March 2004 - Fractint - mailman.xmission.com

Orbit Fractals with an Arbitrary Formula
by Hiram Berry 11 Mar '04

11 Mar '04

Is it possible to get fractint to plot these and if so how? Fractint seems to have specialized orbit types like the Henon attractor, but I want to specify the formula. IOW the "formula" type iterates over the screen pixels in an orderly gridlike fashion, but I want to go from pixel to pixel by iterating Pixel_new = F (Pixel_old) and mark the pixel each time. I found this process that seems to generate continuous(with sufficient iteration) fractal curves that look like wads of string with knots in random places (with greater iteration count, the large-scale length of the curve grows, but less than proportional to the number of iterations, and backfilling occurs at the same time at seemingly random locations so the curve is probably dense): x(n) = summation[m=1 to n]( sin(f(n)) * n^-a) y(n) = summation[m=1 to n]( cos(f(n)) *n^-a) where a is a constant between 0 and 1. One f that gives a fractal curve (briefly described above) is sqr, while f=log gives a smooth spiral. I'd like to plot these with fractint which has deep zooming capabilities, instead of the program I used which does not, and which failed at around 40000 iterated points. I know about the orbit screen in fractint, but it seems to me that if I use that with a "formula" type it will run the hundreds of thousands of iterations for every single pixel of the screen until the maximum iteration count is hit. That would take much too long. Is there some arcane .par magic to get fractint to display an orbit generated from only one point instead of the main screen? Hiram Berry

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FOTD 28-02-04 (Cellular Patterns [6])
by Jim Muth 11 Mar '04

11 Mar '04

FOTD -- February 28, 2004 (Rating 6) Fractal visionaries and enthusiasts: For some reason, today's image reminds me of the cells of a cellular telephone network. I named it "Cellular Patterns". It is actually a scene in the fractal that results when portions of Z^(-1.74) and Z^(-7.4) are combined, and (1/C) is added. Speaking of cell phones, they appear to be taking over the world. A simple 25-mile trip will reveal the network antennas everywhere -- many on their own cell-phone towers, or electric transmission towers, but also lurking in the least likely places such as on the roofs of schools and other buildings, hidden in church bell towers, perched on advertising billboards, water tanks, even on abandoned grain elevators. It appears to be only a matter of time before we will have cell-phone antennas on every light pole, on every telephone and utility pole in every neighborhood. We are living in an ever-increasing ocean of electromagnetic radiation. We can't escape it. We know that the natural electric energy in the human body helps control tissue growth. Tests have already demonstrated that the radiation from a hand- held cell phone causes measurable brain damage in laboratory animals, and does so at levels in the range of those now in use. Can anyone imagine permitting a substance to be added to