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Birds in the Sun
by Albrecht 12 Nov '12

12 Nov '12

Hi, as you can guess from the title this is an image in "natural" colours. Nothing spectacular, but beautiful if you ask me. If you cannot generate it or want to avoid the 16min it needs you can get it from Hal?s homepage: http://www.emarketingiseasy.com/Albrecht/20105A.PAR http://www.emarketingiseasy.com/Albrecht/20105A.GIF. The par-file also contains the frm. As more users now have the possibility to watch the multifractal images, thanks to Hal, I?d be happy to get some feedback. . Albrecht --------------------------------start-par-------------------------------------------- 20105A { ;Birds_in_the_Sun ; mandel-secant-mmods ; Time 0.15.16 1600/1200 reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=-1.30865464456818600/+0.000023479072921\ 85/243.5358/1.1324/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/201\ 05.03564960102/25234.2207090221/151024.0204808192/\ 384.32768524288/384.00482000595/128.1007683001/256\ .1007683001/256.2007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=n0B00z<78>vv4ww3ww2<2>zz0zz0zy0<77>z40z30z2\ 0<3>y01y01x02<3>u05u06t06<8>l0Ek0Fj0G<57>50u40v30w\ <3>00z000 } -------------------------------------------end---------------------------------------------

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Buried in the "Dust of Time"
by Albrecht 11 Nov '12

11 Nov '12

Hi, the image is available in full HD 1600/1200 on Hal?s homepage. http://www.emarketingiseasy.com/Albrecht/55555K.gif Maybe, after a second look you?ll like it. Thank you, Hal! Albrecht

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FOTD 11-11-12 (FOTD for Nov-11 [5])
by Jim Muth 11 Nov '12

11 Nov '12

FOTD -- November 11, 2012 (Rating 5) Fractal visionaries and enthusiasts: Today's image rates a 5. It is one that would normally be discarded, but I made it FOTD for today because I have decided to show the fractals that usually head straight for the trash can. I also have a serious case of fractalist's block. The parent fractal is the same shapeless one that gave us yesterday's image. The scene lies in the same general area as yesterday's image. The central minibrot appears split directly down the middle. The name "FOTD for Nov-11" simply states a fact. The calculation time of 1-1/4 minutes is brief enough to bring no impatience, yet slow enough to let a bit of anticipation build. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Near perfect Autumn weather prevailed here at Fractal Central today, with cloudless skies, light breezes and a temperature of 61F 165C. The next fractional fractal will be posted before long, very likely in 24 hours. Until whenever, take care. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= FOTD_for_Nov-11 { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=mandelbrotbc3 function=ident center-mag=-1.227133792556/+0.007005797985/2555911 params=2.236/0/4/0 float=y maxiter=2700 inside=0 logmap=-132 periodicity=6 colors=000OJSLTaJbjlbpfVe`NWVFMP8CS9GVAKXAN_BRaBVd\ CYfCaiDdkDhnElpEosFsuFvrEspEpnDmlDjjCghCdfBacBZaAW\ _ATY9QW9NU8KS8IODFLICHNAES7AX47a2Bc7FdBJeFNfKRgOVh\ SYiXaj`ekdilimmmqnqtouolskjqggocem_clW`jRZhNWfJUeF\ ScBPa7N_3LZ4NY4PX4RW4TW4VV4XU4ZU5`T5bS5dR5fR5hQ5jP\ 5kP9bRDUSHLULCVP4WR3TS3RT3PU3NV3LX3JY3HZ3F_3D`3BbE\ CdOCfYDhgDjqDf`KbKQZ3WZ4UZ5SZ6RZ7PZ8OZ9MZALZBJZCHZ\ DGZEEZFDZGBZHAXKCWNEVQFUTHTWIRYKQ`LPcNOfONiQMkRLgU\ LdWK`ZKY`KVcJReJOhJLjIHmIEoZMaZNaZN`ZO`ZO__P__P__Q\ Z_QZ_QY_RY_RX_SX_SW_TW_TW_UV_UV`VU`VU`VT`WT`WS`XS`\ XS`YR`YR`ZQ`ZQ`_P`_PXZMZ_O`_Pb`Rd`SfaThaVjbWlbYncZ\ pc_rdatdbwcbvdcudctecsecrfcqfcpgcogcnhcmhclickicjj\ cijdhkdgkdfldelddmddmdcndbndaod`od_pdZpdYqeXqeWreV\ reUseTseSteRteQuePueOveNveMwfNveOueOtdPsdPsdQrcQqc\ RpcSpbSobTnbTmaUmaUl`Vk`Vj`Wj_Xi_Xh_YgZYgZZfZZeY_d\ Y_dX`cXabXaaWbaWb`Wc_VcZV } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 10-11-12 (Split Opinion [6])
by Jim Muth 10 Nov '12

