July 2010 - Fractint - mailman.xmission.com

Minibrot Ice
by Roger Alexander 07 Jul '10

07 Jul '10

Yesterday fire, today a minibrot surrounded by ice crystals. That's what my imagination says anyway. Completed fractal posted at the old standby http://maxitersfractalfollies.blogspot.com fract295.gif { ; minibrot ; blank ; calctime 0:19:51.00 ; created Jul 06, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=frac_ml.frm formulaname=Nuclear_M_k_0 center-mag=+0.28877190200636940/+0.71021293639915940/2637.932/1/-155.000\ 000000016087/1.17175505409683467e-011 params=-0.423688467055269/-0.4882045960875271/-0.1990722373119297/-0.987\ 1822260200812 float=y maxiter=1200 inside=0 colors=000M0fL0eL0dK0cK0bJ0aJ0`I0_I0ZH0YH0XG0WG0VF0UF0TE0SE0RD0QD0PC0OC0\ NB0MB0LA0KA0J90I90H80G80F70E70D60C60B50A50940840730630520420310210100000\ 200400600800A00C00E00G00I00K00M00O00Q00S00U00W00Y00_00a00c00e00g00i00k00\ m00o00q00s00u00w00z01z03z05z07z09z0Bz0Dz0Fz0Hz0Jz0Lz0Nz0Pz0Rz0Tz0Vz0Xz0Z\ z0`z0bz0dz0fz0hz0jz0lz0nz0pz0rz0tz0vz0xz0zz0zz0yz0xz0wz0vz0uz0tz0sz0rz0q\ z0pz0oz0nz0mz0lz0kz0jz0iz0hz0gz0fz0ez0dz0cz0bz0az0`z0_z0Zz0Yz0Xz0Wz0Vz0U\ z0Tz0Sz0Rz0Qz0Pz0Oz0Nz0Mz0Lz0Kz0Jz0Iz0Hz0Gz0Fz0Ez0Dz0Cz0Bz0Az09z08z07z06\ z05z04z03z02z01z00z00z03z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0uz1t\ z1sz2rz3pz3oz4nz5mz5kz6jz7iz7hz8gz9ez9dzAczBbzB`zC_zDZzDYzEWzFVzFUzGTzHS\ zHQzIPzJOzJNzKLzLKzLJzMIzNGzNFzOEzPDzPCzQAzR9zR8zS7zT5zT4zU3zV2zW0zW0zV0\ yV0xU0wU0vT0uT0tS0sS0rR0qR0pQ0oQ0nP0mP0lO0kO0jN0iN0hM0g } frm:Nuclear_M_k_0 { ; p1, p2 parameters. Use float=y. k is Mandel parameter, ; critical point 0. a=p1, c=p2, k=pixel, a2=a*a, ac=a*c, r3=sqrt(3), r3a2=r3*a2 a6=3*a2, r3ac=r3*ac, ack=k*ac z=0: z2=sqr(z) z3=z*z2 z=(r3a2*z3-a6*z2-r3ac*z-ac)/(r3*z+1)+ack, lastsqr<=1000000 } Roger Alexander _________________________________________________________________ Learn more ways to connect with your buddies now http://go.microsoft.com/?linkid=9734388

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Subject? It's a Tad Volcanic
by Roger Alexander 06 Jul '10

