January 2008 - Fractint - mailman.xmission.com

FOTD 31-01-08 (Seahorse Asymptote [7])
by Jim Muth 31 Jan '08

31 Jan '08

FOTD -- January 31, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today is the last day of January, and the last day of the theme of January -- scenes in Seahorse Valley. The tour has taken us far afield, even into spaces of 8 dimensions to explore Hyper- Seahorse Valley. Today's image focuses on a point very near the point where the classic valley's two branches would reach the X-axis if they were calculated to infinity. I named the image "Seahorse Asymptote", a name that makes it look like I know what I'm talking about when I discuss fractal mathematics. Then I gave it a rating of a 7, a rather generic rating which means that, even though I can find nothing excep- tional in the image, I am not disappointed by it either. It is immediately apparent that HyperSeahorse Valley is a far more complex thing than classic Seahorse Valley. The hyper version of the valley has networks of arms spanning the empty spaces between major elements that are far more intricate than those in the more familiar valley. Today's image is but a small example of the intricacy lurking in the HyperSeahorse Valley. It is also apparent that the image is actually a perturbed one. Since the HyperMandelbrot set is 4-dimensional, the hyper-mini- brots within it must be 4-dimensional also. And I assume they are oriented in any possible direction within the 4-D Mandelbrot set, just as the classic minibrots are oriented in all possible directions in the classic 2-D M-set. But who knows what variety of perturbed slices this means are possible. The theme for February will be HyperEast Valley of the Hyper M-set. I will not refer to it as HyperElephant Valley, since elephants are already hyper enough without expletives added. I expect quite a few strange and perhaps entirely new things to show up on the eastern fringes of the main hyperbay. The calculation time of today's image is 6-1/2 minutes. This time may be cut by 1/3 by using one of the faster calculating algorithms, but when this is done, there is always a chance that some of the finer detail will be missed. Considering all of the above, the best way to see the complete scene intact is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is or soon will be posted for instant gratification. Overnight rain ended at daybreak Wednesday here at Fractal Central, and the sky cleared by 9:00am, but the high winds of 50mph (80kph) that prevailed for the rest of the day made the temperature of 34F 1C feel far too chilly for comfort. The fractal cats agreed and rolled over on their shelf on top of the radiator. My day was fairly busy; tomorrow will likely be the same. The next FOTD will appear in 24 hours. Until then, take care, and be at one with the secular universe. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Asymptote { ; time=0:06:38.48-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.74371926345344550/0/3475050/1/-90/0 params=0/0/0/0/0.1/0/1.091e-005/0 maxiter=1800 float=y inside=0 periodicity=0 colors=000q`MqZMrXMrWMrUMrTMrRMrPMrOMrMMrKMrJMrHMq\ ELrGMrHNrIOrKOrLPrMQrORrPRrQSrSTrTTsUUsWVsXWsYWs_X\ s`YsaZscZsd_se`veZsf`qfaogbmgcjgdhhffhgdhhaii_ijYi\ kWjmTjnRjoPkpNkqLkrKiqKgqJfqJdpJbpIapI_pIYoHXoHVoG\ UoGSnGQnFPnFNnFMmENmENmENmENmENmENmENmEOmEPmEQmERm\ ESmESmESmESmESmESmESmESmERmEShETcDUdDUaDTaDVcDZd9c\ n9bn9an9`n9_n9Zn9Yn9Xn9WnEVnIUnLTnOSnQRnTRnWWmYVm`\ TmcSmeQmhPmkOmmOmlRlkTkkUjjWiiXhiYhhZgh_fg`efadfbc\ eccedbdeacf`cg_bhZbiZajY`kX`lW_mVCvh_nVYlTWjSUiQSg\ PQeNOdMNbLL`JJ_IHYGFWFDVDBTCASBDUAGVAJW9LX9OY9RZ8U\ `8Wa7Zb7ac7dd6fe6if5lh5oi5qj4tk4wl3zm3zn3xl6uk9qjB\ nhEkgGgfJdeLacOYbRVaTS_WOZYLY`IXbP_ZWbVbeSihOplFoj\ LniQmhVli`mg_mf_md_nc_na_n`_nZ_oY_oW_oV_oT_pSZpQZp\ PZqNZqMZqKZqJZrHZrGZrEZqB`rDZsEYtFWtHVuITvJSvLQwMP\ xNNxPMyQKzRJzTHzUGzVEzXDzYBzZAz_9zaAzbBzcCydCxeDvf\ EugEthFsiGrjGqkHolIqcMqaM } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 30-01-08 (Minibrot Madness [7])
by Jim Muth 30 Jan '08

