June 2010 - Fractint - mailman.xmission.com

FOTD 26-06-10 (A Near-Oblate Set [No Rating])
by Jim Muth 26 Jun '10

26 Jun '10

FOTD -- (No Rating) Fractal visionaries and enthusiasts: Today's image lies near a small minibrot on the main stem of the Mandelbrot set, quite near the main body of the set itself. It is neither a Mandelbrot nor a Julia fractal. It is oriented at an angle 16 degrees from the Oblate plane of the Julibrot. The orientation explains the name "A Near-Oblate Set". Since I put almost no effort into the image, I gave it no rating. And the calculation time of 13 minutes is far too slow for the un- impressive result. The cure of all these shortcomings is a trip to the FOTD web site at: <http://www.Nahee.com/FOTD/> to see the finished image there. Lots of sun, reasonable humidity and a temperature of 86F 30C kept the fractal cats of Fractal Central subdued on Friday. The lazy conditions kept me subdued also, while FL still worried about the lack of rain on her garden. The next FOTD will be posted in 24 hours. Until then, take care, and where are the multiple universes? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Near_Oblate_Set { ; time=0:13:01.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 symmetry=none center-mag=+0.64407582162/-0.00000162218/704047.3/\ 0.183/180 params=0/0/90/16/-1.4013068817/0/0/0/2/0 float=y maxiter=10000 inside=0 logmap=534 colors=000L9qF6s93uC4nE5hH6bJ7XM8RO9LQAFODGMGHLJIJ\ LJIOJGRKFULDWMCZNAaN9dO7fP6iQ4lR3nR2RL13F24I25K26M\ 26O27R28T28V29X2A_2Aa2Bc2Ce2Cg4Z`5uV8sWBrWEqWGpWJo\ XMnXOmXRlXUkXXjYZiYahYdgYffYdfWbfU`fSZfQXfOVfMTfKR\ fIPfGOfFPWOPMXQPWRSWSVVTYVU`UUcUVfUWiTXlTYoSZrSZuS\ YtOYsLXsIXrFXrCZtD`vEbwFdyGezGcyJaxL`wNZvQYvSWuUVt\ XTsZSs`QrcPqeNpgMpiPqhSqgVrfXre_rebsddscgsbjtamtao\ t`ru_uuZwuZpgYjUXdGWZ3V_7X_BY`FZ`I_aMaaQbbUcbXdc`f\ cdgdhhdkicgjbckb_laWm`Sn`Oo_KpZGqZCqVGmSJjPMgLPdIS\ aFVZBYW8`T5cQ2fN1_I1TD1N91G41A05E38H5BL7EOAISCLVEO\ ZHRaJUdLWZHYUE_OBaJ7cD4d81eB5eD8eGBeIEeLHeNLeQOeSR\ fVUfXXf_`facfdfffifilfkoghkhehhcdi`aiYZjWVjTSkQOkO\ LlLIlIEmGBmD7nA4n81i84e86a88Y8AUmDQmFMmHImJEmMAmO6\ mQ2mSBmQKmPTmN`mMWmQSmTOmWJm_zmbzmezmhzmezmbzm`zmY\ zmVzmTzmQzmOzmLzmIzmGzmDzmAgz8jz5lz3IzMDzK8zJ3zI6z\ J8zJBzJDzJGzJIzKLzKNzKPzK } 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 25-06-10 (Cometary Residue [7])
by Jim Muth 25 Jun '10