06 Jul '10

Today's fractal might make good wallpaper if you're in a volcanic state of mind. Look-fractal lava! Before and after versions at - you guessed it - http://maxitersfractalfollies.blogspot.com fract293.gif { ; wallpaper ; blank ; calctime 0:07:39.70 ; created Jul 05, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=_b.frm formulaname=BEES corners=1.730718/3.511423/-0.4553519/0.8801776 params=-0.1692159794915616/-1.652272103030488/2.886104922635579/0.705648\ 9761040071 float=y maxiter=1200 fillcolor=0 periodicity=0 colors=000000000000000000000000000000000100100200400500700900B00D00G00I0\ 0L00O10Q10T10W10Z10a10e10h20k20o20r20v20y20z30z50z60z80z90zB0zC0zE0zF0zH\ 0zI0zK0zL0zN0zO0zQ0zR0zT0zU0zW0zX0zZ0z_0za0zb0zd0ze0zg0zh0zj0zk0zm0zn0zp\ 0zq0zs0zt0zv0zw0zy0zz1zz3zz4zz6zz7zz7zy7zx7zx7zw7zv7zv7zu7yt7ys7ys7yr7yq\ 6yq6yp6yo6yo6xn6xm6xl6xl6xk6xj6xj6xi5xh5wh5wg5wf5we5we5wd5wc5wc5vb5va5va\ 5v`4v_4vZ4vZ4vY4vX4uX4uW4uV4uV4uU4uT4uS3uS3uR3tQ3tQ3tP3tO3tO3tN3tM3tL3sL\ 3sK3sJ2sJ2sI2sH2sH2sG2sF2rE2rE2rD2rC2rC2rB1rA1rA1r91q81q71q71q61q51q51q4\ 1q31p20p20o20n20m20m20l20k20j20j20i20h20g20g20f20e20d20d20c20b20a20a20`2\ 0_20Z20Z20Y20X20W20W20V20U20T20T20S20R20Q20Q20P20O20N20N20M20L20K20K20J2\ 0I20H20H20G20F20E20E20E20D20D20C20C20C20B20B20A20A20A2092092092082082072\ 0720720620620520520520420420420320320220220220120120010 } frm:BEES {; Ray Girvan ; Newton variant giving biomorphs ; z -> sin(z)-k before Newton iteration ; use floating point, periodicity=no ; and smooth colour palette ; p1 controls twist of spirals ; p2 controls number of lobes ; try p1=0.1, p2=3 for 'bees' ; p1=0.1, p2=6 for 'scorpions' z=pixel: z1=sin(z)-p1 z2=z1^p2-1 ; any function f(z) z3=p2*(z1^(p2-1)) ; its derivative f'(z) z=z-(z2/z3) |z2| >= 0.00001 ;SOURCE: 97msg.frm } Roger Alexander _________________________________________________________________ MSN Dating: Find someone special. Start now. http://go.microsoft.com/?linkid=9734384

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FOTD 06-07-10 (Total Discrimination [6])
by Jim Muth 06 Jul '10

