January 2008 - Fractint - mailman.xmission.com

FOTD 24-01-08 (Hyperseahorse Valley [8])
by Jim Muth 24 Jan '08

24 Jan '08

FOTD -- January 24, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's circular image is a scene in Hyperseahorse Valley of the Hypermandelbrot set. I know that it looks nothing like a scene in the familiar Seahorse Valley, but Hyperseahorse Valley is a horse of an entirely different color. The HyperMandelbrot formula that created the image is the most enigmatic one in my active list. It appears to draw some of the Mandelbrot slices that the type=hypercomplex formula misses, though actually, I am not sure exactly what it does draw. We know that these hyper-elements exist in the 8-dimensional Hyperjulibrot figure because we see them in the images created by the type=hypercomplexj formula, which draws a far greater variety of slices than the type=hypercomplex formula, but some of the images appear so unlikely that I cannot shake the impression that they are artifacts of mathematical imprecision rather than true fractals. But whatever the images are, the HyperMandelbrot formula is infinitely versatile, and I have barely scratched the surface of what it can do. The rating of an 8 is based mostly on the mathematical interest of the image. The artistic worth is merely average. The name "Hyperseahorse Valley" describes the location of the scene in its parent fractal. The calculation time is a disappointingly slow 1/2 hour even on the super-speedster 2000mhz machine. The calculation is so slow because the periodicity must be turned off when working with the HyperMandelbrot formula. But all is not lost, for the completed image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it may be enjoyed at leisure. A fairly average but brilliantly sunny day here at Fractal Central on Wednesday went un-noticed by the fractal cats, who spent the day chasing each other up and down the hallway. By the time the evening tuna treat was served, they were totally exhausted. My day was fairly busy, but under control. The next FOTD, which will be another scene in Hyperseahorse Valley, will be posted in 24 hours. Until then, take care, and what the heck are those 'rods' the UFO fans are talking about. I doubt that they are discussing the anatomy of the eye. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= HypersehorseValley { ; time=0:29:22.50-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot center-mag=-0.743377645/+0.1010200296/4126.308 params=0/0/0.2/0/1e-007/0 float=y maxiter=32767 inside=0 logmap=212 periodicity=0 colors=000`PWaRYbS_cUadUbfUdgUfhUgiVijWkhXjcYiZZhU\ _gP`fOaePacQbaRbbSccTcdUdeUdfVegWehXfiYfjZgk_gl`hm\ ahnbiobipYghUfaQeVLcNHbGDa99`2DY7GVCJTHMQMPORSLWVI\ `YGe`DjcBof8ti6xhCvhHuhNthSshYrgbqghpgmogsngxmhsei\ nYjiQkdIl`AiZ9gX9eV8bT8`R7ZP7WN6UL6SJ5QH5NF4LD4JB3\ G93E72C52A32C45D58E6BG7EH8HI9JJAMLBPzCuzDmzDczBLvA\ 9rC9mE8cG8UI8RK7RM7QO6QQ6PS6PU5OW5OY4N_4Na4Mc3Me3L\ g2Li2Kk2Um1co1mq0wu0wz0mq3cm6Ui9KeCCaFBYIAUK9QN8MQ\ 7Iz6EW5Az46a33z9DdFNzLWzRezWnzUgzSazRW6SU8TTAUSCVR\ EWQGXPIYOJZNL_MN_LP`JRaITbHVcGWdFzeEzfDzgCzhBzhAvg\ BrfCmeDhdEgdFgcGgbHgaIg`Jh`Kh_LhZMhYNhYOhXPhWQhVRi\ USiUTiTUiSViRWiRXiQYiPZjO_jN`jNajMbjLcjKdjKejLfkMg\ kNgkOhlPhlQilRjlRjmSkmTkmUlmVlnWmnXnnYnnYooZoo_po`\ qoaqpbrpcrpdspdsqetqfuqguqhvrivrjwrjwrixqiypizohzn\ hznhzmgzlgzkgzjfzjfzifzhezgezfezfdzedzddzcdzcczdbz\ eazf`zf_zgZzhYzhXziWzjVzj } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

