October 2010 - Fractint - mailman.xmission.com

FOTD 26-10-10 (Blazing Slices [5])
by Jim Muth 26 Oct '10

26 Oct '10

FOTD -- October 26, 2010 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a view of the western part of the Mandelbrot set rotated so that west is facing up. It is sliced at an angle rotated 66 degrees toward the Oblate orientation. The image is actually a scene in the four-dimensional Z^2+C complex known as the Julibrot, which holds all the perturbed Mandelbrot sets as well as all the Julia sets. Over the years I have stumbled upon countless other Julibrot scenes sliced in odd directions, which look nothing at all like either Julia or Mandelbrot images. Perhaps I'll use some of these odd images as FOTD's before too long. They certainly are interesting enough even though they might not always excel in artistic worth. The spurious buds in today's image are neither Julia nor Mandelbrot things. They exist only at the orientation of today's image. Changing the P1 or P2 parameters will show how critical the orientation is. The name "Blazing Slices" has no connection to an old western comedy movie. It refers to the fiery colors I intentionally gave the image. The calculation time of 10 seconds makes even a 5-rated image such as today's a bargain. The image may also be viewed, this time in finished form, on the FOTD web site at: <http://www.Nahee.com/FOTD/> I made a big mistake Monday afternoon when I caught FL watching one of those mushy latin soap operas and asked her what the show was about. When she described the plot, it went something like this: `that woman loves that man but he doesn't love her and the woman he does love doesn't know that he is her brother. This other woman wants a divorce from her no-good husband, but he has just won a huge lottery and now she doesn't know what to do about the man she really loves. This other man loves the first woman but he has a crippled wife who depends on him.' On and on the convoluted plot description went until, after a few minutes of trying to fathom the intricacies, I dozed off. When I jerked to my senses, I asked FL where does the action fit in. The resulting laughter made my day. A fairly pleasant day passed almost un-noticed here at Fractal Central on Monday. The fractal cats did notice the intermittent periods of sun and the unseasonably warm temperature of 72F 22C, but the humans were involved in other things. The next FOTD will be posted in 24 hours. Until then, take care, and the golden rule is supposed to work both ways. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Blazing_Slices { ; time=0:00:10.10-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/1.10231/\ 1.5/2.0709 params=0/66/0/90/-0.75/0/0/0/2/0 float=y maxiter=450 inside=0 logmap=yes passes=1 colors=00091ZB2_E3`H4aK5bM6cP7cS8cV9cYAc`BccC_fDWj\ ESmFOpFMqEKs9Iv2Jz0KzALzDMvGNsJOpMPpPQpSRpVSpYTp`S\ ocSofSoiRpiRpjQpkQqlQqlPqmPrnOroOroNspNsqNsrMtrMts\ LttLuuLuuKuvKvwJvxJwzKvxJvwJuvJutJtsJtrJspJsoJrnJr\ zJqzJqzJpzJpzJozJozJnzJnzJmzJmzJlzJlzJkzJkzJjzJpzK\ mzJjzJhzIzzzbzzzzzYzzWzzzzzQzzOzzzzzKzzJzzJzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Fractal animal: Fractofusus
by david 25 Oct '10

25 Oct '10

http://en.wikipedia.org/wiki/Fractofusus -- David gnome(a)hawaii.rr.com authenticity, honesty, community

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FOTD 25-10-10 (Seahorse Abomination [6])
by Jim Muth 25 Oct '10