25 Jun '10

FOTD -- June 25, 2010 (Rating 7) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's formula, FinDivBrot-2J, is a new one. Actually it's simply a Julia version of the FinDivBrot-2 formula. Today's image is the first one I found with the new formula, and it rates FOTD status. I cannot recall this ever happening before. The 'comet' with the long, long tail that streaks across the entire frame is actually a complete Julia set, one of the most unlikely Julia sets I have yet stumbled upon. The corresponding Mandelbrot fractal is a Mandeloid with everything scrunched around toward the main stem, and the east side of the main bay cut off by a straight wall. Today's image corresponds to the point where the curving north shore line meets the straight wall. The image resembles a comet zooming across the sky. (In fact, comets do not zoom across the sky except in the movies.) I rated the image at a 7, which is above average. The colors are quite smooth, and it has some math interest, all of which add to its worth. The name "Cometary Residue" came about when I turned the image upside down. It originally was rotated 180 degrees from its present orientation. The coloring smoothness was achieved by rendering the image with the outside set to 'tdis', which colors the points according to how far they travel before escaping. The calculation time of under 2 minutes is not too high a price for the result, but all calculation may be avoided by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Partly cloudy skies, a temperature of 88F 31C, lower humidity and a refreshing breeze made Thursday quite an acceptable day here at Fractal Central. The fractal cats came out of hiding long enough to get into a squabble over who would spend the afternoon on the foot stool. My day was satisfactory, as far as that goes. And if all goes well, tomorrow will be a repeat. With the drought growing worse here in Pennsylvania, FL is concerned with her garden, but so far, with generous watering, the plants appear to be holding up rather well. The next FOTD will be posted in 24 hours. Until then, take care, and be satisfied. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cometary_Residue { ; time=0:01:50.09-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2J function=recip center-mag=10.892/-14.7808/0.052083/1/90/0 float=y params=1/1/10000/0/0.79606/0.19699 periodicity=0 maxiter=5000 inside=255 outside=tdis symmetry=none colors=000zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzMzzNzzNzzOzzOzzPzzPzzQzzQzzRzzRzzSzzSzzTzzT\ zzUzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzbzzbzzczzczzdzzdzzezzezzfzzfzzgzzgzzhzzizzizzjz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzASsASsBSrBSrBSqCSqCSpCSpDSoDSoDSnDS\ nESmESmESlFSlFSkFSjGSjGSiGSiHShHShHSgHSgISfISfISeJ\ SeJSdJSdKScKScKSbLSaLSaLS`LS`MS_MS_MSZNSZNSYNSYOSX\ OSXOSWPSWPSVPSVPSUQSTQSTQSSRSSRSRRSRSSQSSQSSPTSPTS\ OTSOTSNUSNUSMUSMVSLVSKVSKWSJzzJzzIzzIzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz9zz8zz8zz7zz7\ zz6zz6zzzzzzzzzzzzzzzzzzzzzzzzzzzzz4zz4zz5zz5zz6zz\ 6zz7zz7zz8zz8zz9zz9zzAzzBzzBzzCzzzzzzzzzzzzzzzzzzz\ zzzzzzzGzzHzzHzzIzzJzzJzzKzzKzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzTzzUzzUzzVzzVzzWzzWzz\ XzzXzzXzzWzzVzzUzzTzzSzzz } frm:FinDivBrot-2J { ; Jim Muth z=pixel, c=(p3), 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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Floral
by Roger Alexander 25 Jun '10

25 Jun '10

Now open to the public my colorful fractal garden a product of the versatile orbit trap algorithm. Ready made at http://maxitersfractalfollies.blogspot.com fract273.gif { ; my fractal garden ; blank ; calctime 0:27:53.20 ; created Jun 24, 2010 ; Fractint Version 2004 Patchlevel 9 reset=1960 type=formula formulafile=frac_ml.frm formulaname=gallet-10-02 center-mag=+0.58981458500000010/+1.17073695700000000/112.4031/1/-5.00000\ 044121758425/5.02228108135993612e-007 params=0.25/1000/0.005/0.005/3/85 float=y maxiter=1023 inside=atan outside=summ periodicity=0 cyclerange=1/250 colors=mz0mz0lz0ky0jy0iy0hx0gx0fx0ew0dw0dv0cv0bv0au0`u0_u0Zt0Yt0Xt0Ws0Ws\ 0Vr0Ur0Tr0Sq0Rq0Qq0Pp0Op0Np0No0Mo0Ln0Kn0Jn0Im0Hm0Gm0Fl0El0Dk0Ck0Cj0Cj0Bj\ 0Bi0Bi0Bh0Ah0Ah0Ag0Ag09f09f09f09e09d08d08c08b07a07a07`07_06Z06Z06Y05X05W\ 05W05V04U04T04T03S03R03Q03Q02P02O02N01N01M01L00K0zKkzKkzKkzJkzJjzIjzIjzI\ izHizHizGhzGhzGhzFhzFgzEgzEgzEfzDfzDfzCezCezCezBdzBdzAdzAdz9cz9cz9cz8bz8\ bz7bz7az7az6az6`z5`z5`z5`z4_z4_z3_z3Zz3Zz2Zz2Yz1Yz1Yz0Xz0Xz0Wz0Vz0Uz0Tz0\ Sz0Rz0Qz0Pz0Oz0Nz0Mz0Lz0Kz0Jz0Iz0Hz0Hz0Gz0Fz0Ez0Dz0Cz0Bz0Az09z08z07z06z0\ 5z04z03z02z01z00u0zt0zr0yq0yo0xn0xl0wk0wi0vh0vf0ue0tc0tb0s`0s_0rY0rX0qV0\ qU0pS0pR0oP0nO0nM0mL0mJ0lI0lG0kF0kD0jB0iB0iB0hB0gB0gA0fA0eA0eA0dA0c90c90\ b90a90a90`80_80_80Z80Y80Y70X70W70W70V70U60U60T60S60R50R50Q50P50P50O40N40\ N40M40L40L30K30J30J30I30H20H20G20F20F20E10D10D10C10B00A } frm:Gallet-10-02 {; Modified Paul W. Carlson formula ( Petals_Mset) ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; p1 = radius of the circles ; p2 = circle offset factor ; real(p3) = number of color ranges ; imag(p3) = number of colors in each color range ; ; Note that the equation variable is w, not z. Always ; initialize z to zero. ;**************************************************** w = 0 c = pixel r = real(p1), bailout = imag(p1) r2 = r * r ro = r + r * p2 f = 1 - (2 + p2) * p2 k = r * (p2 + sqrt(f)) ;abs val of petal center (k,k) k1 = k*(1,1), k2 = conj(k1) plsqd = 2 * r2 * f ;petal length squared z = 0 num_ranges = real(p3) colors_in_range = imag(p3) range_num = 0 iter = 0: ; w = 1 / (w*w + c) ;**************************************************** ; Determine which pair of overlapping circles the ; orbit point falls in, if any. ;**************************************************** c1 = (|w - ro| < r2) c2 = (|w + flip(ro)| < r2) c3 = (|w + ro| < r2) c4 = (|w - flip(ro)| < r2) IF (c1 && c4) d = |w-k1| ELSEIF (c1 && c2) d = |w-k2| ELSEIF (c2 && c3) d = |w+k1| ELSEIF (c3 && c4) d = |w+k2| ELSE d = 0 ENDIF ; IF (d > 0) ;************************************************ ; Set z equal to the index into the colormap. ;************************************************ index = colors_in_range * d / plsqd z = index + range_num * colors_in_range + 1 ENDIF ; range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter d == 0 && |w| < bailout ;SOURCE: 98msg.frm } Roger Alexander _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9734384