1 0

FOTD 20-01-08 (Spiritual Zen Tree [No Rating])
by Jim Muth 23 Jan '08

23 Jan '08

FOTD -- January 20, 2008 (No Rating) Fractal visionaries and enthusiasts: Every now and then I just have to create a fractal tree. Today the urge became irresistible, and the result was another fractal tree. Since this is the fourth or so similar fractal tree in the FOTD series, I did not give the image a rating, but it is a rather good tree and well worth a look, especially by those who have missed the previous fractal trees. I named the image "Spiritual Zen Tree" when I checked the day's snail mail and found the Jan 28 issue of 'Time' magazine in the box. The issue is yet another one claiming that 'love is just a brain chemical'. Its standpoint is that we are largely slaves of our genes, and our behavior is pre-programmed by random evolu- tion to perpetuate the species. But this makes me wonder. If we are slaves of our genetic pro- gramming, how can anyone be held responsible for a crime he was pre-programmed to commit? The same thing can be said in a dif- ferent way by claiming that we are pre-programmed by God's know- ledge of the future to do what God already knows we will do. The name of the image indicates that I feel the scientific arti- cles in the magazine, as well as the woefully lacking theories of conventional theology, are missing something very important of a very spiritual nature. The image lies in a near-Julia set of the (-Z)^sqrt(2)+C Mandeloid. It was created with the EvenMoreSlices formula, though a number of other formulas could have created it. The calculation time of the image is a zippy 51 seconds, about the same time it will take to view the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cloudy and chilly weather prevailed here at Fractal Central on Saturday, when the high temperature reached 36F 2C. The fractal cats, who still appear to be feuding, ignored the outside condi- tions. The better part of my day was spent reading a magazine. The next FOTD will appear by technological magic in 24 hours. Until then, take care, and for all we know, we might be as pro- grammed as the fractals we admire. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Spiritual_Zen_Tree { ; time=0:00:51.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=t center-mag=-0.766409/0.13473/39.4/0.7974/6.1233740\ 3837406224/-0.253135479727083945 params=1.4142/0/1e-005/1e-005/-1.125/0/-0.2/0 float=y maxiter=416 inside=255 logmap=312 symmetry=none periodicity=10 colors=0000Zzc_Pc_Qc_Qc_Rc_Sc_Sc_Tc_Uc_VcWVZSWUOXU\ KXZNYYQZYSZYU_YW`YYaZZa__b``caacbbdccebceecffdgfdh\ gchebCc`CaYC`WC_UB_TBZQBZOBYMBYKAXHAXGAXFAWEAWD9VB\ 9VB9UB9UB9TA8TA8S98S88W36S88OCAKGBGLDCPF7SF8UG9VHA\ cIBmJCtJDzKDzLEzMFzNGzNHzOIzPIzQJzQKzRLzSMzTNzUzzU\ zzVzzWzzXzzYzzYzzZzz_zz`zz`zzazzbzzczzdzzdzzezzfzz\ gzzgzzfzzfzzfzzfzzfzzfzzezzezzezzezzezzezzdi`dj_dj\ ZdkYdkYdkKek7fk7ej7dj7cj8bj8ai8`i8_i8Zi9Yi9Xh9Wh9V\ hAUhATgASgARgAQgBPfBOfBNfBMfBLfCKeCJeCIeCHeCGdDFdD\ EdDDdDCdDBcEBcEBbFBbFBaFBaGB`GB`GB_HB_HBZIBZIBYIBY\ JBXJBXJBYICYIDYIDYIEZIEZIFZIFZHGZHG_HH_HI_HI_HJ_HJ\ `GK`GK`GL`GLaGMaGMaGNaFOaFObFPbFPbFQbFQbFRcERcEScE\ ScETdEUdEUdEVdDVdDWeDWeDXeDXeDYeDYdEXdFXdGXcGXcHWc\ IWcJWbJWbKVbLVaMVaMVaNUaOU`PU`PU`QT_RT_ST_ST_TSZUS\ ZUSZVSYWSYXRYXRYYRXZRX_QX_QW`QWaQWbPWbPVcPVdPVeOUe\ OUfOUgOUhNThNTiNTjNTjN0Zz } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