06 Jul '10

FOTD -- July 06, 2010 (Rating 6) Fractal visionaries and enthusiasts: After 3 days in the (near) pristine wilderness, it's good to be back at the fractal desk. At least the cats must think so. I have never seen them demanding so much attention. Today's image is a quickie, and as such, can rate no more than a 6. The parent fractal is a near-shapeless thing that at first glance appears totally non-critical. Today's scene is located in a debris-filled hole lying a short distance northwest of the main body. Much of the image consists of holes, which cause the swiss- cheese effect. The rating of a 6 equals just the slightest above average. The name "Total Discrimination" once meant something, but the meaning has long since been forgotten. The calculation time of 3 minutes may be saved by viewing the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> The 3 days' vacation went reasonably well, even though I almost got into a dispute with FL. While watching a soaring eagle, she commented how enjoyable it was to get away from the hectic every- day world, and said she hoped we soon do something about climate change. I saved the day by remaining silent. The heat wave remained in full force here at Fractal Central on Monday, with blazing hot sun, little wind and a temperature of 97F 36C. The fractal cats were so glad to see us return that they forgot about the heat. The next FOTD will be posted in 24 hours. Until then, take care, and do your part to fight climate change. (IMO, 'climate change' is real, the climate always changes, but the danger is grossly exaggerated by the media, which is motiva- ted by profit and politics. And I doubt that the planet would obey any laws we might pass to fight the change.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TotalDiscriminaton { ; time=0:03:09.93-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritMinZ function=ident float=y center-mag=+0.0000091918653/+0.0028961512608/8.880\ 02e+008/1/-27/0 params=1/3/0.05/13/0/0/0/0 passes=1 maxiter=1500 inside=0 logmap=258 periodicity=6 colors=000_MqZJkZGfYDaYAWX7RX5MSELXMKUVJcbImkHzsG6\ rzzqL6pzzoPzoR6nT6mV7lY7k_7ka7jc7ie7hz7mz7qzCuzHqz\ LmzQkqVgsZgt_ju_mv_pw`nsampblmbkicjfdicdh_egXfeUfd\ QgcNhbKhaGi`Dj_AjZ7k_9k`BlaClbEmcGmcHndJneKofMogOp\ gPphRqiTqjUrkWrkXnjYkjYhjZejZbj__j_Xi`Ui`RiaOiaLib\ IibFibJjdMjfPjhVjjcjkmjmvkozkqzkrvktskvpkxskymgthc\ pc_kZWgTTbOPZJLUEHQ9EMECQJBTNAWS8ZX7a`6d_8aZ9ZYAWX\ BUWCRVDOUEMTGJSHGRIDQJBPK8OL5NM3PN2QO2RP2VN5YL8`JA\ cIDfGFiEIlDKkERjEYiEdiEkpLUvRCuTGtVJtWMsYQr_Tr`Wt`\ Xv_Yx_Zy__tZdzfytbqoZiiVadRUZNK_OM`OO`PQaPSbPUbQWc\ QYdR_dRaeRcfSdfSfgShhTjhTliUnjUpjUrkVtlVvlVwlctllq\ ovpluojunhtmetlctkasjZsiXrhVrhSrgQqfOqeLpdJpcHpbEo\ aCo`2wV5tX8rZAo`DmbFkdIhfKfhNcjPalS_nUXpXVr`Qt_SsZ\ TsYUsXWrWXrWZrVcqUhqTmqSrpSvpzzpzzozzozzoNznNznMzn\ LzmKzmzzUzzVzzWzzYzzZzz_zz`lzbnzcpzdqzelzdhzcdzc`z\ bzzSzzPzzMzzJzzGzzDzzAzzW } frm:MandAutoCritMinZ {; 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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Self-Similar, Looks Like Worms
by Roger Alexander 05 Jul '10

05 Jul '10

Happy July 4th! Bits and pieces of self-similarity all over the place. Go to http://maxitersfractalfollies.blogspot.com for the ready made version. To the dark imagination it might look like worms. fract292.gif { ; blank ; blank ; calctime 0:09:31.38 ; created Jul 04, 2010 ; Fractint Version 2004 Patchlevel 9 reset=1900 type=formula formulafile=fract002.frm formulaname=mask function=asin/atan/tan center-mag=+0.06954360169420207/-0.10547296438733110/190405.8/1/90/3.885\ 78058618804789e-016 params=-0.125/2.125/2.125/-0.125 float=y maxiter=1200 inside=0 cyclerange=0/255 colors=000430320220210110000000100200310310420520620730730840940A40B50B5\ 0C60D60E60E70F70G80H80I80I90J90KA0LA0MA0MB0NB0OC0PC0QC0QD0RD0SE0TE0UE0UF\ 0VF0WG0XG0XH0YH0ZH0_I0`I0`J0aJ0bJ0cK0dK0dL0eL0fL0gM0hM0hN0iN0jN0kO0lO0lP\ 0mP0nP0oQ0oQ0pR0qR0rR0sS0sS0tT0uT0vT0wU0wU0xV0yV0zW0zW0zX0zY0zZ0z_0z`0za\ 0zb0zc0zd0ze0zf0zg0zh0zi0zj0zk0zl0zm0zn0zo0zp0zq0zr0zs0zt0zu0zv0zw0zx0zy\ 0zz0zz4zz8zzCzzGzzKzzOzzSzzWzzZzzbzzfzzjzznzzrzzvzzzzzvzzrzznzzjzzfzzbzz\ ZzzWzzSzzOzzKzzGzzCzz8zz4zz0zy0zx0zw0zv0zu0zt0zs0zr0zq0zp0zo0zn0zm0zl0zk\ 0zk0zj0zi0zh0zg0zf0ze0zd0zc0zb0za0z`0z_0zZ0zY0zX0zW0zW0yW0xW0wV0wV0vU0uU\ 0tU0sT0sT0rS0qS0pS0oR0oR0nQ0mQ0lP0kP0kP0jO0iO0hN0gN0gN0fM0eM0dL0cL0cL0bK\ 0aK0`J0_J0_J0ZI0YI0XH0WH0VG0VG0UG0TF0SF0RE0RE0QE0PD0OD0NC0NC0MC0LB0KB0JA\ 0JA0IA0H90G90F80F80E70D70C70B60B60A50950850740740630530 } frm:Mask = {; Ron Barnett [70153,1233] ; try fn1 = log, fn2 = sinh, fn3 = cosh ;P1 = (0,1), P2 = (0,1) ;Use floating point z = fn1(pixel): z = P1*fn2(z)^2 + P2*fn3(z)^2 + pixel, |z| <= 4 } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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Ferns and Fronds
by Roger Alexander 04 Jul '10