10 Nov '12

FOTD -- November 10, 2012 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows another image in a fractional fractal. The fractional exponent of the image is 2.236, which, not accidental- ly, is the square root of 5. This expression was calculated 4 levels up the hyperladder with no function applied. The parent fractal produced by this operation is little more than a shapeless blob with a prominent split along the X-axis. But some distance west of the main mass, just north of the X-axis, lies a totally cut-off minibrot. Today's scene lies in an East-type valley of this minibrot. The rating of 6 indicates that inspiration for the fractal was lacking. The name "Split Opinion" points to the split along the X-axis. The relatively fast calculation time of 1-1/2 minutes assures that not too much time will have been wasted if the image fails to satisfy. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Light rain ruled the early morning here atF.C., while clouds ruled the rest of the day. The light winds and temperature of 55F 13C made the day seem quite comfortable however. The next FOTD will be posted before too long. Until whenever, take care, and my current dis-spirited attitude is not connected to the outcome of the recent election. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Split_Opinion { ; time=0:01:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=-1.28787966181/+0.043392037384/2.52e+007 params=2.236/0/4/0 float=y maxiter=3600 inside=0 logmap=224 periodicity=6 mathtolerance=0.05/1 colors=00050X61Y82_93aA4cB5eC6gG7iJ7kN8kQ8lT8lX9m_\ 9mcAnfAniAomBopBpsBptGmuLjuQhvUewZcwc`xhZylWyqUzvR\ zzPvxOswOpvOmtOisOfrNcpN`oNXnNUlNRkMOjMKhMHgMEfMBe\ MFaPJZSNVVRSYVO`ZLcbHffEijAln7or3ru0tr3sp6sn8slBsj\ EshGsfJsdLsbOs`RsZTsXWsVYsQShLNYGINBDC6818A2AC3CE4\ EF5GH6HJ7JL8LM9NOAPQBRSCSTDRTEPTFOTGMSILSJKSKISLHR\ NFROERPDRQFPRGNRIMRJKSLISMHSOFTPETRCTSAUU9UV7UX5VY\ 4V_2V`1Vmzeivbfr_cnY`jVYfSVbQSZNPVLLRI020INFFJDCFA\ 9B7675332gxScsQ`oOYjMVfKSbIPYGMUEIQCFLACH89D668434\ 298v87q76l66g65b54Y44T33O32J22E119004TAZP8UL7QI6LE\ 5HA3D7283142ZN1WL1TJ1QH1OF1LE1IC0GA0D80A7085053021\ OL2MJ1LI1JH1IF1GE1FD1DB1CA1A90970760650430320110qg\ tjalcXeXRZRMSKGLDBE657xs3so2ok2kg2gd2cc2vcEucEtcEr\ cEqcEpmEomEmmDlmDkmDjmDhmDgmDfzDezDczCazC_zCYzBWzB\ VzBmzAmzAmzAmz9mz9mz9mz8mz8zz8zz8zzLzzXzzYzzYzzYzz\ XzzXzzXzzXzzXzzXzzZzz_zz` } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Four By Four
by Mike Frazier 10 Nov '12