3 2

FOTD 23-01-08 (Fractured Seahorses [6])
by Jim Muth 22 Jan '08

22 Jan '08

FOTD -- January 23, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows a scene in Seahorse Valley of the Z^2.001+C Mandeloid as it appears at a level 0.03 up the logarithmic ladder when the function is eliminated. At this quite unlofty level, the parent fractal, which appears as a perfectly normal Mandelbrot set, is rotated clockwise just far enough for the southern arm of Seahorse Valley to intersect the negative X-axis. In the area of the X-axis some rather unusual things often happen to fractals with fractional exponents of Z, and today's image is no exception. The unfamiliar features are all caused by the nearness of the scene to the X-axis, which lies only 0.00001 to the south. Unable to find anything of knockout value in the image, I could rate it at only an everyday 6. The name "Fractured Seahorses" indicates that the scene lies in a very fractured part of its parent's Seahorse Valley. The calculation time of just under 10 minutes is a bit slow, but relief is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image has been or soon will be posted for immediate gratification. Heavy clouds that threatened snow and a temperature that hovered around freezing all day made Tuesday rather unpleasant here at Fractal Central. The fractal cats made their day as pleasant as possible by hovering around the heat all day. Except for the fractal, which put up a bit of a fight, my day was peaceful enough. The next FOTD will be posted in 24 hours. Until then, take care, and knowing the future is the same thing as changing the past, though it is now seen from the opposite direction. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FracturedSeahorses { ; time=0:09:55.84-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident center-mag=-0.76117950836326/+0.00001163773987/\ 8.014934e+008/1/-60/0 params=2.001/0/0.03/0 float=y maxiter=6250 inside=0 logmap=1075 periodicity=10 colors=000GGGFzzBrwCmsDihDjiEjiFjjFkjGkkGkkHllIllI\ mmJmmKmnKnnLnoLnoUibbdQk_DtV1qU7oUClUHjUMhUReTXcTa\ `TfZTkXTp`WncYmf`libjleioghrjfulexndijeld_o_UrUOtP\ JsOMsNPrNSrMVqLYqL`qKbpJepJhoIkoHnnHqnGtnGvhHubItX\ JtRKsMLsQRrUWrY`qafqekpippV_fGJX23N76QC9TGCVLFYQI_\ UKbZNecQggTjlWlqZou`qr_noZllYjiXhfWedWcaVaZU_WTXTS\ VQRTORRMOPLMOKKMJHLIFJGDIFAGE8FD6DC4CG5FJ5HM5JP5LS\ 6NV6PY6S`6Uc7Wf7Yi7_l7ao7cmAdkCeiEfgGgeIhcLiaNj`Pj\ ZRkXTlVWmTYnR_oPapNcqMeqOgmPhjQigRjcSk`UUYVXVW_RXa\ OYcLZcIVcGRbENaCJ`AF_9EZGEYMDXTDWZCPdCIyYB_B4zG7pK\ 9iPBcTDXXGQaIKeKDZH7zZBgOFfPJeQNeRRhUQjXQl_QnbPqdP\ sgPujOwmOyoOsmQnlRikSdiT_hVVgWQOXLdYGcZIc_Kc`Mc`Oc\ aQcaScbUccWccYcd_Odacecced`ceYbfVafT`gQ_hNZhLYhKui\ ItiHtjGtjFtkEtkDtlBslAsm9sm8sn7sn6soUWoq9peJpvYqv_\ qvarvbruast`ts_us_vrZwqYxpXypXzoWznVznVzmUzlTzkSzk\ SzjRz_GziQziQzhPzgOzfNzfN } 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=========================================

1 0

FOTD 22-01-08 (Minibrot Minibrot [7])
by Jim Muth 21 Jan '08

21 Jan '08

FOTD -- January 22, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows the outline of a large twisted minibrot in East Valley of the Mandelbrot set, which in itself is nothing unusual. But inside this East Valley minibrot lies a smaller minibrot from Seahorse Valley, which at first is quite puzzling. The puzzle is solved when we see that the image was created by the type=hypercomplex formula, which draws four-dimensional Mandeloids consisting of two overlapping classic M-sets. By changing the cj and ck parameters, the two sets may be made to overlap at any two points chosen. Today's parent fractal was drawn with East Valley overlapping Seahorse Valley in such a way that a small Seahorse Valley minibrot shows through a larger minibrot in East valley. (The c and ci parameters of the formula are fixed to the screen and cannot be changed, but the z, zi, zj, zk axes are all perpen- dicular to the screen. It would be nice to have a way to perturb the images in these four directions, and also to rotate the orientation of the images through the entire 4-D Mandeloid.) Since it took a bit of effort to find the overlapping midgets, I decided to add an extra point to the rating in recognition of my effort. The image itself is perhaps a bit above average, though similar images have been seen in some earlier FOTD's. The name "Minibrot Minibrot" accurately describes the image. The rather slow calculation time of 5-3/4 minutes is due to the maxiter of 14400, but it was needed to get full definition inside the outer minibrot. And all but a minute or so of this time may be saved by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Full sun could not offset a temperature of only 25F -4C here at Fractal Central on Monday. The fractal cats avoided the more drafty windows to keep warm on their shelf by the window over the radiator. My M.L.K. holiday was reasonably slow. The next FOTD will come from nowhere in 24 hours. Until then, take care, and if free will is but an illusion, why is it such a convincing one? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Minibrot_Minibrot { ; time=0:05:43.45-SF5 on P4-2000 reset=2004 type=hypercomplex function=sqr passes=1 center-mag=-0.2434276956/+0.0177325261/24493.47/1/\ -162.5/0 params=0/0/0.020008/0.505996 float=y maxiter=14400 inside=0 logmap=86 periodicity=0 colors=000ZUXWUXSUXOUXKUXGUXCUX9UX8UX7Ua6Ua6Ua8UaA\ UaCUaGUaKUaOUaSUaWUbZUbZUcZUcZUdZUdZUe_Ud_Ub`Ub`U`\ aU_aUYbVXbVVcWUcWSdWRdXPeYNe_Mf`KfbJgcHgeGhfEhhDii\ BijAggBfdBebBd_BcXBaVB`SB_QBZOBYMBWKCVICUGCTECSCCQ\ 9CP7CO5CN2CM0CR10L0CF0O9KZCKXFKVIKTLKROKPRKOUKMXKK\ ZKIYKGXJ8WI6VH4UG3TF4SE5RD6QA7Q88Q98QA9QB9QCAQDAQE\ BQFBQGCQHDQIDQJEQKEQLFQMFQNGQOGOJCIE9CA56520103306\ 51872B93EA4GC5JE6MG7OH8RJ9ULAWNBZOCaQDcSEfUFhVFfWG\ eXHcYIbYJ`ZK__LY`MX`NVaOUcPShQRlRVpS_pTduUiuViuWnu\ XruXvuVzzzzzzzzzzzzzzzPFfQFfRFfQFfQFfQFfQFfPEePDdP\ DcPDbPDaOD`OD_OCZOBYOAXN9WN8VN7TN6RN5RM4RM3RM2SM1S\ M0SN1TN1UO1VO1WP2X`NZ`MXaKVaITbHRbFShDzhCziAziAzxA\ zyAzzAzuAzvAzvAzwAzrAzmAzdAz_AzWKoSKkNKfQKaVKa_Uad\ U_iUYnUWrUUvZRvcPvhNvmLvr7vvJvzVvzevzcvzhvzmvzrvzv\ vzzvzzvzzvzzvzzvzzvzzvzzvzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