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Sparklies Before and After
by Roger Alexander 24 Jun '10

24 Jun '10

A before and after duo today. The chaotic nature of the coloring of the included par generates a sparkly image. After anti-aliasing the wispy structure produced by the formula is clearly visible. Because the anti-aliased version is a jpg you will have to go to http://maxitersfractalfollies.blogspot.com to compare the two versions. fract271.gif { ; wispy ; blank ; calctime 0:06:41.50 ; created Jun 23, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=conic-near_jul16 center-mag=-2.22045e-016/2.22045e-016/0.8130081/1/-77.4999999999999858/3\ .88578058618804789e-016 params=0.8/0.7361369670705282/0.2491225928525651/-0.6531876583147679/-0.\ 1228370006408887/-0.3843806268501846 float=y maxiter=1500 inside=0 outside=atan decomp=256 periodicity=0 colors=05F05F05F16G16G16G16G16G27H27H27H27H27H38I38I38I38I38I49J49J49J49\ J49J5AK5AK5AK5AK5AK6BL6BL6BL6BL7CM7CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9E\ O9EOAFPAFPAFPAFPAFPBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJ\ TFKTGKUGLUHLVHMVIMVINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_OT_PT_PT`QU`QUaRV\ aRVaSWbSWbTXbTXcUYcUYcVZdVZdW_eW_eX`eX`fYafYafZbgZbg_ch_ch`ch`diadiaeibe\ jbfjcfjcgkdgkdhlehleilfimfjmgjmgknhknhlniloimojmpjmpknpknqloqloqmprmprnq\ snqsorsortpstpstqtuqturuuruvsvvsvwtwwtwwuxxuxxuxxvyyvyywzzvyyvyyuxxtxxtw\ wsvwsvvruvquuqtupstostorsnqsnqrmprlpqloqknpjnpjmoimohlnhkngkmgjmfjleileh\ kdhkcgjcfjbfibeiaeh`dh`cg_cgZbfZbfYaeX`eX`dW_dW_cVZcUYbUYbTXaSWaSW`RV`RV\ _QU_PTZPTZOSYNSYNRXMQXLQWLPWKPVKOVJNUINUIMTHLTGLSGKSFKRFJREIQDIQDHPCHPBG\ OBFOAFN9EN9EM8DM8CL7CL6BK6AK5AJ49J49I38I37H27H16G16G05F } frm:conic-near_jul16 { ; Kerry Mitchell 11may98 cc=(0.2882,0.0106), zc=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 _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9734384

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FOTD 24-06-10 (Double-Scepter Scene [5])
by Jim Muth 24 Jun '10