10 Nov '12

This fractal has a lot of four way symmetry which gives it the name Four By Four. I found it by zooming into a four way symmetry in a tiny disconnected fragment of the parent fractal. It is interesting that this formula often generates minibrots in disconnected fragments. The equation is: z = 1 / (1 / ((z ^ 3) * (exp(z) - 1) + pixel + 1) + 1 / (z ^ 4 + pixel - 1)) Here is a link to an image: http://dl.dropbox.com/u/33642054/image/four_by_four_1200_5.jpg The PAR file for the image is: Four_By_Four { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20121110_1031 passes=1 float=y center-mag=-3.543046540411976/-1.700151082216331e-\ 15/410256415384.6154/1/0/0 params=1/1/4/4/-1/0/1/0/0/0 maxiter=2000 inside=0 logmap=12 periodicity=6 colors=000640C80IC0OG0UK0ZO0cS0hW0lZ0ob0sf0uj0xn0y\ r0zv0zz0zv0yr0xn0uj0sf0ob0lZ0hW0cS0ZO0UK0OG0IC0C80\ 640000000630C60I90OC1UF1ZI2cL3hO4lR5oU7sX8u_9xbBye\ CzhEzjFzhEyeCxbBu_9sX8oU7lR5hO4cL3ZI2UF1OC1I90C606\ 30000000620C40I61O82UA3ZC5cE7hG9lIBoKEsMGuOJxQMySP\ zUSzVVzUSySPxQMuOJsMGoKElIBhG9cE7ZC5UA3O82I61C4062\ 0000000610C21I31O43U55Z67c7Ah8Dl9HoALsBOuCTxDXyEaz\ FfzGjzFfyEaxDXuCTsBOoALl9Hh8Dc7AZ67U55O43I31C21610\ 000000500901E02I04M07Q0AU0EY0I`0Mb0Se0Wg0ai0gj0mj0\ tk0yj0tj0mi0gg0ae0Wb0S`0MY0IU0EQ0AM07I04E029015000\ 00000300601901C03F05I07K0AM0DO0HQ0LS0OT0TU0XV0aV0f\ W0jV0fV0aU0XT0TS0OQ0LO0HM0DK0AI07F05C0390160130000\ 0000100300401602703905A07B09C0BD0EE0GE0JF0MF0PG0SG\ 0VG0SF0PF0ME0JE0GD0EC0BB09A07905703602401300100000\ 00000000000000100100200300400500700800900B00C00E00\ F00E00C00B009008007005004 } frm:F_20121110_1031 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2)-1,d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*(z^b)*(exp(z)-1)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

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FOTD 09-11-12 (Everyday Minibrot 6])
by Jim Muth 10 Nov '12