25 Oct '10

FOTD -- October 25, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a "Seahorse Abomination", which is what I named it. Seahorse Valley never deserved to have such things done to it. The valley is a nice little place, a four-dimensional complex, so what have we done to the innocent valley to cause the gross disruption apparent in today's image? To begin, the image is not a Julia set of the familiar Seahorse Valley of the Mandelbrot set. It is a Julia set of Seahorse Valley of the Quaternion Mandelbrot set, which is actually an eight-dimensional Julibrot complex, with a 4-D Mandelbrot aspect and a 4-D Julia aspect. I'll not go into details about the wonders of the eighth dimension; I'm still working on understanding the fourth. But one thing certain is that in 8-D space, 28 two-dimensional planes pass through every point, with every plane perpendicular to all the others. (There is something puzzling about the two quaternion formulas. Today's image was created by the type=quatjul formula, which plots Julia sets. This formula has six variable parameters, all of which are necessary if we are to move off from the screen in the six perpendicular directions. Yet the type=quat formula, which plots Mandelbrot sets, has only two changeable parameters [plus two unused parameters] both of which have the same effect, giving the impression that the quaternion Mandelbrot set is a simple three-dimensional thing that would result from rotating the classic M-set around the X-axis.) Be that as it may, today's image, with its minor mathematical interest and only slightly better artistic worth, rates a 6. The fireball-fast calculation time of under 3 seconds will leave little time to wonder about higher dimensions before the image bursts onto the screen in a blaze of mediocrity. Those who prefer to remain burst-free may see the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Sunday here at Fractal Central featured a mixture of sun and clouds, and a very pleasant temperature of 70F 21C. The fractal cats complained that there was not enough sun then went to sleep on the living room carpet. After my trip back to the nostalgia-infested land of Old Fractal Central on Saturday, Sunday seemed relaxing. (Though I still wish the Phillies had won the NL pennant.) FL occupied herself wondering why I end my FOTD discussions with so many 'silly and unanswerable' comments. The next FOTD will be posted in the generally accepted 24 hours. Until then, take care, and if the belief in God and an afterlife is a defense mechanism evolved to enable us to cope with the awareness of our ultimate mortality, how would society react if it were ever demonstrated beyond all doubt that these things do not exist? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= SeahorseAbomnation { ; time=0:00:02.70-SF5 on P4-2000 reset=2004 type=quatjul center-mag=-0.0300864/0.01\ 38653/1.05286/1/32.5/0 params=-0.75/-0.055/-0.113/\ -0.013/-0.048/-0.134 float=y inside=0 periodicity=0 colors=000KIcLJcMKcNLcOMcPNcQOcTQcWScYUc`WcbYceZch\ `cjbcmebohcrjetffu_dvTawLZwCXs6Uo0Ti1Td3T`5TY6RV6P\ S6NR6JP4EM38H3BB4C56C58E3BG4EI5HK5KM6NO6PR6SU6VX6X\ _6_b6be6ch8ae9ZcBWbCTaDQ_FN_GK_HH_IF`IE`JD`JC`KB`K\ AaL9aL8aM7aM6aJ2eH0hC0c70Z30V51W62W83X94XB5YC6YD7Z\ F9ZGA_IB_JC`LD`MEaNFa7MeANdDNdFNcIOcKObNObPPaSPaUP\ aM0oN1mO5kP8iQCgRFeSJcTMaUQ_x3pr9llEhfJe`OaR0iS3gT\ 7eTCdUGbULaVP_0J46LABNFGOKLQPQSUCpifQdcRb`SaYT_rp0\ nm2ji9feFb`MZXT7efAceCbdEacG`cI_bLYaNX`PW`RV_TUZ_C\ gZEfZFeYGeYHdYJcXKcXLbXMaWNaWP`WQ_VR_VSZ2gm7djBbhF\ `fJZdNXbRV`faRc_TaYVZWWXUYjY0hX0fW4dW9bVDaVI_UMYUR\ WTVUGTVIUVJVVLVVMWVOXVPXVRYVSZDQNFRPHRQIRRKSSMSTNS\ UPSVRTWSTXUTYk03i17g5Be8EcCIaFL_JPYMSWQWJphKpgLofM\ mfMleNjdOhdPgcPecQcbRbaS`aSZ`TY_UW_VUZbfWadX`cX_aX\ Z`YZ_YYYYXXZWVZVUZ8p9OmYPkZQiZQgZRfZRdZSbZT`ZT_ZUY\ ZUWZVUZ_LiZNfYPdXQbWS`f0V } END PARAMETER FILE=========================================

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FOTD 24-10-10 (Elephant Wreath [5])
by Jim Muth 24 Oct '10