1 0

FOTD 21-01-08 (Not too Deep [5])
by Jim Muth 21 Jan '08

21 Jan '08

FOTD -- January 21, 2008 (Rating 5) Fractal visionaries and enthusiasts: I was kept so busy watching TV on Sunday that I had no time for a proper FOTD. But that old warhorse, the Mandelbrot set, bailed me out by producing an instant image of average quality. The image is a scene on the northeast shore line of the large period-2 bud of the M-set, lying at the border of Seahorse Valley. It's nothing we haven't seen before, so I rated it at an average 5. The name "Not too Deep" indicates that the image does indeed lie in the valley, but not very deep. The magnitude was great enough to require the mathtolerance entry. The calculation time of one minute is more an estimate than a true record. The completed image may be seen at any time on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cold and colder conditions prevailed here at Fractal Central on Sunday, with lots of sun but a frigid temperature of 14F -10C. The fractal cats sampled the chilly draft by the window and retired to the radiator, while I finished some important work in front of the TV. The next FOTD will appear in 24 hours. Until then, take care, and if I have free will, I will refuse to do what God, who can see the future, has told me I will do. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Not_too_Deep { ; time=0:01:00.00-SF5 on P4-2000 reset=2004 type=mandel passes=1 float=y inside=0 center-mag=-0.80359866207152790/+0.164616502313286\ 80/1.152001e+011/1/-35/0 params=0/0 maxiter=5500 logmap=1443 periodicity=10 mathtolerance=0.05/1 colors=00000WrMVqOXoRZnT`lVbkYdj_ehaggdiefkdhmckok\ mqrostruytwzvxzwwvwvrwumwuhwtcwsZwrUxrPxqKxpFxo9xo\ 6xn4xm2xm4to6qq8msAjuCfwEcyF`zE_wE_tE_qE_nEZkEZhEZ\ eEZbEZ_DYXDYUDYRDYODYLDXIDXFDXCDX9DX6FY8GZ9I_AJ`BL\ aCMbDOcEPdGReHSfIUgJVhKXiLYjM_kO`lPbmQcnReoSfpTgqU\ fpWeoXenYdm_dl`ckackbbjdbieahfagh`fi`ej_ek_dmZcnZb\ oYaqY`rX_sX_tujusdsr_qqVooPmnKkmFilAgmDemFdnHbnJao\ L_oNZpPXpRWqTUqVTqXSr_QraPscNseMtgKtiJukHumGvoEvqD\ vsCfmERgGCbHDdIEeIEfJFgJFhKGjKGkLHlLImLInMJpMJqNKr\ NKsOLtOLuO`jao_omaplbqjdqierggsfhsdjtcktalu`nvZovY\ qwWrwVtxTuySwyQxzPyzQxuQxpQwkRwfRvaRvYUsVWqTYnQ_lO\ bjLdgJfeGzbUk`BmZ9oW6qU4sS2rR3qQ4pQ5oP6oP6nO7mO8lN\ 9lN9lO6lP4jO5iO5gN5fN5eM6cM6bL6`L6_K7ZK7XJ7WJ7VI8T\ I8SH8QH8PG9OG9MF9LF93FJ2AH1AF4cH6cJ8cLAcNCcPEcRGcT\ IcVKcXMcZOc`QcbShdUmfWrhYviUzeRzbOzZLzWIzTFzPCzM9z\ J9zO9zU9zZZzc_ze`zfazgbzi } END PARAMETER FILE=========================================