food intended for human consumption if that substance has been demonstrated to cause brain damage in laboratory animals? If this were done, the outcry would be overwhelming. But where is the outcry about cell-phone radiation. All we hear are hints of concern and not very convincing assurances that all is well. I wonder whether cell phones will be the asbestos and cigarettes of the future, and the telephone companies will have a reputa- tion like the giant tobacco corporations have today. Or perhaps we will need to shield our homes in faraday cages to escape the sea of deadly radiation. . . . Hmmmm . . . look at the outburst that a simple fractal just caused. Today's image rates a nominal 6 and has an overall value of 84. It was rendered with the outside set to the 'tdis' option, which stands for 'total distance' -- the total distance the points travel before escaping beyond the escape radius. The scene is nearly as interesting when rendered with the traditional equal- iteration-band method. I chose the 'tdis' method by the flip of a coin. The render time of 7 minutes may be bypassed by downloading the finished image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature of 48F 9C, Friday was pleasant enough here at Fractal Central. At least the cats must have thought so. They spent over three hours on the porch, enjoying the sun, which is just now making it over the holly trees in the afternoons. My day was acceptable, and the fractal I found was acceptable. This is just about all one could ask for. Hopefully, today will be a repeat, and the fractal will be even better. Until next time, take care, and we survived for thousands of years without carrying telephones everywhere we go. Why has it now become almost impossible to go about our everyday lives without one? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Cellular_Patterns { ; time=0:07:09.25--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.88786870396801200/-0.000456232474488\ 38/6.944164e+011/1/-10.0008080291402823/0.00695999\ 736778776107 params=1/-1.74/0.4/-7.4/0/0 float=y maxiter=1200 inside=0 outside=tdis periodicity=10 colors=000pHEhRN``WTjdLtmMqjMohMlfMjdNhbNe`NcZNaXM\ cTLdPLeLKfIJgEJhAIi6Ij3PhHWgVafhYikVlnRoqOrtKuwHwz\ FuxDtvCstArr8qp7pn5ol4nj7ikAelCamFYmHUnKQoMMoNQjOT\ fOXaP_YPcTQfPQiL3gfKXX_MORBmL9nF8o97p46p6Dq8JqAPrC\ VrE`sGfsIlsHooGrkFugFwcJwbNwbQwbUwbYwb`wbdwbgwbhqc\ hiciadiVdjNejFej8eNJELKKJKQHKWFKaDKgBKm9Ks7KyBMoEN\ fIOXLPOOQFQUBSX8U_5heDvjLlmMcoNUrOLtPHuNDvL9wKDrOG\ mRJiUMdXQ__TWbWReZNhCkDGmPKo_OqjSsuNdWTcZZcadbcjbf\ paiuakpfikjgfneascXwaSw_NwZTwaZwddwgjwjpwm`5tljpjc\ riWsgPueIvdBw`FlXJaTMSYNQaNOeOMiOKmPIqPGuQEyQDjOAW\ N8HN63N44Q94TE4WI4ZN4aS4dWAfUGhTLiRRkQWlPTmQRrRPwS\ NzTLNUJLUIN_HOeGPkKQpPXjUbdZhZcoThuNmwHqwFuwDwwBzw\ 9zw7zw5zw3zw2zl9zaGzRMmGTh5ZcI`_UaWfbSrcjwrbwsWrtP\ muJitDes7ar1Yr2Wq2Vq3Tq3Sq3Rp4Pp4Op4Np9GqEAq6t2AjL\ E`bE`bF_bF_bFZaFZaFYaFYaFX`FX`FX`FW`FW_FV_FV_FU_FU\ _FTZFTZFSZFSZFRYFRYFQYy74 } 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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Ternary Julibrot (or other process phase space) Slicing
by Hiram Berry 11 Mar '04