24 Oct '10

FOTD -- October 24, 2010 (Rating 5) Fractal visionaries and enthusiasts: Elephants are everywhere in Seahorse Valley of the Mandelbrot set. They come in all sizes, shapes and colors. They also enjoy doing tricks. The elephants in today's image have formed themselves into a wreath, a bit too early for the season to be sure, but decorative just the same. The name "Elephant Wreath" describes the scene well enough. The image is stretched more than 1000 times (1083 to be exact) in the horizontal direction. Such stretching is necessary to correct the natural distortion of the scene, which lies in an orientation rotated 10 degrees from the Rectangular toward the Oblate. The rating of a 5 might be a bit too conservative, but how much can a holiday wreath decorated with elephants be worth? The calculation time of 11-1/2 seconds is fast by any standards. Viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> is equally fast, and could be a lot more fun. A frosty morning gave way to warm sunshine and an afternoon temperature of 64F 18C here at Fractal Central on Saturday. (It reached 73F 23C at Old Fractal Central 150 miles 240km south of here.) The fractal cats slept through most of it. My day, which was occupied with a trip back to Old Fractal Central, was otherwise uneventful. The next FOTD will likely be posted within 12 hours, which will bring the FOTD up to date if it happens. Until next time, take care, and keep alert for that quantum stuff. It's lurking everywhere. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Elephant_Wreath { ; time=0:00:11.52-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.003041525\ 45290287/0/16.30635/1083 params=100/90/0/90/0.265/\ 0/0/0/2/0 float=y maxiter=1500 inside=0 logmap=48 symmetry=xaxis periodicity=6 mathtolerance=0.05/1 colors=000BaMCbODcOEdQFeSGfUHgWIhYJiZKjYMkYOlXQmXS\ nWUoWZrVcuVhxUmzUruVvrVwnVzkWwhWmeWcbWUZXKWWJVVHTV\ EQUCNTAKS9IS8HS7GS6FR5DS4CQ3AO25M10K00K40K70KA0KD0\ KG4PK4UN4ZQ4cT4hW4lX6nY7oY8pZ9rZBs_Ct_Dv`Ew`FxaHub\ IrcKpcLmdNkeOheQffRcgT`gUZhWWiXUiZRj_PkaMkbKhaMe`O\ c_Q`_RYZTWYVTXXRXYOW_LVaJUcGUdDTfBSh8Rj6Rk8ShATfBU\ cDUaFV_GWXIXVKUULVUNWUOXUNYUNYUMYUMXVLXWLXXLWYKWZK\ W_JV`JVaJVbIScIQdHNeHLfGMgGNhGNiGOjGPkGPlV0PX1OY1N\ Z1M_1L`2La2Kb2Jc2Ie3Hf3Hg3Gh3Fi4Ej4Dk4Dl4Cn5Bo5Ap5\ 9q59r68s67t66u66r9BoCGlFLiHQfKVcN_pIZaPcP_mOWhNTcN\ Q_MNVMJRLGMLDIKADK79M9ANBBODCPEDRGESIFTJGULGVNHXOI\ YQJZSK_ULaVMbXNcZNd_OeaPgcQhdRifSjhTjlVkiTkfSkdQka\ Pk_NlXMlUKlSJlPHlNGlKEmHDmFBmCAmA8m77m56l66k76k86j\ 96jA6iB6iC6hD6hE6gF6gG6fG6eH6eI6dJ6dK6cL6cM6bN6bO6\ aP6aQ6`R6`R6_TD_UK_VQZWXZXcZYibVeeSaiPZlMVoJRsGOvD\ KyBHo9DqjdsleunfvT9vpghQY } frm:SliceJulibrot4 {; 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Twilight Minibrot
by Roger Alexander 24 Oct '10