24 Jun '10

FOTD -- June 24, 2010 (Rating 5) Fractal visionaries and enthusiasts: Most likely due to the hot weather, I never did work up the usual enthusiasm for fractal work on Tuesday. But once again the work-horse Mandelbrot set came to the rescue with an acceptable if not outstanding image. The image takes us to the third valley out the negative X-axis of the M-set. The first valley is the well-known Seahorse Valley; the second valley is Scepter Valley. I'm not sure if the third valley has an official name, though I call it 'Double Scepter Valley'. Today's image is named "Double-Scepter Scene" because IMO that's what it is. Most of the effect was achieved by setting the logmap to an artificially high 10250, which creates the brilliant flat areas that make the central minibrot stand out. The rating of a 5 says that the image is just another scene in the Mandelbrot set. The calculation time of 1 minute says that the type=mandel fractals run very fast on a P4-2000mhz machine. The URL listed below says that calculation may be totally avoided by viewing the finished image there. <http://www.Nahee.com/FOTD/> The fractal cats wilted when the temperature reached 95F 35C here at Fractal Central on Wednesday. The fractalist also wilted. FL was busy however, watering her wilting flowers. The rest of the day was under control. The next FOTD will be posted in 24 hours. Until then, take care, and be with it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= DoubleScepterScene { ; time=0:01:01.36-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.3680989308005\ 03/+0.00047736474376778/1.7e+011/1/-7.5/0 passes=1 params=0/0 float=y maxiter=125000 bailout=5 inside=0 logmap=10250 periodicity=6 mathtolerance=0.05/1 colors=000szzBW`9Ub7Sd6Rf8QdAQbCQ`DQZFPXHPVIPTKPRM\ PPNONPOLROJSOHUOFWNDXNBZN987n44p77nA9mDBlGDkJGjMIi\ PKgSMfVOeYRd`TccVbfX`iZ_laZocYreXugWwiVuhTshSqhRog\ QmgOlgNjfMhfLffJdfIbeHaeG_eEYdDWdCUdBVc9TdASdAQdAP\ eANeAMeAKfAJfAIfBGgBFgBDgBChBAhB9hB6j88hB9gEAfGBeJ\ DdLEcOFbQGaTI_WJZYKY`LXbNWeOVgPUjOTkQTlRTmTTnUToWT\ oXTpYTq_Tr`TrbTscTtdTufTugTviTwjTxkTxhUteVpbVl_WhX\ XdUX`RYXOZTGWNLZPQ`RVbT_eVdgXql_iiYafXUcVNcTMaUL`U\ K_VJZVJYWIXWHWWGVXGUXFTYESYDQYCPZCOZBN_AM_9L_9K`8J\ `7Ia6Ha69Y6Ga6Nd6Ug6`k6gn0kv6mqBnmGoiLpeQq`VrX_sTd\ tPiuKnvGswCyz3xx8wvCwtGvsLuqPuoTtmXslasjerhirgmphm\ oimnimmjmlkmkkmjlmimmhmmgnmfomeomdpmcpmbnjblhbkfbi\ cagaaf_adXabV`aT`_R`YO`XM_VK_TH_SF_QDbM8_PBXREVTHS\ WKQYNN_QLaTIdVGfYDh`Bjc8mf6oizqlzsnzskzsizsfzsdzsa\ zs_GszIszLszNszPszRszTszVszXszZszbuz`szZqzXozVmzTk\ zRmzPmzNmzLmzJmzHmzFmzDmz } END PARAMETER FILE=========================================

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FOTD 23-06-10 (Gear World [6])
by Jim Muth 23 Jun '10