11 Mar '04

The technique that Jim has been using to generate FOTDs over the past ~3 weeks isn't limited to just the Julibrot space. It seems to be a general technique of looking at phase spaces for parameterized processes. In this particular case, Jim has made the observation that the M-sets, perturbed M-sets and quadratic Julia sets are all products of the same process, ie. z->z^2+C, which has two complex variables. Thus the process can be parameterized on 2 complex variables (the beginning value of z, z0, and C), each of which he splits into 2 real variables to get a four dimensional R-space. Defining planes by an anchor point and a pair of angles, and a viewing direction by another pair of angles, he generates the planar cut through the space to be viewed. I guess I stated the very obvious here, but that procedure leads naturally to a way to generalize the slicing to spaces defined by other processes. IOW, generally one has a process z->F[K1,K2,K3,...](z) parameterized by the K, one constructs the space K1xK2x..., then defines a linear slice through it which can be viewed on the screen. The means of definition of the sliceshould be in such a way that it's easy to understand variations in the K and do manipulations to get different views. So, when David brought up the cubic Mandelbrot sets, which have a third parameter, it occurred to me that we could do slicing in their Julibrot-equivalent spaces, ie. an R2 slice in an R6 space, if you are comfortable with splitting a complex dimension into two real parts. I am not comfortable with that approach, preferring to work natively in the complex dimensions and mapping the slice to R2 only in order to view it on my computer screen. Probably the two approaches are equivalent, but I'm not positive the views generated are the same. In any event, one can generate such slices for _any_ process with 3 process constants, which for wont of a better term I'm calling "ternary slicing" for the obvious reason. Now, I haven't worked these up into a .frm yet for the Rudy sets, cubic Mandelbrot sets, whatever you want to call them. I'm sure I will in the next few days, but in the meantime I noticed that the power-Msets make another natural extension of the Jbrot process, ie. z -> z^a + c, gives a phase space in C3 of {z0,a,c}. The Julibrot becomes a special case of the plane through the Ternary Julibrot space that is defined by a=2+0i constant, and arbitrary Julibrot slices are defined by lines on that plane. I'm sure everyone gets the idea. But the nice thing is that plane is parallel to ones containing the quartic Julibrot, etc., which can be generated by changing a single value in the parameters on the fractint z-screen. And, of course exploring the perpindicular and oblique slices through this extended space by varying other, angle parameters. Some results are not what one would expect; I have only looked at a few views, but here is a view I would never have thought was inherent in a M-set-like space. This was generated with the first .frm I tried, which inputs angles in complex format and so is not really user friendly at entering the viewing angle, and possibly my entering what should have been "pi/2" as "1.57" may have contributed to the strangeness, but... /************FRM BEGIN***********************/ TernaryJulibrotSlc { ; C1 linear slice of a C3 parameter phase space ; slices the power Julibrot (the quadratic Julibrot is the subset ; with a=(2,0) ). ; The phase space is of {z0,a,C} in the process z->z^a+C ; p1,p2,p3 are complex coords of an anchor point in the space ; p4,p5 are the complex latitude,longitude direction of the line ; emanating from the anchor point. IF (scrnpix==(0,0)) ; once per screen initialization hack ismand = true lim = 100 ; don't know what this should be-- may depend on "a" ;lat = (real(p4)*pi/180, tan(imag(p4)*pi/360)*pi/2) ;long = (real(p5)*pi/180, tan(imag(p5)*pi/360)*pi/2) lat=p4 ; temporary patch -- conversion from (deg,deg) to complex long=p5 ; angle failed to parse so enter angles in raw form Muz= cos(lat) * cos(long) ; meaning of lat and long accid. transposed Mua= sin(lat) * cos(long) ; but retained because used in Xtampak series Muc= sin(long) ; slice's polar coord unit direction in C3 space ENDIF k = pixel ; pixel position is the parameter of variation z=p1+k*Muz, a=p2+k*Mua, c=p3+k*Muc ; find pos in (z0,a,c) space : z = z ^ a + c |z| <= lim } /**************FRM END***********************/ /**************PAR BEGIN**********************/ ThePalaceAtXtampak { ; This was supposed to be a mundane slice of the ; ternary phase space cubic julibrot. It doesn't ; look anything like the typical Mandelbrot features. ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=ternaryjulibrotslc ismand=y passes=1 center-mag=-2.02478/-0.0573754/0.5629118/0.3572/90/1.31075705844807544e-\ 014 params=0/0/2/0/0/0/1.57/0/0/0 float=y maxiter=200 inside=zmag logmap=yes colors=000h`z0e0<3>eL0eeeLLL<4>ssLzzLzzz000555<3>HHHKKKOOO<3>ccchhhmmmss\ sU0cxzw<3>xjUxfNxbFxi8wU0<4>ZfQUiV0e0Koe<3>0zz<2>0Gz<3>rVzzVzzVrzVjB`0zV\ V<3>zzV<3>VzV<3>VzzVrzVjzLW0hhz<3>zhz<3>zhh<3>zzhvzhqzhWQ0hzh<2>hzvm00xi\ 8hqzhlz00S<3>S0SS0LS0EeL0000S70<2>SS0<3>0S0<3>0SS0LS0ESeee000IES<2>SES<3\ >SEE<3>SSEPSELSELLL000ESI<2>ESS<2>EHSKKS<2>QKSSKSSKQSKOSSL000SMKSOKSQKSS\ K<2>MSKKSKKSMKSOKSQKSSKQSKOSZZL000<8>PPCRRDUUF<3>eeL000<8>TTCWWDZZF<3>ll\ L000<8>XXC``DddF<3>ssL000<8>``CeeDiiF<3>zzL000<6>XXXaaafff<3>zzz000zzz } /*******************PAR END**********************/ Now, I did cobble together one possible mapping between complex angles and what Jim calls double angles in the R4 space, based only on the observation that the transcendental functions repeat every 2*pi the real direction, but not in the imaginary direction, and applied it to this more user friendly version of the .frm that takes ordinary degree measured angles as input for the directions (maps the imaginary part of the angle with tan() so that 90 deg -> pi/2*i and 180 deg -> inf * i). Here is it: /***********************FRM BEGIN******************/ TernaryJulibrotSl2 { ; C1 linear slice of a C3 parameter phase space ; slices the power Julibrot (the quadratic Julibrot is the subset ; with a=(2,0) ) in 6 dimensions with a 2 dimensional slice ; The phase space is of {z0,a,C} in the process z->z^a+C ; p1,p2,p3 are complex coords of an anchor point in the space ; p4,p5 are the complex latitude,longitude direction of the line ; emanating from the anchor point. They are input in user friendly ; (degree,degree) form instead of complex angular form. ; To start with the classic M-set initialize p2=(2,0);p4=(90,0);rest 0. IF (scrnpix==(0,0)) ; once per screen initialization hack ismand = true lim = 100 ; ? lat = real(p4)*pi/180+flip(tan(imag(p4)*pi/360)*pi/2) long = real(p5)*pi/180+flip(tan(imag(p5)*pi/360)*pi/2) ;lat=p4 ; temporary patch if ;long=p5 ; angle fails to parse then enter in complex angular form Muz= cos(long) * cos(lat) Mua= sin(long) * cos(lat) Muc= sin(lat) ; slice's polar coord unit direction in C3 space ENDIF k = pixel ; pixel position is the parameter of variation z=p1+k*Muz, a=p2+k*Mua, c=p3+k*Muc ; find pos in (z0,a,c) space : z = z ^ a + c |z| <= lim } /**********************FRM END**************************/ And here is a nice view of the quintic Mandelbrot that serves as a quick rendering entry point for z-screening your way through the TJ space: /************************PAR BEGIN**************************/ JovianCrown { ; Jumping-off place to explore the ternary Julibrot ; z->z^a+c. p1..p3={z0,a,c};p4,p5={lat,long}each(deg,deg) ; This is the power a=5 M-like ((lat,long)=((90,0),(0,0))) ; Fractint Version 2003 Patchlevel 1 ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=TernaryJulibrotSl2 ismand=y passes=1 center-mag=-8.88178e-016/6.10623e-016/1.041667 params=0/0/5/0/0/0/90/0/0/0 float=y maxiter=200 inside=zmag logmap=yes cyclerange=2/10 colors=000m00eee0000000L00e0<3>eL0SSLllLssLzzLzzz000555<3>HHHKKKOOO<3>cc\ chhhmmmsssU0cxzw<3>xjUxfNxbFxi8wU0<4>ZfQUiV0e0Koe<3>0zz<2>0Gz<3>rVzzVzzV\ rzVjB`0zVV<3>zzV<3>VzV<3>VzzVrzVjzLW0hhz<3>zhz<3>zhh<3>zzhvzhqzhWQ0hzh<2\ >hzvm00xi8hqzhlz00S<3>S0SS0LS0EeL0000S70<2>SS0<3>0S0<3>0SS0LS0ESeee000IE\ S<2>SES<3>SEE<3>SSEPSELSELLL000ESI<2>ESS<2>EHSKKS<2>QKSSKSSKQSKOSSL000SM\ KSOKSQKSSK<2>MSKKSKKSMKSOKSQKSSKQSKOSZZL000<4>EE7HH8JJ9MMBPPC<3>__IbbKee\ L000<4>GG7JJ8NN9QQBTTC<3>eeIiiKllL000<4>II7MM8QQ9TTBXXC<3>llIooKssL000<4\ >LL7PP8TT9XXB``C<3>rrIvvKzzL000<3>JJJOOOSSS<6>zzz000zzz } /************************PAR END*****************************/ Hopefully this is interesting to someone, -- Hiram Berry