30 Jan '08

FOTD -- January 30, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a scene somewhere in HyperSeahorse Valley. The area of near total chaos at the center of attraction is the remains of a perfectly normal M-set minibrot. (To see the true minibrot, reset all parameters to zero.) As I continue to experiment with the HyperMandelbrot2 formula, I am becoming more convinced that the images it draws are true slices of the 4-D HyperMandelbrot set, and not mere artifacts. In the true classic M-set version of today's image, there are 8 well-defined yellow-orangish elements surrounding the minibrot, while in today's version, there are 14. What has happened is that the original 8 elements have each split into two, but two of the split pairs overlap in such a manner that they both appear as a single broader element, giving the impression of only 14 elements in all. Inside the space that once was the original minibrot, much the same thing has happened, but the area is so chaotic that little sense can be made of it. I will continue to work with this formula for a while, trying to figure it out. The image is named "Minibrot Madness", which is a fair name for it. The rating of a 7 means that I think it is above average, though not exceptional. The calculation time of 2-1/2 minutes may be eliminated by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday began with freezing rain and icy pavements here at Fractal Central. But by midday the temperature rose above freezing, and the rest of the day brought just plain rain. The fractal cats enjoyed the view for a while, then went to sleep. My day was busy enough for satisfaction, but not too busy for a fractal. The next FOTD will appear in 24 hours. Until then, take care, and it was hard enough to think in four dimensions. Now we have eight dimensions to worry about. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Minibrot_Madness { ; time=0:02:34.26-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.748072864967/+0.071474507622/773813/\ 1/-5/0 params=0/0/0/0/0.08/0/1e-012/0 float=y maxiter=1200 inside=255 logmap=316 periodicity=0 colors=000P28P38P48P58P68P88P98PA8QB8RC8TD8WG9ZJA`\ LBaOBbSCcVDc_EccEdgFdlGdnGanLZlPXkTUiXSg`PfeNdiKbm\ IaqF_uDZyEYtFXoGWjGVfHUaITXISTJROKQJKPFLOAMN5MN1RM\ 4WL6_K8dJBiIDmJFnOEoSEpXEqaDrfCsiApfAmaAjXAgSAdNAZ\ PAZRAZUAZXAY_AYbAYdAYgAYj9Ym7Yp5Yr4Zs7Zs9_tC_tE_uG\ `uJ`vLavOawQawSbxVbxXbxZawaavcaue`tg`si`rk_qn_pp_o\ rZntZmvZlxRhqJdjBadBdXBgPBjHCeMDaQEXVFTZGPbHKgIGkJ\ BpK7tK3xM7uOBrQFoSJmTKmUKmUKmUKmUKmUKmUKmUKmUKmUKm\ UKmUKmUKmUKmUKmUHmUAmU4lW8jYCi_FgaJfcNdeQcgUaiY`k`\ _hb`edcbgm`jrYnvVqzTuzQzzNzzLzzOnmRicUdZWZYZUXaPWc\ KVdMWeNWfOWgQWhRWhSWiNQiJKiFFhGGgGHfGIeGIdGJdHKcHL\ bHLaHM`HN`HNYIRWJUUKYRL`PMdNNgKOkIPnGQrEQuFVpG_lHd\ hIicJn_KsWUxScvRmuQzsPzrOmpNcoMYmL_lKajJciIdgHffGh\ dFjcElaDm`DnZCoXBpVAqT9rR8sP7tN6uL5uK4rM3pN3nO3lQ3\ jR3gS3eU3cV3aW3_Y3XZ3V_3Ta3Rb3Pc3O_5OX7OU8ORAOOBOK\ DOHEWJ7YF7_B8a78c39e09JFS } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 27-01-08 (Steps on the Steppes [6.5])
by Jim Muth 29 Jan '08