10 Nov '12

FOTD -- November 09, 2012 (Rating 6) Fractal visionaries and enthusiasts: Today's image lies at the edge of the infinitely subdivided main spike of the Z^2.00001+C Mandeloid, just east of the large minibrot. This parent very closely resembles a Mandelbrot set, a great magnification being necessary to reveal the difference. I named the image "Everyday Minibrot" because that's what it is. The rating of a 6 indicates a scene that will never set the world afire. The calculation time of 2-1/3 minutes is slow enough to make the image worth less than its cost. The web sites have a better deal however. View the finished image on the official FOTD web site without the need of calculating it. The web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> Weather conditions took a decided turn for the better here at Fractal Central today. The sky was mostly sunny, the winds were much lighter, and the temperature reached a high of 54F 12C, making the day pleasant for almost any outdoor activity. START PARAMETER FILE======================================= Everyday_Minibrot { ; time=0:02:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-1.749357747989381/+0.00019329584512746\ /2.0456e+010/1/147.5/0 params=2.00001/0/0/0 float=y maxiter=2250 inside=0 logmap=277 periodicity=6 mathtolerance=0.05/1 colors=000fJOeHOdGOcEOcCObAOa8Oa7OY6MU6LQ6JN6IJ6HF\ 6FB6E86DNAHaKKpUNkcMgmMcpMhtMmwMrzMvzMzzMzrMzmMzhP\ zcRz_TvVVrVXmUPiSPiQPhPPgNPfLPWJKYGV_DfaAqbXabrMco\ JcmHckEciCcg9ce7dcCebGfaKg`Oh_SiZWjY_f_fYamR_oJZpE\ YnCUjAQd8KY6EQ48J7BK9ELBGMDJNFMOHOOQTNYYNfaNnfNvjN\ smVqpansilvpjxwTZhUbaUfVVjO1cG6ZF8UE6PD4KC2FB0AB6F\ DCIEIMF7SC8XD9aE9eFCaHFYIIUKLRLONNRJOUFQXCRVNgTXxQ\ `xOdxMgxKkxIoxGrxEvxCyxBpYBg8GPBL7DTKQ`Xahinouzgrj\ _oWSlGLi1Tj9`kGhlOpmVwnaspepqhmrkisoftrcuudqodmidi\ cdeZdaTdYNdVIeXJeYKfZLf_LgaMgbNhcOhdOYWIONCEF7F74F\ 01VnHWrAWu4Zs7`q9coCenEglGjjJdRLzgNZ`SKVW5P_AN`EL`\ IK`MI`RH`VF`ZE`bC`fB`bLWCEkBGmAIo9Lq9Nr8Pt7Sv6Ux6W\ yDVrJVlQVfWV`bUUhUOoUIuUCqWFmXIjcKfcNccQ_mSXmVTmYQ\ m_MzbUzeUzgczjczmczomzqmzrmzszztzzuzzvzzrzzozzlzzh\ zzezzbzz_zzWzzTzzQzzNzzHzzBzz5zz9zzCzzFzzJzzMzzPzz\ TzzWzzZzzMzzLzzKzzJzzIzzH } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Albrecht's multifractal_10 fractal, "Multiple Directions"+ a zoom
by Hal Lane 10 Nov '12

10 Nov '12

I put a rendering of Albrecht's multifractal_10 fractal, "Multiple Directions" on my server: http://www.emarketingiseasy.com/TESTS/FOTD/MULTDRCT.GIF And here's an anti-aliased zoom into the top of "Multiple Directions" along the centerline: http://www.emarketingiseasy.com/TESTS/FOTD/MultDrct1.jpg If you calculate other Multifractal_10 fractals, make sure that the capitalization of the first letter of the "formulaname" in the par -- (Multifractal_10 or multifractal_10) is the same as the frm:'s formula name... Albrecht's .par specification -- with the Multifractal_10 formula added is below. - Hal Lane ######################## # hallane(a)earthlink.net ######################## -----------start par------------------------------- 1536164e { ; Multiple Directions ; jul-sec-bees-phoen-mand ; time 24.52 1600/1200 ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr_10.frm formulaname=Multifractal_10 function=sin/exp/exp/sin passes=t center-mag=+1.33193274819753900/-0.000000000005385\ 46/9.345637e+008/1/90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/413\ 62.64595712822/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000zzizzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I\ 88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8\ xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6\ >vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4H<3>P\ 3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>\ u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3\ >5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvl\ qvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI\ <3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0c\ e7_jFRoNIzb0zj0000zr0zz1zzCzzT } frm:Multifractal_10 { le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) c=p1 else z=z*le+pixel*(le==0) c=p1 endif elseif (ab) c=z z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) z=0 endif elseif (d3) if (ab) c=p1 z=z*le+pixel*(le==0) else c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z z=0 else c=z z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c c=c*sp+z else z1=z^p-1 z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold zold=z z=z1 else z2=fn1(z)+c z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp else z2=z*z z=z2*z2+p6*z2+c-p0 endif else z3=z z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ---------------------------------------------------

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Multifractal_10
by Albrecht 10 Nov '12