1 0

FOTD 19-01-08 (Cave of the Dragon [8])
by Jim Muth 19 Jan '08

19 Jan '08

FOTD -- January 19, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a near-Julia set of the mouth of the valley leading to the large period-3 bud on the northeast shore of the main bay of the (-Z)^(1.5)+C Mandeloid, which is actually a rather interesting fractal. The outer outlined shape is very close to the Julia set of the point where the two branches of the valley would reach their limit. The pinkish wedges are a grossly magnified view of the two branches of the Mandelbrot aspect of the valley itself. The cobweb-like elements are added attractions brought about by the odd angle of the slice. The name "Cave of the Dragon" came about when I fantasized a dragon lying just inside the mouth of its cave-lair, guarding its treasure trove and watching for approaching dragon-slaying knights. The rating of an 8 indicates that I consider the image quite a bit of an improvement over yesterday's image. The calculation time of 1-3/4 minutes is brief enough to make no one impatient. And the image may be seen even more conveni- ently by viewing it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An un-midwinter-like temperature of 43F 6C and strong sunshine here at Fractal Central on Friday got rid of the little snow that fell on Thursday. But a cold wave is due in a day or so, so we'll see how it goes from here on. The fractal cats are still sulking at each other. But only they know why. My day was moderately busy. Luckily, the snow on the sidewalk melted before I needed to clear it away. And best of all, the next FOTD will be posted to these same lists in 24 hours. Until then, take care, and even if we do not have free will, we still have the freedon to think about it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cave_of_the_Dragon { ; time=0:01:45.84-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=t center-mag=-0.0312989/0.169102/0.9082652/1/52.5/0 params=1.5/0/0.05/0/0.5187656/0.3853761/0.2/0 float=y maxiter=6000 inside=0 logmap=3 symmetry=none periodicity=10 colors=000LHIMIINJIPKIRLITMIVNIXOIZPI_RIaSIcUIgVIl\ XIqXIv`IweIxkIyqJzuKzwYztXzqWznVykUxhTweSvcRvaQvaP\ u`Ou_Nu_MuZLuZLuYKuXJuXIuWHtVGtVFtUEtTDtTCtSBtRAtR\ 9tQ8UarX_mZZiaYecX`fWXhVTkUPmTKpSGrRCk`el_cl_blZam\ Z_mYZmYYnYXnXVnXUoWToWSoWQpVPpVOpUNqULqUKqTJrTIrSG\ rSFsSEsRDsRBtQAtQ9EF3JH4NI4RJ5WK5_L6cM6hN7lO7pP8Mx\ fQtbUpZYlVahRedNi`JmXFqTB6_V8ZUAZTBZSDYSEYRGYQIXPJ\ XPLXOMWNOWNQWMRVLTVKUVKWVJYUIdMNcMObNQ`NR_OTZOUYOV\ aQTdSRhUPkWNoYLr_JvaHycFxbExaExaEx`Dx`Dw_Dw_DwZCwZ\ CwYCvYCvXBvXBvWBvVAuVAuUAsQAuUAuT9uT9tS9uS9vR8wR8x\ Q8yz5zw6zu6zs6zq6zo6zl7zj7zh7zf7zd7zb7z_8zY8zW8zU8\ zS8zbgzaez`cz`az__zZZzZXzYVzXTzXRzWQzVOzVMzUKzTIzT\ HzSFzRDzRBzQ9zzPzkGzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzz\ UzzngzihzeizakzYmzUoznwzmuzlszkzzjzzizzhzzgzzfzzez\ zdzzczzbzzazz`zz_zzZzzYzzXzzWzzVzzUzzTzzSzzRzzQzzJ\ zzKzzKzzKzzKzzLzzLzzLzzLz } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