04 Jul '10

Another plant inspired fractal. Do I need a policy on giving posts names? I could say "the description is swirling ferns" which is analogous to giving it a title but I could also use the terms "caption" or "tag". Just can't make up my mind I suppose. Looking at the color of the dark green I could have also used "a plate of spinach" but that doesn't sound dignified enough. fract291.gif { ; ferns ; blank ; calctime 0:28:53.39 ; created Jul 03, 2010 ; Fractint Version 2004 Patchlevel 9 reset=1960 type=formula formulafile=frac_ml.frm formulaname=tri-fn+fn function=sqrt/sqr center-mag=0.55523/1.10691/2.73224 params=1000.235145115513/1.456831568346202/0.3772087771233253/0.02272103\ 030487991 float=y maxiter=12000 inside=0 outside=atan periodicity=0 cyclerange=0/255 colors=0R00Q00P00O00N00M00L00K00J00I00H00G00F00E00D00C00B00A009008007006\ 00500400300000200000000000200300500600800A00B00D00E00G00I00J00L00M00O00Q\ 00R00T00U00W00Y00Z00`00a00c00e00f00h00i00k00m01m03m04n06n07o09o0Ao0Cp0Ep\ 0Fq0Hq0Iq0Kr0Lr0Ns0Ps0Qs0St0Tt0Vu0Wu0Yu0Zv0`v0bw0cw0ew0fx0hx0iy0ky0mz0mz\ 1mz3nz5nz7oz9ozBpzDpzFpzHqzJqzLrzNrzPrzRszTszVtzXtzZuz`uzbuzdvzfvzhwzjwz\ lwznxzpxzryztyzvzzxzzzzzyzzwzzvzzuzztzzrzzqzzpzznzzmzzlzzkzzizzhzzgzzezz\ dzzczzbzz`zz_zzZzzXzzWzzVzzTzzSzzRzzQzzOzzNzzMzzKzzJzzIzzHzzFzzEzzDzzBzz\ Azz9zz8zz6zz5zz3zz2zz0yz0xz0vz0uz0tz0sz0qz0pz0oz0mz0lz0kz0iz0hz0gz0fz0dz\ 0cz0bz0`z0_z0Zz0Yz0Wz0Vz0Uz0Sz0Rz0Qz0Oz0Nz0Mz0Lz0Jz0Iz0Hz0Fz0Ez0Dz0Bz0Az\ 09z08z06z05z03z02z00z00y00x00w00v00u00t00s00r00q00p00o00n00m00l00k00j00i\ 00h00g00f00e00d00c00b00a00`00_00Z00Y00X00W00V00U00T00S0 } frm:tri-fn+fn { ; Sylvie Gallet ; Thanks to Kerry Mitchell for the idea! ; real(p1) = bailout ; imag(p1) must be different from 0 (>=1 recommended) ; z=fn1(z) + p2*fn2(z) ; This formula must be used with decomp = 256 and periodicity = 0 ; z1 = pixel , mz1 = cabs(z1) , 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 , za = fn1(z1) , a = cabs(za) zb = p2*fn2(z1) , b = cabs(zb) z1 = za + zb , 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 } Roger Alexander _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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Re: [Fractint] Jim's Blunder
by JackOfTradeZ＠comcast.net 04 Jul '10