24 Oct '10

Today's post is a minibrot in twilight colors. At the usual http://maxitersfractalfollies.blogspot.com Twilight Minibrot { ; fract483.gif ; blank ; calctime 0:03:23.94 ; created Oct 24, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=hermanm_man-polar center-mag=-2.00319/-0.00306882/27.01637/1/90/3.88578058618804789e-016 params=3/2/1/45/1/0 float=y maxiter=1500 inside=0 outside=atan decomp=256 colors=000302403503504604705805806907A07B08B08C09D1AE1AF1BF1BG1CH1CI1DI1\ EJ1EK1FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21w00z03\ z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0zz0xz0vz0tz0rz0pz0nz0lz0jz0h\ z0fz0dz0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0Iz0Gz0Ez0Cz0Az08z06z04z02z00z00\ y10x20v20u30s40r50p50o61n71l81k91i91hA1gB1eC1dC1bD1aE1_F1ZF1YG1WH1VI1TJ2\ SJ2RK2PL2OM2MM2LN2JO2IM2GJ2EH2CE1AC18916614312000101302503605806A07C19D1\ 9E1AF1AF1BG1BH1CI1DI1DJ1EK1EL1FL1FM1GN1HO2IO2JQ2IS2HV2GX2F_2Da2Cd2Bf2Ah1\ 9k18m17p15r14u13w12z00z20z50z70zA0zC0zF0zH0zK0zM0zP0zR0zU0zX0zZ0za0zc0zf\ 0zh0zk0zm0zp0zr0zu0zw0zz0zw0zu0zr0zo0zl0zj0zg0zd0za0z_0zX0zU0zS0zP0zM0zJ\ 0zH0zE0zB0z80z60z30z00x01v02s03q04n06l07i08g19e1Ab1B`1CY1EW1FT1GR1HO2JN2\ IM2HK2GJ2FH2DG2CE2BD2AB19A18817715514413212000000101201 } frm:hermanm_man-polar { ; Kerry Mitchell 16feb98 ; ; real(p1) = z exponent (use integer >= 2; m=n-1) ; imag(p1) = g exponent (integers) ; real(p2) = alpha magnitude (try 1) ; imag(p2) = alpha polar angle (try integers) ; real(p3) = critical point selector (>0 for positive root) ; imag(p3) = unused (<0 for negative root) ; use decomp=256 ; zero and infinity bailouts hardcoded to 1e-6, 1e6 ; coloring speed hardcoded to 4 ; c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1 maxr=1e6, minr=1/maxr, speed=4*pi/128 r=real(p2), t=imag(p2), alpha=r*(cos(t)+flip(sin(t))) oln=1/log(n), fac=log(0.5*log(maxr)) c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1 hypden=sqr(n-m), hypfac=hypnum/hypden if (real(p3)<0) pn=-1 end if if (real(c2)>hypfac) pn=-pn end if if (imag(c)<0) pn=-pn end if afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n d=sqrt(bfac*bfac-4*afac*cfac) z=(bfac+pn*d)/(2*afac) : g=(z-c)/(1-c*z), z=alpha*z^n*g^m iter=iter+1, r=|z| ; ; orbit trap around 0 ; renormalize iteration count via decomp angle ; set "iteration done" flag (iter=-1) ; if (r<minr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed z=cos(angle)+flip(sin(angle)) iter=-1 end if ; ; orbit trap around infinity ; renormalize iteration count via decomp angle ; add pi to angle to separate from 0 orbit trap ; set "iteration done" flag (iter=-1) ; if (r>maxr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed angle=angle+pi z=cos(angle)+flip(sin(angle)) iter=-1 end if iter>0 } Roger Alexander

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Algae
by Roger Alexander 23 Oct '10

23 Oct '10

I usually don't give my posts names but if I did I would call this one "Algae" because it reminds me of algae. Am I consistent or oh so predictable? Pre-calculated at http://maxitersfractalfollies.blogspot.com Algae { ; fract482.gif ; blank ; calctime 0:05:29.50 ; created Oct 22, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=conic-near_man center-mag=+0.00133886277847312/+1.00493995512520900/10743.32 params=-0.5/-0.4000061037018952/0.03488265633106479/0.125/0.557969908749\ 6567/-0.06808679464094974 float=y maxiter=1500 inside=0 decomp=256 periodicity=0 colors=0100200300400500700800900A00B00D00E00F00G00H00J00K00L00M00N00P00Q\ 00R00S00T00V00W00X00Y00Z00`00a00b00c00d00f00g00h00i00k00k01k02k03l04l05l\ 05m06m07m08n09n0An0Bo0Bo0Co0Dp0Ep0Fp0Gp0Hq0Hq0Iq0Jr0Kr0Lr0Ms0Ns0Ns0Ot0Pt\ 0Qt0Ru0Su0Tu0Tu0Uv0Vv0Wv0Xw0Yw0Zw0Zx0_x0`x0ay0by0cy0dz1dz1ez1ez1fz2fz2gz\ 2gz2hz3hz3iz3iz3jz4jz4kz4kz4lz5mz5mz5nz5nz6oz6oz6pz6pz7qz7qz7rz7rz8sz8sz\ 8tz8uz9uz9uz9tz9tz9tz9sz9sz8sz8rz8rz8rz8qz8qz7qz7pz7pz7oz7oz7oz6nz6nz6nz\ 6mz6mz6mz5lz5lz5lz5kz5kz5kz4jz4jz4iz4iz4iz4hz3hz3hz3gz3gz3gz3fz2fz2fz2ez\ 2ez2dz1dz1cz1bz1ay1`y1_y1_x1Zx1Yx1Xw1Ww1Vw1Uv1Uv1Tv1Su1Ru1Qu1Pt1Ot1Ot1Nt\ 1Ms1Ls1Ks1Jr1Ir1Ir1Hq1Gq1Fq1Ep1Dp1Cp1Co1Bo1Ao19n18n17n16m06l06k06j06i06h\ 06g06f05e05d05c05b05a05`05_05Z04Y04X04W04V04U04T04S04R03P03O03N03M03L03K\ 03J03I02H02G02F02E02D02C02B02A0190180170160150140130010 } frm:conic-near_man { ; Kerry Mitchell 11may98 zc=0, cc=pixel, maxr=1e12, minr=maxr, iter=1 a=real(p1), b=imag(p1), c=real(p2), d=imag(p2) e=real(p3), f=imag(p3): iter=iter+1, zc=sqr(zc)+cc, x=real(zc), y=imag(zc) conic=|x*(a*x+b)+y*(c*y+d)+e*x*y+f| if (conic<minr) minr=conic end if if ((|zc|>maxr)||(iter==maxit)) iter=-1 t=log(minr) z=cos(t)+flip(sin(t)) end if iter>0 } Roger Alexander