2 1

FOTD 18-01-08 (Something Valley [No Rating])
by Jim Muth 18 Jan '08

18 Jan '08

FOTD -- January 18, 2008 (No Rating) Fractal visionaries and enthusiasts: Today's fractal is named "Something Valley". I gave it this name because I'm not sure which type of valley it lies in. It's parent valley is kind of like a Seahorse Valley, but it's on the east side of the parent fractal's main bay. And it's kind of like an East Valley, but there are two of it. But regardless of what one calls the parent valley, the minibrot in the image betrays the fact that the exponent of Z is between 2 and 3. In fact, the exponent is 2.5, and to make matters even more confusing, it is not Z being iterated, but negative Z. With so much confusion floating around, I could hardly give the image a proper rating. And the calculation time is a frustrat- ingly slow 18-1/4 minutes even on the P4-2000mhz fireball. With all this in mind, I recommend that all interested fractal fans exercise their free will by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the moderately impressive finished product there. As for the problem of free will, I doubt that God's image can be much damaged by the lack of or existence of human free will. To me, the paradoxes raised by God's assumed nature merely show how insufficient are the God-images created by the infinitesimal imaginations of puzzled theologians, which reduce the creating power to the status of a glorified human being. Light snow fell all day Thursday here at Fractal Central in central Pennsylvania, but the temperature remained just above freezing and the snow melted on the pavement. Only on the grass did a measly 1-inch (2.5cm) pile up. The fractal cats were fas- cinated for a time by the big sloppy flakes, but soon grew bored with the show and started chasing each other up and down the long F.C. hallway. My work-day was pleasingly average, as average as the day's fractal. And the next fractal, hopefully considerably above average, will be posted to this very same list in a short 24 hours. Until then, take care, and exercise your free will. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Something_Valley { ; time=0:18:16.24-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices center-mag=+0.162919462\ 1248572/+0.2821811066023142/8.109735e+008/1/-135/0 params=2.5/0/1/0/0/0/0/0 float=y maxiter=32767 inside=0 periodicity=10 colors=000_Rv3fm7diAbfEacH_`LYYOXUSVRVTOZSLaQIdPFa\ TIZWLW_NUbQReSOiVMlYJp_GsbEvdoXBjVAfU9bT8ZS8VR7QP6\ MO5IN5EM4AL36K3CN4IQ4OT4TW4ZY4d`4ic4of4uf4xh4sd6o`\ 7eZ8XW9QSAINBBGC43D8AIBHMEOQHVUKaYUgaZiacjahlammar\ oavpazrazsaruamvahqfdljkjyghndgd`fUYeKVdAUcFUbJUaN\ U`RU_WUZ_UYcUXgR`jUXkXUk_QlbNleKlZYiSjf`fILwdNvgOu\ iQtlRsnTrqUqsWpvXpxeXanDFkCIhCLfBNcBQ`ATZAVW9YT9`R\ 8bO8eL6hM8gNAfOCfPEeQFePHcOJbOLaNN`NP_MRZMTYLVXMWT\ LXWKXZJXaIXdHXgGYjFYmEYpDYsE_yDYuCWrCUnBSkBRgAPdAN\ `9LY8JU8IR7GN7EK6CG3A76BD8CIACNCDSFDYHEbJEgLFlNFqT\ IdZLTdOGiQ4qh3xz2vt5uo7tjAseCr_FqVHpQKoLMnFPmARl5U\ k0Wj3Vi6Uh9TgCSfFReIQdLPcOObRNaUMbXP`XMZXKXXIVXFTX\ DP_9RXBSVCTTEVRFWPHXMIZKK_IL`GNbEOcBQd9Rf7Tg5Uh3Ve\ 4Yb4`_4bY4eV4hS4jP4mN4oJJqFYs7nwCltGkqKinOhlSfiWef\ _cccbag`Zk_WoYTuVSsXRrYQq_Pp`OobNncMmeLlfKkhJjiIij\ HhiKghNfgQefTdeWddZccabbd } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