29 Jan '08

FOTD -- January 27, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: I know that today's FOTD is late, but the wait was worth it. The image shows a scene on the northeast shore line of the large period-2 bud of the HyperMandelbrot set, which is just starting to undergo some very strange things. The result looks surpris- ingly like a scene on some alien planet, perhaps even a fractal planet. I named the image "Steps on the Steppes". The buds appear to recede into the distance in a very step-like manner. I rated the image at a 6-1/2, which includes an extra half-point for my coloring efforts. And why not? The coloring is 98 percent of the image. The calculation time of 9-1/2 minutes is somewhat slow, especi- ally for an image that rates only a 6.5 and is almost 12 hours late. The image will soon be posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But due to the lateness of the FOTD posting, Paul might not have a chance to post the finished image for several hours yet. So be patient and try later if the visit to the web site comes up blank. Some clouds, some sun, periods of light snow, and a temperature of 30F -1C mixed together here at Fractal Central on Saturday to produce a typical midwinter day. The fractal cats wasted most of the day sleeping, while I wasted most of the day pondering the meaning of fractals. Not surprisingly, I found no answer. But regardless, the next FOTD fractal will be posted in 24 hours. Until then, take care, and the meaning of fractals is most likely the same as the meaning of life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= StepsOnTheSteppes { ; time=0:09:27.06-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.8342207552006937/+0.187609876583259/\ 1376.26/1/41.5/0 params=0/0/0/0/0.0125/0/1e-011/0 float=y maxiter=3850 inside=255 logmap=-100 symmetry=none periodicity=0 colors=000EBREBREBRDBRDBSDBSDBSDBSDBSDBSDBSDBSDBTC\ BTCBTCBTCBTCBTCBTCBUCBUCBUCBUBCUBCUBCUBCVBCVBCVBCV\ BCVBCVACVACWACWACWACWACWACWACWACWACX9CX9CX9CX9CX9C\ X9CX9CY9CY9CY9CY8CY8CY8CY8CZ8CZ8CZ8CZ8CZ8CZ8CZ7C_7\ C_7C_7C_7C_7C_7C_7C_7C`7C`6C`6C`6C`6C`6C`6Ca6Ca6Ca\ 6Ca5Ca5Ca5Ca5Cb5Cb5Cb5Cb5Cb5Cb5Cb4Cc4Cc4Cc4Cc4Cc4C\ c4Cc4Cc4Cd4Cd3Cd3Cd3Cd3Cd3Cd3Ce3Ce3Ce3Ce3Ce2Ce2Ce2\ Cf2Cf2Cf2Cf2Cf2Cf2Cf2Cf3Dg3Dg3Dg4Dg4Dg4Dg4Dg5Dg5Eg\ 5Eg5Eg6Eg6Eg6Eg6Eg7Eg7Eh7Fh7Fh8Fh8Fh8Fh8Fh9Fh9Fh9F\ h9GhAGhAGhAGhAGhBGhBGiBGiBGiCHiCHiCHiCHiDHiDHiDHiD\ HiEHiEIiEIiEIiFIiFIiFIjGIjGIjGIjGJjHJjHJjHJjHJjIJj\ IJjIJjIJjJKjJKjJKjJKkKKkKKkKKkKKkLKkLLkLLkLLkMLkML\ kMLkMLkNLkNLkNMkNMlOMlOMlOMlOMlPMlPMlPMlPNlQNlQNlQ\ NlQNlzmczmczlczkczjcziczhczgczfczecydbxcawb`v__uYZ\ tXYsXXrWWqWVpVUoVTnUSmURlTQkTOjSMiSKhRIgRGfRFeREdR\ DcRCbRBaRA`RB_RCZRCYRDN00 } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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Re: FOTD polygons and artifacts
by JackOfTradeZ＠comcast.net 29 Jan '08

29 Jan '08

. The pentagon-heptagon FOTD is one of the most interesting and unique images I've seen in a long time. If you back out you see a triangle and then a couple squares - else all the polygons are odd numbered, and they increase in number of sides forever untill a circle is approximated. The "black hole" in the center appears to be like the "peanuts" seen in The Canyon (REAL= -0.75, IMAG=0). in that there is no minibrot or lake structure there, the black just shrinks if you up the iterations. I think it is an infinite tunnel, but the render times start getting rediculous. Same with FOTD Jan 24. The parent fractal is awesome - has the form of a normal Mandelbrot but looks weird at the boundary. Animation sequence is in progress - looking way cool so far. FOTD Jan 27 - looks like a planet surface. I did an animation sequence on this type a long time ago if NY1 interested: http://www.fractal-animation.net/vid/planet.zip 6 Meg file. Stay Amazed! JoTz .