23 Jun '10

FOTD -- June 23, 2010 (Rating 6) Fractal visionaries and enthusiasts: On its outer edges, today's image is a Julia set of Seahorse Valley of the Mandelbrot set. But it is not a Julia set; it is a Mandelbrot set. And it is hardly quadratic. Those circular objects in the center have 32 lobes, which makes them of order-33. So I leave it to the viewer to decide what to call the image. As for me, I took it for what it is, rated it at a 6 and named it "Gear World". I had a quick impression of a gear train as I searched for a name. The calculation time of 6-1/2 minutes is not the briefest ever, but it is not the longest either. To see what all the excite- ment is about, run the included parameter file or hurry to the FOTD web site at: <http://www.Nahee.com/FOTD/> and enjoy the finished image there. I wisely avoided another meaningless discussion at lunch time on Tuesday, when FL asked me if I think the end of the world is coming. "Of course it's coming," I told her. The only ques- tions are when it's coming and what will cause it. I did not tell her that I believe our current obsession with technology is pathological, and is probably the beginning of the end. Now for some news that is more immediate. Lots of clouds prevailed all morning here at Fractal Central on Tuesday. At noontime a short but heavy shower fell, followed by heavy clouds most of the afternoon. The sky cleared around 5pm, but the air was so hazy that the clearing was almost invisible. The high humidity and temperature of 84F 29C merely added to the unpleasantness. The fractal cats spent the day doing what cats do best. They slept. Cassie chose the foot stool, while Nico stretched on the cool floor. My day was about as peaceful as days ever get. The next FOTD will be posted in 24 hours, give or take a few. Until then, take care, and what will we do when the world ends? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Gear_World { ; time=0:06:31.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.780919193881258/+0.00000021348863863\ /4.538402e+010/1/-20/0 params=33/1e+118/0/0 float=y maxiter=3200 inside=0 logmap=680 periodicity=6 colors=000GxsHwrEvqIupMtoQsnTrmUqlUqkUpkUpjUojUoiU\ niUnhUmgUmgUlfUlfUkeWkeUkeSibRh_PfWOeTMcQLbMJ`JI_G\ GYCFX9DV6CU3FT6HT9JSCMSFORIQRLSQOVQRXPUZPXcNb`P_YR\ XVTVSVSQWQNYNK_LHaICgKFbGHYDHR9JUALWBMYCO_DQaERcFT\ fGUhHWjIYlJZnK`pLarLcoMemMgkNiiNkgOmeOocPqaPs_QuYQ\ zbOvWQrQSnKUjEWM2RX5Vg8Yq5dr8brB`rDZrGYsJWsLUsOTsQ\ RtTPtWOtYMt`KwdGtbJq`LoZNlXQiVSgTUdRWaQZ_O`XMbUKdS\ IgPGiMEkK1lKDmKPnK_oKkpMxrLwqKvqJupItpIspHroGqoFpo\ EonEnnDmnClmBkmBkmKmlTnk`ojiqirrhzsgxqfvoetndsldqk\ coibnhblfaje`ic`gb_e`ZaZVc_Xd_Ze``g`ah`ciaekaflbhm\ bjobkpcmqcougtrcpo`mlXjjUfgQcdN`aJY_GUXCRU9OM1HP4J\ S6LU8MXAO_CQzCfmDZaERPFJ893DFBILJMRRRXZOXjS_gVbeYd\ bag`diYglWkocnqmzzzzzzzzzoumjscerVapYXo`SmcNmfJmiE\ ml9mo4mr0mu5mq9mnDmjHmgMmcQm`UzXYzUbzQfzNjzJnzGrzD\ kzKezQ_zWTzbNzhHznBztEzqGzoJzmLzkNziQzfSzdVzbXz`Zz\ ZazWczUfzShzQjzOjzO9z89z7 } 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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Zf_ang Again!
by Roger Alexander 22 Jun '10

22 Jun '10

Another pair of fractals demonstrating the effect of positive and negative skipped iteration values on the Zf_ang formula.What this shows about the math I couldn't tell you, Jim Muth knows more on this subject than I do.I have posted only one par. To recreate both fractals use imag(p2) values of +1 and -1. Also the link for yesterdays blog posting appeared to be broken. It's now fixed, hope I didn't disappoint anybody. Go to http://maxitersfractalfollies.blogspot.com and download two fractals for the price of one. fract267.gif { ; zf_ang blue and red ; negative(-1) skipped iteration value ; calctime 0:05:40.76 ; created Jun 21, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_z.frm formulaname=Zf_Ang function=sqr center-mag=0.296636/0.0627236/1.173709 params=0.5/0.5/0.5/-1/2/128 float=y maxiter=1500 inside=0 outside=summ colors=zffzffzeezddzccyccybbyaay``x``x__xZZxYYwYYwXXwWWwVVwUUvUUvTTvSSvR\ RuRRuQQuPPuOOtOOtNNtMMtLLtKKsKKsJJsIIsHHrHHrGGrFFrEEqEEqDDqCCqBBqAApAAp9\ 9p88p77o77o66o55o44n44n33n22n11m00m00l00l00k00j00j00i00h00h00g00g00f00e0\ 0e00d00c00c00b00a00a00`00`00_00Z00Z00Y00X00X00W00V00V00U00U00T00S00S00R0\ 0Q00Q00P00P00O00N00N00M00L00L00K00J00J00I00I00H00G00G00F00E00E00D00C00C0\ 0B00B00A00900900800700700600500ffzffzeezddzcczcczbbzaaz``y``y__yZZyYYyYY\ yXXyWWxVVxUUxUUxTTxSSxRRxRRwQQwPPwOOwOOwNNwMMwLLvKKvKKvJJvIIvHHvHHvGGuFF\ uEEuEEuDDuCCuBBuAAtAAt99t88t77t77t66t55s44s44s33s22s11s00r00r00q00p00p00\ o00n00n00m00l00l00k00j00j00i00h00h00g00f00f00e00d00d00c00b00b00a00`00`00\ _00Z00Z00Y00X00X00W00V00U00U00T00S00S00R00Q00Q00P00O00O00N00M00M00L00K00\ K00J00I00I00H00G00G00F00E00E00D00C00C00B00A00A009008007 } frm:Zf_Ang {; Copyright (c) Paul W. Carlson, 1998 ; p1 = Julia set coordinates ; real(p2) = controls size of the elements ; imag(p2) = number of iterations to skip ; real(p3) = number of color ranges ; imag(p3) = number of colors in a range ; z = k = iter = range_num = bailout = 0 w = pixel c = p1 prev_modw2 = 1.0e20 size = real(p2) skip_iters = imag(p2) num_ranges = real(p3) colors_in_range = imag(p3) factor = (colors_in_range - 1) / size : w = c * (w - 1 / w) a = 2 * atan(imag(w) / real(w)) a = a * a + c a = fn1(1 - a) / a ; dist = abs(|w| - |a|) IF (dist < size) bailout = 1 IF (iter > skip_iters) k = 1 ENDIF z = (factor * dist + range_num * colors_in_range + 1) * k ENDIF range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 && |w| < 1.0e20 ;SOURCE: 98msg.frm } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 22-06-10 (Negative Minibrot [7])
by Jim Muth 22 Jun '10

