(a)mailman.xmission.com Subject: [Fractint] Re: quaternion product correction (Russell Walsmith) Date: Mon, 21 Nov 2005 20:01:06 -0700 > I think it will look like a gyroscope in precess, and stuff will be flying > off from it from > centrifugal force. And the weird thing will be seen also. > > So when I figure it all out, the final viddie will be a pirouette about the > vertical axis, > simultaneous with morph, and from a distance where it can all be seen. > > I will alert / post it when done, may take a week or so. > > > JoTz Weird thing? This gets curiouser and curiouser... looking forward to the viddie. There are some strange creatures in this section of 3-space, for sure... ---------------------------PAR FILE------------------------------- A_Mantabrot {;Gerald Dobiasovsky's 3D envelope wrapped around ; a T-set variant ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=fromfile formulaname=metat-set passes=3 center-mag=-0.158929/0.144849/0.8743172/1/-44.9999999999999858/-\ 1.23373533611470521e-014 params=180/90/-2/2/0.5/0.5/0/4/150/253 float=y maxiter=2000000000 outside=summ periodicity=0 colors=000555<10>222222111<3>111111000000zzz<64>jjjjjjiii<5>hhhh\ hh000ggg<156>555 } ---------------------------FRM FILE------------------------------- frm:MetaT-set {;periodicity=no, outside=summ ;maxit > p5real*(p5imag+1) ;-------------------------------------------- ;p1real: Rotation about x-axis (1st rotation) ;p1imag: Rotation about y-axis (2nd rotation) ;p2real: Far clipping plane ;p2imag: Near clipping plane ;p3real: Pixel^2 coefficient ;p3imag: ;p4real: z1(0) ;p4imag: Bailout ;p5real: Maxiter per slice ;p5imag: Number of slices - 1 ;-------------------------------------------- ; bailout = imag(p4), tiefnum = imag(p5) delta = (real(p2)-imag(p2))/tiefnum tmp = pi/180 rotXax = exp(flip(real(p1)*tmp)), rotYax = exp(flip(imag(p1)*tmp)) ; HPixXY = rotYax VPixZ = real(rotXax) VPixXY = flip(conj(rotYax)) NXY = VPixZ*VPixXY NZ = imag(conj(rotXax)) VPixXY = -NZ*VPixXY ; tmp = NXY*imag(p2) + HPixXY*real(pixel) + VPixXY*imag(pixel) cx = cx0 = real(tmp), cy = cy0 = imag(tmp) cz = cz0 = NZ*imag(p2) + VPixZ*imag(pixel) ;HPixZ -> 0 tmp = NXY*delta, dcx = real(tmp), dcy = imag(tmp) dcz = NZ*delta x1 = 0 y1 = 0 z1 = real(p4) j = m = i = 0: a = sqr(x1) + 2*y1*z1 b = sqr(z1) + 2*x1*y1 c = sqr(y1) + 2*x1*z1 x1 = imag(p3)*a + real(p3)*a^2 + cx y1 = imag(p3)*b + real(p3)*b^2 + cy z1 = imag(p3)*c + real(p3)*c^2 + cz IF (bailout >= (sqr(x1)+sqr(y1)+sqr(z1))) i = i + 1 ELSE i = 0 m = m + 1 cx = cx0 = cx0 + dcx cy = cy0 = cy0 + dcy cz = cz0 = cz0 + dcz x1 = 0, y1 = 0, z1 = real(p4) ENDIF z = m - j j = j + 1 tiefnum >= m && p5 >= i } ------------------------------END PAR----------------------------

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FOTD 23-11-05 (On a Windy Hill [7])
by Jim Muth 23 Nov '05

23 Nov '05

FOTD -- November 23, 2005 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal image shows a tree clinging to a high and windy hill, so I named it "On a Windy Hill". Well, actually it shows an entire Julia set of the Z^1.15 Mandeloid as it appears 115 levels up the complex-log hyperspiral. The windy hill of the name, and the tree as well, are only figments of my imagination. But sometimes figments can be quite attractive, as today's image shows. One can almost feel the brisk east wind blowing along the ridge top from the right. And yes, I realize that the colors of the tree are unusual, but the tree is located on an alien planet, so this is no problem. When the time arrived to rate the image, I decided on a rating of 7. I rather like the image of a tree with dark blue branches and dull red flowers. The render time of a very brief 66 seconds helped justify the rating of a 7. Most of the speed is due to the unusually low maxiter of 50. The low maxiter is needed to keep the background sky from filling in with too much debris. But speed is of no importance to machines with a Fractint phobia, which will never know the joy of running Fractint. Those with such machines may download the completed GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Occasional rain, cold 41F 5C temperatures, and high winds, made Tuesday totally hopeless for the duo of fractal cats. Realizing that they would not be able to enjoy their usual outing, they settled themselves on the shelf by the double window to pass the day dreaming and wishing. An extra treat of tuna in the early afternoon helped ease their distress. My day was moderately busy, with nothing to set the day apart from hundreds of similar days. The next glorious FOTD will appear in 24 hours. Until then, take care and search for the real. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= On a Windy_Hill { ; time=0:01:06.64--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC passes=1 center-mag=-1.41759\ /0.0889863/1.173709/1/70/-2.50563458870090017e-014 params=1.15/0/115/0/-0.364/-0.925/0/0 float=y maxiter=50 inside=60 logmap=yes periodicity=10 colors=000KA0KA0KA0KA0KA0KA0KA0KA2KA4KA7KAAKADKAGK\ AJKAMKAPKAPKASKAVKAXKAYKAZKA_KB`MHbOMeQRfVWi_`jdfk\ iklntztzzzzzxxzttzrmhqfgnbejYcgTbeO`cJZcFYcJSfNNeQ\ HeUCdY6d`1aZBZXLWVVTTdQSnKZfRYpQ_nP`mAaz_ihWhhThhQ\ ghMfhJfhGehCeh9dh6dh6ai5Zk5Wl5Sm4Po4Mp4JqBMcIORPRD\ VT0SU6QUCNUHLUNJVTGVYEVcCVhEUiFTiGSjISjJRkKQkLQkNP\ lOOlPNmRNmSMnTLnULnQRpMXrIatEguAlw6ry2wz4ux6tw7su9\ rtBqsCpqEopGnnHmmJllLkjMjiOigQhfRgeVl`ZqWbvSfzNjzJ\ upWpl_kibffeaciX`lSYoNVsISvEPyDTvCXtB`rBcpAgn9kl9n\ j8rh7vf7ydQ9JhLWaRYWWZP`_JfaCkb6pc0ud5pf9lgDhiHdjM\ `lQXmUToYPp_Ql`QhaQdcQ`dRXeRTgRPhRLiSzkSzlSzmSznSz\ mQzmPzlNzlMzlKzkJzkHzjGzjEzjDzlIzmNzoRzpWzq_zkkzew\ zjmzndzrWzvNzzEzwFztGzqHzoIzlJziJzgKzdLzaMz_NzXNzU\ OzSPzPQzMRzKRzFYzAdzCgzEizGkzImzKozMqzOszQuzRqzRmz\ SjzSfzTczT_zTXzTXzUWzUWzUWzUVzVVzVVzWTzVUzVUzWUzWT\ zWTz7xz9vzBtzCrzEpzFnzDnz } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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