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Once per image calculations in formula functions
by Hiram Berry 10 Mar '04

10 Mar '04

Somewhere in the fractint documentation I came across explanation to the effect that calculations done in fractint fell into one of three categories, once per image, once per pixel, and every iteration. I assume an example of the first is assignment of p# values on the z-screen, stuff before the ':' encompasses the second, and stuff after the ':' is the third category. But what about expressions that will be constant over an entire image, but need to be specified in the body of the formula before the ':' ? Is there a way to explicitly tell the parser to do that so that it doesn't redo the unnecessary calculations every pixel? I think it is too much to ask to expect the parser to make this optimization implicitly, and my benchmarking indicates that such optimization is not done. Maybe I missed something in the documentation for using the formula editor on this count, but if so then so did others; I notice that Jim M's formula for slicing Julibrots in R4 space, "SliceJulibrot2.frm" could very profitably take advantage of once per image evaluation. In it he converts input angles from a user friendly degree form into the machine friendly radian form, and generates some expression coefficients from the sines and cosines of those angle which are constant over the duration of the image. Once-per-image evaluation of those terms would let that .frm run much faster, yet I noticed that the very accomplished and knowledgeable Jim does not do anything to explicitly force such an evaluation scheme for those terms, which leads me to suspect that there isn't a "nice" syntactic mechanism for doing so. And yet I do recall the categorization somewhere in the documentation that implied it was possible to do once per image calculations. So if anyone knows _how_ to do this "the right way", please reply. I raise the question of syntactic orthodoxy only because I did find a hack, which follows, that seems to accomplish it. It really doesn't feel right though. The hack is to put the once per image initialization code inside an IF..ENDIF block that (hopefully) executes only on the first pixel of the image. It worked when I applied the technique to "SliceJulibrot2.frm", speeding up the rendering of an "easy" image severalfold. However, the code just doesn't feel right. It relies on an assumption that the drawing technique will render pixel (0,0) first, which I tried to ensure by setting the PASSES=1 option, but I really don't think that can be assumed. So I really hope someone will tell us the orthodox way to accomplish once per image initialization. In the meantime, Jim's original .frm was: SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } , while my hack to speed it up (which it does substantially in most cases tried) with o.p.i.i. is: SliceJulibrot2a {; SliceJulibrot2 with per screen initialization IF (scrnpix==(0,0)) 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), term1=cg*cd, term2=ca*sb*sg*cd+ca*cb*sd, term3=cg*sd, term4=ca*cb*cd-ca*sb*sg*sd, term5=ca*sb*cg ENDIF pix=pixel, u=real(pix), v=imag(pix), p=u*term1-v*term2, q=u*term3+v*term4, r=u*sg+v*term5, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } Again, the drawing method should be set to single pass, but if anyone has a better solution or can shed more light on this problem, PLEASE reply. Sincerely, Hiram Berry

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fixed formula file
by David Lowenstein 10 Mar '04

10 Mar '04

since the fractals had the wrong names, I renamed them. -david

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Colors of Posted Pars
by Lee H. Skinner 10 Mar '04

10 Mar '04

I also need to note that Hiram did attach sloshdun.map to his message, but the list moderated has specifically said not to post any attachments to the list. The Fractint recordcolors=Y command easily gets around this restriction. Lee

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Colors of Posted Pars
by Lee H. Skinner 10 Mar '04

10 Mar '04

SherLok Merfy and Hiram Berry have recently posted some pars. Unfortunately I (and presumably others on this list) cannot generate them as posted because the pars contain reference to non-standard map names. Whereas chroma.map is included in the Fractint distribution files, kayos.map and sloshdun.map are not. Anybody can name a color map, but others will not have access to the map file. The way to get around this is to put recordcolors=Y into your sstools.ini file, so that the colors will get recorded into the par entry submitted for posting. 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! Thanks. Lee

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FOTD 10-03-04 (Entropy [7])
by Jim Muth 10 Mar '04