10 Nov '12

Hi, like Jim, every now & then, when the time is right, I will submit an image only using above frm which by now every one should have downloaded. Today?s image came about zooming into one of my MFR-10 basic images and using Lee?s colours. After completion, checking my records I found that an almost identical image is on Lee?s Multifractal DVD. If two people find the same image by chance there must be something special to it! The Mandel in the middle, MIM image I call it, is Jim?s territory- but not completely this time, check it out. As possibly not everyone can generate MFR images I think it would be great if Hal or Paul could make it available for watching/ download . Fractals Are Fun! Albrecht ------------------------------------------Start Par---------------------- 1536704 { ; Unexpected_mandel ; Secant-mmods-bees-phoen-newt ; time 0.07.44 (XP dos shell) ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50145103141349900/+0.100170572669321\ 20/6662.918/1/-105.000000000013912/1.6730103413742\ 3699e-011 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000oNIzb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>M\ b8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiOD\ jQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE\ 6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2C\ K2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1\ ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotv\ sww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XC\ AaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI\ <3>UnXRm_NlcJkgFfpAaz<6>_5fc0ce7_jFR }

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FOTD 08-11-12 (Slightly Deficient 6.5])
by Jim Muth 08 Nov '12

08 Nov '12

FOTD -- November 08, 2012 (Rating 7.5) Fractal visionaries and enthusiasts: The exponent of Z in the past few days' images has been somewhat greater than two. The exponent of today's image is 1.9, which is somewhat less than two and also explains the name "Slightly Deficient". The parent fractal is basically shaped like a Mandelbrot set, as are all such fractional fractals with an exponent close to 2. This parent is rotated about 180 degrees, with two large period-2 buds on the eastern side of the main bay, one north and one south of the X-axis. A large disconnected minibrot lies just east of the southern bud, with a smaller disconnected minibrot nearby. Today's scene with its scrambled minibrot at the center lies not too far from this smaller minibrot. The rating of 7-1/2 is based on the colors. The little math interest is hardly enough to deserve a higher rating. The calculation time of 2-5/6 minutes is reasonable, though slower than would be preferred. Avoid all impatience by viewing the finished image on the official web site at: <http://www.crosscanpuzzles.com/Archives.html> Check the glorious high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget the back images at: <http://www.Nahee.com/FOTD/> Decreasing clouds and increasing temperatures prevailed here at Fractal Central today. The high temperature of 46F +8C would have felt warmer if the winds had not been so brisk. The next FOTD will be posted in 24 hours. Until then, take care, and see the official web site for the closing remark. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Slightly_Deficient { ; time=0:02:50.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+1.519854358476405/-0.2217400613360854/\ 5.712965e+007/1/-95/0 params=1.9/0/1.9/0 float=y maxiter=3200 inside=0 logmap=277 periodicity=6 colors=000A0Q50LA0P50JA0O50IA1M52GA3N54FA5O56IA7N5\ 8HA9LAAZABZA7OADXAEXAFXABUAFRAITAHQAKNAIPAMLAKIAOF\ AKCAN9AL6AH1AJ3AK4AL5AN7AO8AP9AQBASCATDAUFAVGAXHAY\ JTMPXKLaIHeGDiE9y80zF6zSBgGCQ7CTACVDCXFCZIC`KCbNCd\ PCfTChVCjZCl`CndCpfCrjCtlCvpCxrCtoBqkAmg9jd9f`8cX7\ _U6XS6UP5QM4NJ3JH3GE2CB1980660881AA2BC3DD4EF5GH6HJ\ 7JK7KM8MO9NQAPRBQTCSVDTXEVYEW_FYaGZcH`dIafJchKhmLd\ iK`fKXcKU`JQYJMVJISJFPIBMI7JI4GIERNN`RXjVetZcqbamf\ _jjYgm_bk`ZjaUibQhdNifKihIjjFjlCknAklBjkCijDiiEhhF\ ggGgeHfdIfcJebKdaLd`McZGX_Nc_Tj_ZqVcjlVcmUgnTlpSqq\ RvrRzsWss`mtegtjauoWutQuyKotJipIclHZhHTcGN_FHWECSE\ BUE5P_5Tc5WgQhcLlXGqQBvCCuKCtRCtYgmjknhongsoevodok\ YihSbdMXaGRZAV_BY`B`aBdbBgcBjdBneBqfBtgBpdDmbEicGf\ hHbmJ_mKWmMTmNPmPMmQJmRMrPPvOSzMVzLYzK`zIczHfzGizE\ lzDozCzz8zzNzzGzz9zzHzzPzzXzzdzzlzzszzbzzMzz5zzKzz\ ZzzlzzkzzkzzkzzkzzczzWzzO } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 07-11-12 (More of the Same [No Rating])
by Jim Muth 07 Nov '12