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FOTD 23-10-10 (Star of the Spike [8])
by Jim Muth 22 Oct '10

22 Oct '10

FOTD -- October 23, 2010 (Rating 8) Fractal visionaries and enthusiasts: The 2-second calculation time of today's image is no mistake. The image is a scene in the best-known fractal of all -- the Mandelbrot set. And on my particular fractal dedicated machine, the Mandelbrot set runs at faster-than-light speed. I originally planned on naming the image "Not Quite Dead Yet" to indicate that the M-set is no tired warhorse on its last lap around the track. It is chock full of interesting and lively scenes, not only of minibrots, but of countless other undiscov- ered wonders. But then I decided that such a name was much too downbeat for such an upbeat image. I finally decided on the name "Star of the Spike", which has a far more positive sound and also indicates the location in the M-set. The image rates an 8. I'm not sure how much of that rating is due to my coloring, but I did work on the colors for well over an hour. The scene lies on a filament extending from the Seahorse Valley of a minibrot located on the main spike of the M-set, not far west of the main body of the set. As I said earlier, the calculation time is an incredibly brief 2 seconds. But there is still the hassle of copying this letter into your parameter file in text mode with a .par extension, hoping that no spurious characters get inserted, then running it as you would any other parameter file. This minor inconvenience may be avoided by going to the FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the finished image there. A mixture of clouds and sun, a brisk wind from the northwest and a temperature around 52F 12C gave Friday a very autumnal feeling here at Fractal Central. The fractal cats enjoyed the sun when it was shining and the house heat when the clouds prevailed. My day was slow enough to put the extra coloring work on the FOTD. FL had a slightly more active day. I think a trip back to Old Fractal Central, 130 miles (200km) south of here, is coming up on Saturday, so do not be surprised if the FOTD for October 24 is late. Until whenever, take care, and wouldn't it be great if humans had designed the laws of the natural world instead of the great unknown? (But could we have done it with- out fighting?) Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Star_of_the_Spike { ; time=0:00:02.11-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.40473711526\ 07/+0.0001010790714/8e+008/1/180 params=0/0 float=y maxiter=5200 inside=0 logmap=538 periodicity=6 colors=0000AL0AM0AN0AO0AP0AQ0AR0AS0AT0AU0AV0AW0AX0\ AY0AZ0A_0A`0Aa0Ab09c08d07e06f07g08h09i0Aj0Bk0Bl0Cm\ 0Dn0Eo0Fp0Gq0Gr0Hs1It2Ju3Kv4Iy5Kv5Ms6Nq6Pn7Ql7Si8T\ g8Vd9Wb9Y_AZYA`VBaTBcQBdOEcQHcSJbUMbVPbXRaZUa`WaaX\ bbXbcXbcXbdXbdYbeYbeYbfYbfYcgZcgZchZchZciZcgZcd_ca\ ZdZYeWXfTWgQVhNUiKUjHUkEUlCUm9Uo6Uq3Us1Ut2Ut3Yt4bu\ 5fu6ju7ov8tv9zz8zvAztBwrCwpDwnEvlGvjHvgIveJvcKvaLu\ _NuYOuWPuTQuRRtPTtNUtLVtJWtHXyA`tFYoJWkOUfSSaXQY`O\ TeMOiKKmILlKLlMMkOMkPYkA_hB`eBbbBc_CeXCfUEgPIhKMiF\ QjAUk6Yk1an9epHhsOluWoxcszevzUWm85cKX1Vx4_t7dq9grC\ ivEmzDrzDqzDovDcmCbaCSVCHRCANJNMQWBkd0zc0qlFejEbiD\ XgDVfCUeCVaAWY9XV7YR6ZN4ZK3T_COoLRkITgGVcEX`C_X9aT\ 7cP5eM3cOCaQK_SSZU_XWgVYoU_wbbskdotfkqkXnpIku4ovOR\ wP2xQ5tI8qAAn3CoBEpIGpPIqXPmTSlNVkGfzzczzazzZzzXzz\ UzzSzzPzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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<David> 4 variables define a 4D space
by Hal Lane 22 Oct '10