10 Mar '04

FOTD -- March 10, 2004 (Rating 7) Fractal visionaries and enthusiasts: To find today's image I returned to the same parent fractal that held yesterday's scene, and investigated the large eastern Mandeloid. Instead of the East Valley area, I checked the tip of the negative, or in this case, the main positive stem. In contrast to the main stem of the classic Mandelbrot set, the stem of the Mandeloid in today's fractal winds into a loose spiral as it nears its end. This spiral nature is reflected in the pattern surrounding today's midget. I named the image "Entropy", which is a word that refers to the amount of disorder in a closed system. Disorder refers to the amount of energy unavailable for useful work. Unless outside energy is introduced, entropy always increases and the system reaches a state of luke-warm death. In some fractals, the disorder seems infinite, in others there is nothing but order. Some day soon I might wax philosophic about this, but today is not the day. Today's image is in a state of partial entropy, a fact that inspired the name. The rating of a 7, combined with the render time of just under 14 minutes, gives an overall value of an even 50. The curious will run the parameter, the wise will download the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday passed chilly and cloudy here at Fractal Central. The temperature of 45F 7C was a bit too cold for the cats, who ventured outdoors only long enough to smell a few bushes. When they sulked back inside, a generous treat of tuna eased their troubles. In my case, it will take a bit smaller pile of work waiting to be done to ease my troubles. The work will be finished however, and the next fractal will appear on schedule in 24 hours. Until then, take care, and keep iterating. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Entropy { ; time=0:13:54.76--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+4.77816002409709700/+1.319995900632449\ 00/1.15829e+011/1/-25/0.0294780650801364785 params=0.55/-1.1/0.11/-3.1/0/0 float=y maxiter=1500 inside=0 logmap=288 periodicity=10 colors=000M0SM0SM0SM0SM0SM0SM0SM0SM0SM0SM0SM0SM0SM\ 0SM0SM0SN0SN0SN0SO0SO0SO1SP2SP3SP4SQ5SQ6SR7SR8SS9S\ SASSBRTCQTDPUEOUFNVGMVHLWJKXIJZIH`IGbIFgHElHDrHCwU\ CzUCwHBrIBmJBiJBgKBfLAdLAbMA`NAZNAYO9WP9UP9SQ9QR9P\ R9TUAWWAZYAb`AebAhdBkfBoiBrkBumByr7xoBwmEvkIuiLtgP\ seSrcWqaZp_boYenWimUllSpqUxnSukQshPpeNnbMk_KiXJfUH\ dRGaOE_LDYPGZSJ_WM_ZP`bS`eVaiYal`bocbggd`kfTogMsiE\ wk7zlChfGR`K9VLBYLC`MDcMEeNFhNGkOHnPEsOIpNLmMOjLRg\ KVdJYaI`ZHcWFhTGfUGdUHbUHaUH_UIYUIXVJVVJTVJSVKQVKO\ VKNVHKTFHRCDP9AN77MC9KGAILBGPDEUECYFBWLEURHSXKQbNO\ hQMnTGxTKsWOoZSj`Wfc_bebYhfUjjQmnLorHruDttFssGrsHq\ rJqrKpqLovHuqMolRjgWdb`_YeUVmOUjPTgPSdPRaQSZQUWQWT\ QYRR_OR`LRaIRbFSdCSf9Sh7SjQGjQLjQQjQVjQ_jQdjQijQnj\ QsiTzjQxkNwlMumLtmKrnLqoMopNnpOmqPnrQosRptSquTrvUs\ wVtxWuyXvzYwzZxz_yz`zzazzbzzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczzcz } 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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[Fractint] so noel giffin, the rudy sets and your sets belong to the same family
by David Lowenstein 10 Mar '04

10 Mar '04

so what will it be called? -david

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FOTD 09-03-04 (Jeweled Minibrot [7])
by Jim Muth 09 Mar '04