04 Jul '10

. Hey Jim - you just discover the negative exponents ?!? I have known about them for some time; I even made an animation of the default MSet with exponent -7 -> +7 a while back. A few years ago I was investigating these, and most of the images are very similar to yours - characterized by all sorts of roundish blobs and very complex patterns. You should look into it more - should come up with some interesting FOTD images in the future. BTW, in science we don't call things like this "blunders"; we use the word "serendipity", that is, a good result or discovery resulting from chance error. .

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A Fractal and Some Mustard Talk
by Roger Alexander 03 Jul '10

03 Jul '10

More before and after wispiness at Action Central. Yowwzaa look at the difference! The weather report for Calgary (actually the whole prairies)-wet wet wet. This place is described as semi-arid. Who thought that one up? Nature being contrary I suppose. If I had a speculative nature I would invest in mustard futures-seriously (almost seriously). Canada is the worlds largest grower of mustard seeds and there has been so much rain farmers have had trouble getting crops of any type in. But I'm not a big risk taker. For some non-mustard related graphics go to http://maxitersfractalfollies.blogspot.com and have a gander. fract288.gif { ; filaments not nematodes ; blank ; calctime 0:02:14.35 ; created Jul 02, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=star_dup_rjr passes=1 center-mag=-0.177622/0.591426/7.251421 params=33/0/0.5/-0.375 float=y maxiter=1500 inside=atan decomp=256 periodicity=0 cyclerange=0/255 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:star_dup_rjr {; Kerry Mitchell ; renamed to distinguish from ; other frm called star ; also p2 added so user can directly input ; julia parms previously hard coded to .439,.493 ; p1 appears to specify degrees zc=pixel, c=p2, r=1e30 t=real(p1)/180*pi, ct=cos(t), st=sin(t), qmin=99: zc=sqr(zc)+c, q=|ct*real(zc)+st*imag(zc)| IF (q<qmin) qmin=q t=log(q) z=cos(t)+flip(sin(t)) ENDIF |zc| < r ;SOURCE: frac_ml.frm } Roger Alexander _________________________________________________________________ Game on: Challenge friends to great games on Messenger http://go.microsoft.com/?linkid=9734387

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No FOTD for July 2,3,4,5
by Jim Muth 02 Jul '10

02 Jul '10

Fractal visionaries and enthusiasts: We have decided to take a grossly overdue holiday here at Fractal Central. The next FOTD will be posted on July 6. The fractal cats will be well cared for while we are away. Until the next FOTD, take care, and be environmentally alert. Jim Muth

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Blue Minibrots
by Roger Alexander 02 Jul '10