1 0

FOTD 16-01-08 (Pipefish Valley [6.5])
by Jim Muth 17 Jan '08

17 Jan '08

FOTD -- January 16, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: We have another new formula today, so be sure to copy it into one of your formula files. The formula draws oblique slices of (-Z)^n Julibrots. I named the image "Pipefish Valley". A pipefish is a kind of seahorse without the curly tail, and today's image is a near- Julia set of the large valley of the (-Z)^(1.125)+C Mandeloid. This valley cannot honestly be called a Seahorse Valley, since it has no curly-tailed seahorses, but it is interesting nonethe- less, and especially so in its near-Julia aspects. The pure Julia set of the valley is a rather drab empty figure-8 shaped figure, but by centering the view on the inside of the upper arm of the valley and rotating the view 2-1/2 degrees toward the Mandelbrot orientation, I managed to make a rather interesting image of it. A good part of the scene consists of 'inside' stuff made visible by the 'bof61' inside fill. The coloring adds an unusual textured smoothness to the scene. I credited myself the usual 1/2 point for the coloring, and rated the image at a 6-1/2. The image is a slow one, taking over 41 minutes on the fast machine, so I recommend viewing it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A typical midwinter day prevailed here at Fractal central on Tuesday, with cold winds, lots of gray clouds and a temperature of 34F 1C. And the forecast is for things to become even more winterish over the next several days. The fractal cats were too busy sulking at each other to notice the weather. My day was about average. The next FOTD will appear in 24 hours. Until then, take care, and if God, who is never wrong, tells me the future, will I still have the free will to avoid the things he tells me will happen? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pipefish_Valley { ; time=0:41:38.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot5 passes=1 center-mag=-0.344371/0.0122124/1.180338 params=87.5/87.5/87.5/87.5/-0.7362027083/0.04/0/0/\ 1.125/0 float=y maxiter=30000 inside=bof61 outside=tdis logmap=12 periodicity=10 colors=000YT0WTBWSAVSAURAUR9TQ9SQ9SQ9RP8QP8QO8QO7P\ O7PN7ON7NM6NM6MM6LL5LL5KK5JK5JK4IJ4HO4GM3HJ4IF4IH4\ JI4JK4KL5KN5LO5MQ5MR5NT5NU6OW6OX6PZ6Q_6Qa7Rb7Rd7Se\ 7Sg7Th7Uj8Uk8Vm8Vn8Wp8Wq8UnDTlHRjLQhQOfUNdYLabK_fI\ YjHWoFUsESwFPvFNuFLtFJtFHsFFrFDqFBqF9pF7oE4qF5oG5m\ G5kH5iI5gI5eJ6cJ6aK6_L6YL6WM6UM7SN7QO7OO7MP7KO6GP7\ IP7JP7KQ7LQ7MQ7NR7OR7PR8QR8RS8SS8TS8UT8VT8WT8XT9YU\ 9ZU9_U9`V9aV9bV9cW9dWAeWAfYAgZAhcAihAjmAkrAnvBqzMt\ zUwzUzwXzrNzmBzjByf9wcAtaBq`CnZClYDiYEfXEdWFaWG_VH\ ZVHXUIVTIVTHUSHTRHTRHSQGQQGPPGPOGOOINNKNMMLMNJLPIL\ RGKSEJUDJVBIW9HW8HX6GY4GY3FZ4KZ5PZ6UZ7ZZ8cZ9hZAmZB\ rZBvZCzZDzZEzZFzZGz_Hz_Iz_Jz_Jz_Kz_Lz_Mz_Nz_Oz_P9_\ Q8_R8_R8_S8_T7`U7`V7`W7`X6`Y6`Z6wZ5w_5w`5wa5wb4wc4\ wd4we5wf4we4we4we4we4we4we4wemwzmwzmwzmwzmwzmwzmwz\ mwzmwzmwzmwzmwzmwzmwzmwzmwzmzzmzzmzzmzzmzzmzzmzzmz\ zmzzmzzmzzmzzmzzmzzmzzmzz } frm:SliceJulibrot5 {; draws slices of (-Z)^n 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=========================================

6 5

FOTD 17-01-08 (The Tenth Valley [5])
by Jim Muth 17 Jan '08

17 Jan '08

FOTD -- January 17, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today brings another trip to a Seahorse Valley, this time to one of the 9 Seahorse Valleys of the (-Z)^10+C Mandeloid. The valley I chose is naturally the one centered on the negative X-axis, which is by far the easiest to work with. Another new formula was required to do the job, so another new formula was created. The formula is included at the bottom of today's parameter file. It does the same job as the 'More Slices' formula, but can calculate any power of negative-Z. I chose (-Z) instead of (+Z) because the fractals created when it is raised to powers between 1 and 2 are far more interesting, and the images drawn by the integer powers of (-Z) are identical to those drawn by the customary (+Z). In today's image I chose a near-Julia set of a Seahorse Valley of the (-Z)^10+C Mandeloid. A grossly magnified but reasonably undistorted image of the valley fills the inside of the order-10 Julia set. I named the image "The Tenth Valley" for obvious reasons. Then I rated the whole thing at a rather boring 5. I really cannot find too much to get excited about in the image. The calculation time of 6-1/2 minutes does border on the tire- some side. But perhaps the best news of the day is that the finished image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A fairly typical midwinter day prevailed here at Fractal Central on Wednesday, with a temperature of 36F 2C and partial sunshine. The fractal cats, who remained in bad moods, paid no attention to the outside conditions. My day was a little busy but still under control. The next trip to a seahorse-type valley will appear in 24 hours. Until then, take care, and live a life of fractal joy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Tenth_Valley { ; time=0:06:37.28-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=t center-mag=0.2845/0/0.93 params=10/0/1.5e-005/0/-0.851698/0.00144/-0.2845/0 float=y maxiter=5200 inside=0 outside=tdis logmap=yes periodicity=10 colors=000XEZskFrgGrcIr_JqWKqSLqONpKOpGPpCQp8RoCSn\ FSnISmLSmOSlRTlUTkYTUdGUYGQRGKHGGUKO_NWeRckUkqXmnU\ olRqjOsgLueIwcFxaDYaM7aU8`U9`UA`UB`UC`UD`UD`UH_GK_\ 3S`C_aLgbUocbwcjsalo_mkYngWocUq_SrWQsSPtWkbViZVgVU\ fRUdNTcJTaFT`CVlWWwn`qhdlbhfXmaRqWLuRFyM9oRIeVRX_Z\ NcgEgoAjf7lY4nP5iS6eU7`W7XYDZUJ`QPaMVcI`eEffAbgGZg\ MVhRShXOhbkFclOXnXRoeKpmERZD1LCAMGJNJSOM`OQiPTrQWz\ QZrOWkMUdKSYIPRGNKFLJRTIa_HlgHwnCiW7XECOUHGhOOaVWW\ acQhkKosEvbsdTmOKh7Bc6G`5KY5PW4TT4YR3aO3eMBm_JulQm\ kWekaYkgQjmIjsBjOr6ThHX_SaQbeHmdJlcKlbMlaNl`Ok_QkZ\ RkYSkZRi_Rh_Rg`Re`RdaQcWXDTcDSfEShESkFRmFRpGRrGRtG\ WqE_oCdlAhj80nC69hJKdWU`hdXtnUuiRvePw`NwXLxSJyOHzJ\ FzFDmb_cYZUUYKPYALX0HXlNfoRarVXuZSwaNk`L`_KPZIEYH3\ YGDRRMKaVDlYCk_CibBheAgg9ej8dl8ceKb_WbTgaNraLnbKjb\ JgbIcbH`bGXbFUbEQbDNbCJbBGbACb99b85b72b84V86O88H8A\ A8C37D77DB7DF7DJ7DN7DR7DV } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================