22 Oct '10

David, Jim Muth said, "...the formula Z^2+C consists of two complex numbers which have four variables in all. Four variables define a space of four dimensions." Here's as much of one four-dimension fractal as can be seen. I've projected the 4D fractal object to 3D, then put a string of these 3D projections together into a pseudo-4D .gif animation. A different 3D portion of the 4 dimensional fractal object is shown in each frame in the animation: http://home.earthlink.net/~hallane/hals_fractals_n_photos/ - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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FOTD 22-10-10 (Unknown Landscape [6])
by Jim Muth 22 Oct '10

22 Oct '10

FOTD -- October 22, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us back to the 'Patterns in the Mist' image of October 20 -- two days ago. In that discussion I commented that the image had minibrots, but they were not very interest- ing. Since then, I have done further exploring and found that the minibrots are more interesting than I had assumed. I decided that today's image, which shows a minibrot that was hidden in the earlier image, is worth being declared FOTD for October 22. The color palette is basically the same as the one in the earlier image, with only a bit of tweaking to emphasize the hidden patterns. Now, instead of two levels, we have three levels of near-random chaos. The strongly colored highlights are seen to be gathered near the minibrot, with the outlying, more vague features sugges- ting elements of the actual Seahorse Valley location. The rating of a 6 is all I could give today's image, which after all is basically a repeat of the earlier image. The name "Unknown Landscape" is perhaps a bit overdone. The scene does lie in the Seahorse Valley of its parent, so how surprising can it be that the vague patterns resemble the very familiar elements in Seahorse Valley? The calculation time of 3-1/2 minutes is brief enough to make running the included parameter file worth the small effort. The small hassle of setting up and running the parameter file may be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> A brisk west wind, showers of leaves, a mixture of sun and clouds, and a temperature of 59F 15C made Thursday a typical mid- autumn day here at Fractal Central in central Pennsylvania. The fractal cats were fascinated by the falling leaves, and spent several hours in their window, trying to decide what was happen- ing outside. My day was normal; FL's was the same. The next FOTD will be posted in 24 hours. Until then, take care, and if everything is an illusion in the mind, as some mystics claim, in what then is the mind only an illusion? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Unknown_Landscape { ; time=0:03:33.36-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.74125203921/+0.04311355888/633984/1\ /37.5/0 params=-3/10/0/0 float=y maxiter=7500 inside=0 logmap=207 periodicity=6 colors=000HHHmcUUcmcmAmrnwKpmsomsnmsmmrkmqimpgmoem\ ncmmbmc`mcZmcXmcVmcUmcSmcQmcOmUMmUKmUJmUHmUFmUDmUD\ mUAmUAmUAmUAmUAmUAmUAmUAmUAfUAgUAhUAiUAjUAjUAkUAlU\ AmUAnUBoUBpUCqUDqUDmUEjUEgUEdUE`UEYUEVUESUERUDRUDR\ UCH02H52H61G61G71G70L70L80L80K90K90K90KA0KA0K00OB0\ OB0OC0OC0OD0OD0OD0PE0PF0QF0QG0QG0RH0RI0RI1SJ2SJ2TK\ 3TL4TL5UM5UM6UN7VO7VO8VP9WP9WQAXRBXRCXSCYSDYTEYUEZ\ UFZVGZVGYUHXTIXTJWSKWSLVRLUQMUQNTPOTPPSOQSOQRNRQMS\ QMTPLUPLVOKVNJWNJXMIYMIZLH_LH_JFZIEZHDZFCZEAYD9YB8\ YA7Y95X74X63X52X61W71W81V91V91VA1UB1UC1UD1TD1TE1TF\ 1SG1SG1SH1RI1RJ1QK1QK1QL1PM1PN1PO1OO1OP1OQ1NR1NR1N\ Q3OQ4OQ5OQ6OP7OP8OP9OPAOOBOOCOOEPOFPNGPNHPNIPNJPMK\ PMLPMMPMNPLOPLQQLRQLSQKTQKUQKVQK0QJ0QJ0QJ0QJ0QS0bT\ 0bT0cT0dU0dU0eV0eV0fV0fW0gW0gW0hX0hX0iX0jY0jY0kZ0k\ Z0lZ0l_0m_0m_0n`0n`0oa0p`0o`0o`0o`0o`0n_0n_0n_0nO0\ 8Q0AR0DS0FT0IU0KW0NX0QY0S } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 21-10-10 (Man-O-Peace Fractal [5])
by Jim Muth 21 Oct '10