02 Jul '10

It's busy at Action Central and this post is short. It's a minibrot today, check it out at http://maxitersfractalfollies.blogspot.com and as a bonus there is an intriguing video from You Tube on manipulating statistics. fract284.gif { ; minibrot appears to be slightly perturbed ; blank ; calctime 0:06:15.14 ; created Jul 01, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=kerrym.frm formulaname=hermanm_man-cart center-mag=1.79491/1.13844/14.97396/1/60.0000000000000995/-1.26836041669\ 520228e-013 params=3/2/0.5/0.5/2/0 float=y maxiter=1500 inside=0 outside=atan colors=00000000200400600800A00C00E00G00I00K00M00O00Q00S00U00W00Y00_00a00\ c00e00g00i00k00m00o00q00s00u00w00z01z03z05z07z09z0Bz0Dz0Fz0Hz0Jz0Lz0Nz0P\ z0Rz0Tz0Vz0Xz0Zz0`z0bz0dz0fz0hz0jz0lz0nz0pz0rz0tz0vz0xz0zz0zz0yz0xz0wz0v\ z0uz0tz0sz0rz0qz0pz0oz0nz0mz0lz0kz0jz0iz0hz0gz0fz0ez0dz0cz0bz0az0`z0_z0Z\ z0Yz0Xz0Wz0Vz0Uz0Tz0Sz0Rz0Qz0Pz0Oz0Nz0Mz0Lz0Kz0Jz0Iz0Hz0Gz0Fz0Ez0Dz0Cz0B\ z0Az09z08z07z06z05z04z03z02z01z00z00z03z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0j\ z0nz0rz0vz0uz1tz1sz2rz3pz3oz4nz5mz5kz6jz7iz7hz8gz9ez9dzAczBbzB`zC_zDZzDY\ zEWzFVzFUzGTzHSzHQzIPzJOzJNzKLzLKzLJzMIzNGzNFzOEzPDzPCzQAzR9zR8zS7zT5zT4\ zU3zV2zW0zW0zV0yV0xU0wU0vT0uT0tS0sS0rR0qR0pQ0oQ0nP0mP0lO0kO0jN0iN0hM0gM0\ fL0eL0dK0cK0bJ0aJ0`I0_I0ZH0YH0XG0WG0VF0UF0TE0SE0RD0QD0PC0OC0NB0MB0LA0KA0\ J90I90H80G80F70E70D60C60B50A509408407306305204203102101 } frm:hermanm_man-cart { ; Kerry Mitchell 16feb98 ; ; real(p1) = z exponent (use integer >= 2; m=n-1) ; imag(p1) = g exponent (integers) ; p2 = alpha ; 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, alpha=p2 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 _________________________________________________________________ Look 'em in the eye: FREE Messenger video chat http://go.microsoft.com/?linkid=9734386

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FOTD 01-07-10 (Jim's Blunder [No Rating])
by Jim Muth 01 Jul '10

01 Jul '10

FOTD -- July 01, 2010 (No Rating) Fractal visionaries and enthusiasts: Have no concern about today's parameter file, which includes no color information. The program will automatically pick up the default color palette, which works quite well with this image. How can a person rate a mistake? They cannot! So how could I give a rating to today's image? It is an error. With the type=julzpower formula on the screen I decided to try some- thing with the Julia set of Seahorse Valley of the Mandelbrot set. But instead of entering 2 as the exponent, I entered minus-2, and look what happened. I have no idea how I could have missed such an obvious fractal for such a long time, but I did. Anyway, I post the image as today's FOTD. It will never set any world record, but it is interesting and it calculates in a faster-than-light 4 seconds. The name "Jim's Blunder" says it all. The result may be seen by running the included parameter file or by going to the FOTD web site at: <http://www.Nahee.com/FOTD/> where the finished image is posted for instant if not total gratification. Absolutely perfect weather here in the Fractal Central area on Wednesday made for an enjoyable day in the outdoors for FL and myself. The total sun, low humidity and high temperature of 77F 25C that marked the day could hardly be improved upon. The fractal cats showed their approval by getting into trouble while FL and I were traversing a local hiking trail. When we returned, we found a lamp overturned and two totally innocent looking cats. The next FOTD will be posted in around 12 hours. Until then, take care, and do what the doctor says. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Jim's_Blunder { ; time=0:00:04.01-SF5 on P4-2000 reset=2004 type=julzpower center-mag=0/0/0.17425/1\ /90/0 params=-0.75/0/-2/0 float=y maxiter=1500 bailout=1000 inside=0 } END PARAMETER FILE=========================================

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