22 Jun '10

FOTD -- June 22, 2010 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's image was a true-to-life antiminibrot. Today's image is a negative minibrot, which is not quite true to life, since the negative effect was totally created by the coloring. The minibrot itself is nothing more than an everyday run-of-the- mill minibrot given interest by rendering the entire scene with the outside set to 'tdis'. The negative effect gives a rather ominous feeling to the image. I have occasionally seen this effect used in Japanese 'anime' cartoons. The name "Negative Minibrot" is self explanatory. The calculation time of 39 seconds is no error. The parameter file really runs this fast. But running parameter files involves a bit of hassle. This small hassle may be avoided by checking the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> and forgetting about running the parameter file. The parent fractal came about when I combined 0.1 part of Z^10 with one part of Z^1.5 and added straight C. This parent is a mis-shapen Mandelbrot set rotated about 180 degrees, with a large open area extending beyond its east (west) valley and a curled-up main stem. Today's scene lies on a kind of figure-8 shaped hole on this curled stem. The weather here at Fractal Central on Monday was almost perfect. Only a too-warm temperature of 88F 31C kept it from being totally perfect. The fractal cats spent the day relaxing, though at one point Nicholas ducked briefly under the bed when he thought we were getting out the cat-carrying box to take him to the doctor again. My day was about average; FL is concerned about the unusually dry weather we have had so far this year, and the effect it is having on her garden, (and the farmers' crops also). The next FOTD will be posted in 24 hours. Until next time, take care, and does anyone know how to get more water to fall from the sky? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Negative_Minibrot { ; time=0:00:39.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident inside=0 center-mag=+0.5547669664716627/-0.0077870219432185\ /1.259273e+011/1/-120/0 params=0.1/10/1/1.5/0/0/0/0 float=y maxiter=1500 outside=tdis periodicity=6 mathtolerance=0.05/1 colors=000XiXXiXXjXXjXXkXXkX_lWamVdnVfoUipTkqTloSm\ nRnmRolQpkPqjPriOrhNsgNtfMueLvdLwcKxbJxaJudOrfTpiY\ mkbjnghplesqbuv`wzbvvcvseuofulhuiitektblt_cpUWlONh\ IZyEGiDFeCEbCE_CDXCDTCCQCBNBBKBAGBADB00042797BFFIK\ IMMMMRQPVVT__Wcd_nplklkhijeehbbg__eYXeXVeVSfTQfROg\ PLgNJhMHhLPYKXNKcDJdHIeKIfNHgRHgUGhXFi_FjcEkfEkiDl\ lCmpCnsBovBoy_dkYaiW_gUXfSVdQSbOQaMN_KLYIIXGGVEDTc\ BSc8Qc6PcANcDMcGLmJKmMJmPImSGmVFmYEm`DecCzfBzS0z`5\ ziAz0yzSazrFzlDzfBz`9zP4zT6zW7zZ8zbAzeBzhCzkDzoFzr\ GzuHzxIzvKctMdsOfqPgpRhnTilVkkWliYmh_nzapzbqzdrzfs\ zgTzDWzGYzJ_zMazPdzRfzUhzXjz_ozamzalzakzaizahzagza\ fzadzaczabza`za_zaZzaYzaTzdPzfLziHzkEzoDzmCzlCzkBz\ iBzhAzgAze9zd9zc8za8z`7z_7zZCz_Hz`MzaJzvNzkQzaTzRX\ wDWzHWzLWzPWzSWzWWz_VzbVzfVzjVzmVzqVzuVzxYzw_zvazu\ cztezsgzsizrjzqkzpjznjzmizlizjhzihzhgzfgzefzdfzbez\ aez`dzZdzYczXAzxXzXXzXXzX } frm:MandAutoCritInZ {; 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)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Celery of the Gods
by Roger Alexander 21 Jun '10