1 0

FOTD 15-01-08 (Festive Julia Set [7.5])
by Jim Muth 14 Jan '08

14 Jan '08

FOTD -- January 15, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Who knows what absurdities lurk in the heart of Seahorse Valley? (No one but The Shadow knows, and I don't see him around here!) I certainly never expected anything like the indescribable mass that fills the almost-Julia set of Seahorse Valley in today's image. The image is centered at the same point as yesterday's image, though the orientation of the slice, as well as the generating formula, is totally different. I named the image "Festive Julia Set" and rated it at a 7-1/2. Actually, the extra half-point is a bit liberal, since the color palette came about through the efforts of the Fractint program- mer who decided that striking the 'enter' key while in color cycling mode would create a totally new and random palette. One quick click produced the colors. The orientation of today's slice is rotated 0.01 of one degree toward a 90-degree rotation of the Mandelbrot set. This is a very small rotation indeed, but small rotations produce big changes this close to the Julia direction. There is nothing unusual about the calculation time, which at 2-3/4 minutes is close to the FOTD average. But as always, the most convenient way to see the image is to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The forecasted snowfall failed to materialize here at Fractal Central on Monday, not that the fractal cats were bothered by the busted forecast. But the cloudy day with occasional light rain and a temperature of 43F 6C, kept things still a bit on the unpleasant side. My day was busy enough to keep boredom at bay. The next FOTD in the Seahorse Valley series will appear in 24 hours. Until then, take care, and keep alert. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Festive_Julia_Set { ; time=0:02:43.51-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 center-mag=0/0/0.87 params=89.99/89.99/89.99/90/-0.7500101/0.004/0/0 float=y maxiter=250000 inside=0 periodicity=10 colors=000JGl5HjJOjWUjeWjkXgpYcsVYrSSqOMqKGpIMpHSp\ GYsFbvLTyPKzSBtO9iJ7ZD5R63A01Y6c_8g`AkbCncDqeFtfHw\ hJxiKy5K58JCBJIEIPHIVKHaNHgQGnSGtOmYNgTMaOLWJKQFJK\ AIE5Y4iidOVOCXjhUc`RYUPRNMLFJE8FzTGsPGlMGeIGZFHSBH\ L8HE4N87L85K84I828KfAI_BGTDEMECFGA8sSokOdcKVWGLOCB\ pB6kA5gA4b94Z93U92Q82L81UU26lg9aXCSMFIBAuSDdJFOAdw\ oaphZjbWcWTYQQRKNLDKE75mua4HbwrZniVe`SYSOPJKGANEvL\ CjKBZJAOI9C9kICYCFL6GM6HK5HI4HG3HE3HC2HA1ZwOQYCjfT\ 9QiDHNDBaEAXEASF9OF9JG9EG8AH85MNHKJDJF9IB5W7BT89Q8\ 7N85K83zTgcIMytnpjdg`VZRLQHBC3cF6KDmNEdIFXEGO9HG5u\ fNn`JgVF`PCUJ8ND4O2DM4AK57I743_GAphCh`DaUEUNFNFGF8\ KLcJIXJGRIEKICEHA7OffM_YLTQJMHIF9WgWUbSSZOQUKOQGML\ CKH8IC4DcDFO7eWn`SeXOYTKQPGHLC9zpJtjGndEh_CcUAYO7S\ J5MD3bfCg90MUc3nG8_BDM6ofTfYMYPFPG8HMJHJFHGBHD8HA4\ _68W76T75Q74N83K82HZiHVbHRXHNQHJKHFDHB7n6bg7V`7NU8\ GN88z`ClY9bR6TO3UK8FDHYFn } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

1 0