21 Oct '10

FOTD -- October 21, 2010 (Rating 5) Fractal visionaries and enthusiasts: Yes, today's image is late, but here it is in its full glory, better late than never. The image is a scene in the default manowar Mandeloid. I named it "Man-O-Peace Fractal" because I disapprove of violence. With not much going for it, I could give the image a rating of no more than a 5, which indicates an everyday average fractal. The calculation time of 1-1/3 minutes is brief enough to assure that little time will have been wasted if the image lays a rotten egg. The best way to avoid an unwanted omelet is to view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> After a foggy start, Wednesday turned rather pleasant here at Fractal Central, leading to an afternoon with ample sunshine and a temperature of 63F 17C. The fractal cats, Nicholas and Cassie, spent the afternoon on their shelf in the southwest window, basking in the strong sunlight streaming in. My day was unexpectedly busy, which also explains the lateness of today's FOTD. The next FOTD will be posted in 24 hours, more or less. Until then, take care, and don't get lost in the Z^2+C Julibrot. If you do, you'll never find your way out. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Man-O-PeaceFractal { ; time=0:01:20.14-SF5 on P4-2000 reset=2004 type=manowar center-mag=-0.1384789735/0\ /92456/1/90/0 params=0/0 float=y maxiter=1250 inside=255 logmap=810 colors=000G0OH0PI0QJ0RK0SL0TM0UN0VO0WP0XQ0YR0ZS0_T\ 0`U0aU0bU2cU4dU6eU8fUAgUChUEiUGjUIkUKlTMmSOnRQoQSp\ PUqNWrLYsJ_sK`rLaqMbqNcpOdoPeoQfnRgnShmTilUjlVjkWi\ jWfiVcgU_eTWcSSaQO_OMYMKWKIUIGSGEQFCOEAMC8KB6KA4K9\ 2K82K72K62K52K42K32K66K8AKAEKDIKFMKHQKKUMMYOO`PQbQ\ RcRTdRVeSYfS_gTbhTdiUgjUikVklVijWghXffXdeYbcZaaZ__\ _YZ`YX`XVaWTbWSbYTO_T9`WDaYHb_LbbPcdTdfXdh_biXajV`\ kT_lQYlOXmMWnJVoHUoFRiHPdJN_LKVMIQOGKQDFRBAT95V70W\ A1XD2XG3XJ4XM4XP5YS6YU7YX8Y_8Yb9ZeAZhBZkCZmCZlFXlH\ VlJUkLSkNRkPPjROjTMjVLiXJiZIi`GibFgWGfPGeIGdBGc4GR\ A8FF1X8Mm2en6anAYnDVnHRnLNnOKnPJnQInRInSHnTHnUGnVG\ nWFnXFnYEnZElWNkTWjQdiNmhKueJsbIr`HpYHoWGmTFlQEkOE\ iLDhJCfGBeEBdDEfDGgCJiCLjCOlBQmBToBVpAYrA_sAbu9dv9\ gx9iyMMMKKKIIIHHHFFFUfOPfSKfWFfZAfb5ff0fi3df5cd8bb\ A``C_ZFZXHXVKWSMVQOTORSMTRKWPIYOG`LD_NE_OF_PF_QG_S\ GZTHZUIZVIZXJZYJZZKY_LYaL } END PARAMETER FILE=========================================

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