07 Nov '12

FOTD -- November 07, 2012 (No Rating) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that comes about when the expression Z^(2.06)+C is iterated 18 levels up the hyperladder with no function applied. This parent resembles a Mandelbrot set with two main buds and a large split along the negative X-axis. Today's scene is located near the tip of a wedge-shaped area of chaos extending westward just south of the split. The name "More of the Same" indicates that this is the fourth consecutive similar image. The similarity prevents me from giving it a rating. The calculation time of one minute will pass in a flash. The flash may be avoided by viewing the image on one of the web sites. The finished image is at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> The day dawned cloudy here at Fractal Central, then the clouds hung on for the rest of the day. The forecast hints at snow tonight, but the temperature of 43F +6C would seem to make that unlikely. The next FOTD will be posted in the proper universal time. Until whenever that is, take care, and think positive. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= More_of_the_Same { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-1.174308345901659/-0.0904782035179286/\ 6.741058e+012/1/115/0 params=2.06/0/18/0 float=y maxiter=1800 inside=0 outside=tdis periodicity=6 mathtolerance=0.05/1 colors=000nJzjMzfPzcSz_VzWYzT`zPczMezNgzNhzOjzOkzP\ mzPnzPpzQqzQszRtzRvzSwzSyzSzzMvzGszNszUrz`rzfrzdUz\ b6zd3zCBzR5zTTzMbzElz6vzEwzMxzUyzbzz`yzZxzXwzUvzSu\ zQtzOszLrzJqzHpzFozCnzAmz8lz6kz3izE`zQRz`Izl8zfDz`\ IzUNzOSzIXzBbz91zA3zC5zE7zEAzEDzEGzEJzEMzcFzYRTXPT\ VMTUKTXPW_TZbXae`dhdgkhjnlmcWWcXovSjvOevKavFXvLTuH\ OuCJu8Fu4Au06q17m28i38e49a5AY5AU6BQ7CM8CI9DAAAAAAA\ 9AA9AA8AA8AA7AA7AA6AA6AA5AA5AA5AA4AA4AA3A_3La2Mb2M\ d1Nf1Ng1NMMpNNoOOnPPmPQlQRkRSjSTiSThTUgUVfVWeVXdWY\ cXZbY_aY_`Z`__aZ`bY`cXadWbeVcfUcfTbcRaaQa_P`YO_WN_\ UMZSLYQKYOJXMHXKGWIFVGEVEDUCCTABT8AS69S48W4A_4Bc4D\ g4Fk4Go4Is4JoANlFRhKVePZaVaZ_eVdiSimPnpXnrcnsjntqn\ uobqmSnkHki6hi6Pi65g86e97cA7aB8_C9YE9WFAUGBSHBQICO\ KDMLDKMEINFGOFHPFHPFHQFIQFIQFIRFJRFJSFJSFKSFKTFKTF\ LUFLUFLUFOTGQTGSTGVTHXTHZSHaSIcSIeSIhSJjRJlRJoRKqR\ KsRKuNMvKOwGPxDRyASuDUqGW } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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