21 Jun '10

Busy busy today but not so busy I don't have time to post this par "Celery of the Gods". If you're busy as I am go to http://maxitersfractalfollies.blogspot.com and save some precious calculating moments by viewing the finished fractal. fract265.gif { ; fractal chlorophyll ; blank ; calctime 0:04:40.40 ; created Jun 20, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2000 type=formula formulafile=_t.frm formulaname=tri-julia-2 center-mag=-0.338785/-0.449154/4.341378/1/47.5000000000000711/5.12714870\ 559705105e-014 params=1025.653340250862/1.891872920926542/-0.4537186803796504/0.4264961\ 699270607 float=y maxiter=1200 outside=atan periodicity=0 cyclerange=0/255 colors=0000200000000000200300500600800A00B00D00E00G00I00J00L00M00O00Q00R\ 00T00U00W00Y00Z00`00a00c00e00f00h00i00k00m01m03m04n06n07o09o0Ao0Cp0Ep0Fq\ 0Hq0Iq0Kr0Lr0Ns0Ps0Qs0St0Tt0Vu0Wu0Yu0Zv0`v0bw0cw0ew0fx0hx0iy0ky0mz0mz1mz\ 3mz3lz3kz3jy3iy3hy3gy2fx2ex2dx2cx2bw2aw1`w1_w1Zv1Yv1Xv1Wu0Wu0Xu0Yu0Zu1_u\ 1`u1av2bv2cv2dv3ev3fv3gw4hw4iw4jw5jw5kw5lw5mx6nx6ox6px7qx7rx7sy8sy8ry8qy\ 7py7py7oy6ny6my6my5ly5ky4jy4iy4iy3hy3gy3fy2fy2ey2dy1cy1bz0cz0dz0ez0fz0gz\ 0hz0iz0jz0kz0lz0mz0nz0oz0pz0qz0rz0sz0qz0pz0oz0mz0lz0kz0iz0hz0gz0fz0dz0cz\ 0bz0`z0_z0Zz0Yz0Wz0Vz0Uz0Sz0Rz0Qz0Oz0Nz0Mz0Lz0Jz0Iz0Hz0Fz0Ez0Dz0Bz0Az09z\ 08z06z05z03z02z00z00y00x00w00v00u00t00s00r00q00p00o00n00m00l00k00j00i00h\ 00g00f00e00d00c00b00a00`00_00Z00Y00X00W00V00U00T00S00R00Q00P00O00N00M00L\ 00K00J00I00H00G00F00E00D00C00B00A0090080070060050040030 } frm:tri-julia-2 {; Sylvie Gallet <sylvie_gallet(a)compuserve.com>, May 1997 ; Thanks to Kerry Mitchell for the idea! ; real(p1) = bailout (1024 recommended) ; imag(p1) must be different from 0 (>=1 recommended) ; p2 = parameter for the Julia set ; This formula must be used with decomp = 256 and periodicity = 0 ; z1 = pixel, mz1 = cabs(z1), b = cabs(p2), summ = iter = 0 b1 = abs(real(p1)), f = b1^0.1 b2 = b1*f, b3 = b2*f, b4 = b3*f, b5 = b4*f, b6 = b5*f b7 = b6*f, b8 = b7*f, b9 = b8*f, b10 = b9*f, b11 = b10*f iter1 = iter2 = iter3 = iter4 = iter5 = iter6 = iter7 \ = iter8 = iter9 = iter10 = summ_tot = iter_tot = 0 k = imag(p1) * (0.0,6.28319530718) : iter = iter + 1, a = mz1 * mz1 z1 = z1 * z1 + p2, mz1 = cabs(z1), a_b = abs(a - b) summ = summ + (mz1 - a_b) / (a+b - a_b) IF (mz1 > b1) IF (iter1==0) iter1 = iter iter_tot = iter_tot + iter1 summ_tot = summ_tot + summ ENDIF IF (mz1 > b2) IF (iter2==0) iter2 = iter iter_tot = iter_tot + iter2 summ_tot = summ_tot + summ ENDIF IF (mz1 > b3) IF (iter3==0) iter3 = iter iter_tot = iter_tot + iter3 summ_tot = summ_tot + summ ENDIF IF (mz1 > b4) IF (iter4==0) iter4 = iter iter_tot = iter_tot + iter4 summ_tot = summ_tot + summ ENDIF IF (mz1 > b5) IF (iter5==0) iter5 = iter iter_tot = iter_tot + iter5 summ_tot = summ_tot + summ ENDIF IF (mz1 > b6) IF (iter6==0) iter6 = iter iter_tot = iter_tot + iter6 summ_tot = summ_tot + summ ENDIF IF (mz1 > b7) IF (iter7==0) iter7 = iter iter_tot = iter_tot + iter7 summ_tot = summ_tot + summ ENDIF IF (mz1 > b8) IF (iter8==0) iter8 = iter iter_tot = iter_tot + iter8 summ_tot = summ_tot + summ ENDIF IF (mz1 > b9) IF (iter9==0) iter9 = iter iter_tot = iter_tot + iter9 summ_tot = summ_tot + summ ENDIF IF (mz1 > b10) IF (iter10==0) iter10 = iter iter_tot = iter_tot + iter10 summ_tot = summ_tot + summ ENDIF IF (mz1 > b11) iter_tot = iter_tot + iter summ_tot = summ_tot + summ z = exp (summ_tot * k / iter_tot) ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF mz1 <= b11 ;SOURCE: triangl.frm } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 21-06-10 (Great AntiMinibrot [10])
by Jim Muth 20 Jun '10