09 Mar '04

FOTD -- March 09, 2004 (Rating 7) Fractal visionaries and enthusiasts: After a three-day delay, today's image takes us into the oversized fractal that results when unlikely portions of Z^(-1.1) and Z^(-3.1) are combined and (1/C) is added. The parent fractal is an oversized thing, too large for the most interesting part to fit on the default screen. But one outzoom reveals two Mandeloids, sitting butt to butt, with their East Valleys connected by a most extraordinary filament. I have not yet examined the filament, which I suspect has the same appearance regardless of how deep one looks into it. What I did examine was the southern shoreline of the East Valley of the western Mandeloid. A short distance inland I found a network of lacy filaments, spotted with midgets resembling jewels on a string. The midgets are surrounded by the basic 'East Valley' patterns, but these 'brain-like' patterns are surrounded in turn by most interesting networks of filaments, a good example of which is illustrated in today's image. Extending southwest-northeast from the central midget is a lovely network of jeweled filaments like the filament network on which today's image lies. Extending northwest-southeast from the midget are filaments like those that connect the two large Mandeloids in the parent fractal. Most likely, in their depths, these filaments simply go on and on forever. I named the image "Jeweled Minibrot", which fairly well describes it. The unlucky-appearing render time of 13 minutes, 13.13 seconds is one of those unlikely statistical coincidences that happen now and then. But the image itself is worth a moderately high 7, and those who spend 13 minutes watching it slowly appear on their screens will be lucky indeed. They will be lucky because most machines now in use are faster than my old P200 unit, and will render the image in far less time. When the render time is considered, the overall value is 53. Those who download the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will save the most time, but miss some of the fun. The greatest weather excitement since the last FOTD came on Saturday afternoon, when an unexpected severe squall struck the harbor and flipped over a water taxi. Sunday was bright and chilly. Monday was cold and blustery, with occasional flurries of snow. The fractal cats did not appreciate the Monday condi- tions at all, and showed their disapproval by returning inside only a few minutes after going out. Today is starting in a similar manner. We'll see what the cats think of this. For me, the greatest amusement so far today came when I opened my e-mail box and found a spam letter with a subject line telling me that the sender had gotten my password and credit- card information. Imagine that -- an honest thief who warns me of his theft and gives me a chance to cancel the card before he uses it. I wonder what was for sale on the web site the letter directed me to. The graphic-design work is still heavy, but under control. The next FOTD will appear in 24 hours. Until then, take care, and be alert for runaway fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Jeweled_Minibrot { ; time=0:13:13.13--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-6.56488536701683900/+0.815957995544778\ 90/8.81e+005/1/45/-2.44425623421862248e-008 params=0.55/-1.1/0.11/-3.1/0/0 float=y maxiter=3200 inside=0 logmap=279 periodicity=10 colors=000DGMDGNEHOFHPGIQGIRHJSHJTIKUIKVJLWJLXKMYK\ MZLN_LN_MO_MO`NPaNPbOQcOQdPRePRfQSgQShPTiOTjNUkNUl\ MWmMYnL_oKapPcqTerXgs`itdkuhmvlmwpmxtmyumzvmzwmzwm\ zwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzw\ mzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmz\ wmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwm\ zwmzwmzwmzwmzwmzwmzwmzwmzwnzwozwozwnzwmzwlzwlzwkzw\ jzwizwizwhzwhzwhzwizwjzwkzwlwymtxmqwmnwmkvmhvmcrmZ\ rmUomPokKmmHmhFhfChdAeb7ce4cf2fh0ij0ml0po0sn0vr0sp\ 0pp0nn0km4ik8fiDdgHafL_dPXbTVaXT_VSZTRYRPXQOWONVML\ UKKTJJSHHRFGQDFPCIQBLRBOSBRTBUUBXVB_WBbWBeXBhYBkZB\ n_Bq`BtaBwbBybBq_GjXKcUOWRSPOWIL_BIcLRNU_7XX5_V3aX\ 1cY0d_0f`0ha0ic0kd0mf0ng0ph0rj0sk0um0wn0xo0wn0vo0u\ p0tq0sr0rs0qt2pu4ov7nw9mxClyEkzG4zF6zE8zEAzEBzEDzE\ FzEGzEIzDKzDMzDNzDPzDRzDSzDQzAOz8Mz5Kz3Iz1Gz0Ez0Cz\ 0Hz2Mz9RzHlzGzzZkzTYzNKzH } 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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