20 Jun '10

FOTD -- June 21, 2010 (Rating 10) Fractal visionaries and enthusiasts: Minibrots in fractals are easy to find and very widely known, but much less known are antiminibrots, which are quite difficult to find. Minibrots lie at the center of a basin where the iteration count increases as the center is neared, and reaches infinity at the edge of minibrot itself. Antiminibrots are peaks with an area of lowest iteration count at the center. In today's image the center is beyond resolution, so I cannot give the iteration count at the central peak. But the count need not be as low as 1. In a minibrot basin, the number of elements surrounding the central minibrot bifurcates in a 2,4,8,16... series as the 'brot is approached. In an antiminibrot such as the one in today's image, the number antibifurcates in a 16,8,4,2 series. In everyday minibrot images, the lowest iteration bands lie around the edges of the frame, and the automatic logmap feature (setting the logmap to 2) works very well, but in antiminibrot images such as today's, where the lowest count is at the center, the automatic logmap is useless. Luckily, turning off the log- map in today's image works just as well as the automatic feature. Today's image rates an honest 10. Its mathematical and coloring values are both well above average. And its cauculation time of 59 seconds can hardly be beat. BTW, 95-percent of the coloring was created by the Fractint program. I tweaked only 10 or so color registers. The name "Great AntiMinibrot" says it all. The image cauculates in less than a minute, but it still takes some time to set up the parameter file. To avoid this small hassle, the finished image may be seen already calculated on the FOTD web site at: <http://www.Nahee.com/FOTD/> Partly cloudy skies with slightly lower temperatures and notice- ably lower humidity prevailed here at Fractal Central on Sunday. Nicholas, the fractal cat who dislikes heat, spent most of the day stretched on the cool tile floor. Cassie, who likes it warmer, passed the day curled on the foot stool. FL and I spent the day taking it easy. The next FOTD, probably not as great as today but hopefully still quite good, will be posted in 24 hours. Until then, take care, and get a new angle on things. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Great_AntiMinibrot { ; time=0:00:59.09-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-0.2382764653067911/+0.6598651051332169\ /1.26548e+013/1/-15/0 params=6/1e+023/0/0 float=y maxiter=2250 periodicity=6 mathtolerance=0.05/1 colors=000T_IXWMGELHFMIGMJGMKHMKHMLIMMINNJNNJNOKNP\ KNQLNRLNRMOSMOTNOUNOUOOVOOWPOXPPYQPYQPZRP_RP`SPF8_\ QIUT3gU5fU6eV7dV8cV9bWBaWC`XD_XEZXFYYHYYIXYJWZKVZL\ U_NT_OS_PR`QQ`RPmg4ke7jc9ibBg`Df_FeYHcWJbVLaTNvZkt\ YisYhrXgqXfpXdoWcmWblWakV`jVZiUYhUXfUWeTVdTTcTSbSR\ aSQAC_NVgOVfPVePVdQUbRUaSU`TU_TUZUTYVTXWTWXTVXTUYS\ T_SPZSS_SR`SQXubYsaYr`Yp`Yo_YnZZlZZkYZjXZhXZgWZfW_\ dV_cU_aU_`T__S`YS`XR0mz0kz0iz2gz4ez5cz6az7_z9YzAWz\ BUzCSzDQzFOvGMrHLmILhJMcLM_MNZNNYOOYOOXNPWNPVMQUMR\ TLRSLSRKTQKUPJXOI_MKbKMeIOhGQkETnCVqAXt8Zw6ay3ax3`\ u3_r4Zo4Yl5Xi5Wf6Vc6U`6TY7SV7RS8QP8PM9OJ9NGAMMGLTM\ K_Szczzazv_wtYtrWqpUnnSklPhjNehKbeH_cEXaCU_9RY6OV3\ KTAMRHOPORNVTKbWNaXQ_YUZZXX`_VacUbfSciQemPfpNgtLir\ MioNilOijPigQidRhVKVLCHB42B42B52B52B62B72B72B82B82\ B92BA2BA2BB2BC2FE8KHFPKMTNTYQ_bTfaTe_TcZTaXT_WTYUT\ WSTVRTT`SP`SPDp3Hk7LgBPcE } 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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