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FOTD 29-01-08 (Strange New World [No Rating])
by Jim Muth 29 Jan '08

29 Jan '08

FOTD -- January 29, 2008 (No Rating) Fractal visionaries and enthusiasts: Another late FOTD. My excuse -- none. Today's image is named "Strange New World". The name implies that the coordinates of today's image lie well within the main bay of the Mandelbrot set. Strange things happen when four more dimensions are added. In today's case, new material has spontaneously appeared within the main bay, and today's image is a close-up sample of this new stuff, which is arranged in a semi-regular pattern. I could hardly give a rating to an image that I did no work at all on, but it's still worth a look. The image might not be worth the 21-2/3 minutes required to calculate it from the para- meter file, but it is certainly worth the minute or so it takes to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the finished image posted there. But give Paul a chance to post the image before visiting the site. Another typical midwinter day went unappreciated here at Fractal Central on Monday. The fractal cats did check the outside from their window shelf a couple times, but decided they would rather get into mischief. My day was close to average, though it turned a bit busy late in the afternoon. The next FOTD will be posted in about 14 hours. Until then, take care, and be any- thing but always right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Strange_New_World { ; time=0:21:39.48-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.6664694298/+0.3167989708/11522.57 params=0/0/0/0/0/0.3/1e-015/0 float=y maxiter=6000 inside=0 periodicity=0 colors=000k_YqVdvQjqUfmYcia_eeX`iTXmQTqMPtJNmHLfGJ\ `FHVEFRDUOCUMBUMAULAUM9UK9UL8UL8UM7UM7UM6UM6UL9UKB\ UIEUHGUFJUELUCOUBQU9TU8VU6YUL_UPaUSgQ_mOhsNlxLovJq\ uHotFlrDiqBgpJ2QK4RL5RM6RN8RO9ROARPCRQDRRESSGSSHST\ ISUKSVLSWMSWNSZPPaRNdTLgVJjXHmZFp`DsbBuc9t_QsXfv_d\ xabrXemShhOkcJnYEqTAtO5wJ1yK2qK3iK4aMG9CKA2OA9UEGZ\ IMcMThQ_mUerYTnOGjF3g6WQ9x8Cr8Jl8Pf8Va8`_AZZCXYEWX\ GUWHTVJRULPTNOSPMRQLSROTSQUTTUUVVVXWW_WXaXYcYZfZ_h\ Z`j_am`bo`cqZYjXTcVOXTJQREJP9CO46N58M69L7BL8CK9DJA\ FIBGICHHDJGEKGFLIJNJMPLPRMSTOVVPZXRaZSd`UgbVjdXnfY\ qh_tj`wlazn_wlZtjYqhXnfWleUicTfaSc_R`YQZXWbR`fLejF\ jn9imEilIhlMhkQgjUgjZfibfhfehjegnegrdfqdfqcfqceqce\ qbeqbdqadqadqadqx2mw5jv8huBetDcsG`rJZqLWpOUoRSnTPm\ WNlZKk`IjcFifDhhBdfFaeJZcNWbRT`VQ_YMYaJXeGViDUmASq\ 7RtKOpXMmiKjvIgmDYd9OW5EPEBIN8BV6GSALQEQOIVMM_KPdI\ TiGXnE`sCdxAglKXaTN`jLeeS } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 28-01-08 (Deep in the Depths [?])
by Jim Muth 28 Jan '08

28 Jan '08

FOTD -- January 28, 2008 (Rating ?) Fractal visionaries and enthusiasts: Today's 9-1/2 minute fractal is named "Deep in the Depths", a redundant name if ever there was one. It's actually a scene on the northeast shore line of the large period-2 bud of the HyperMandelbrot set. I gave it no rating because I have no idea how to rate the images in this new world of micro-parameters. The partly filled-in minibrot in today's image closely resembles the parent HyperMandelbrot set. In addition to the changes in the minibrot, the surrounding features have become infested with countless small holes, which do not exist at the same spots in the classic M-set. (To see the classic version of the scene, change all parameters to zero.) I have not yet investigated these holes very much, but they appear to be rather interesting. The parameter file calculates in 9-1/2 minutes. Those who would prefer instant fractal satisfaction can enjoy it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed GIF image is posted. An average day with an average temperature of 34F 1C and an average partly cloudy sky went un-noticed here at Fractal Central on Sunday. The fractal cats, Nicholas and Cassie, spent a good part of the day sitting in the sun in the southwest window. I spent some of the day doing nothing and some more in doing the day's fractal. The next FOTD will appear in 24 hours. Until then, take care, and be of good cheer when things look drear. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep_in_the_Depths { ; time=0:09:24.53-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=1 periodicity=0 center-mag=-0.8332758481765483/+0.187712892187422/\ 4.388e+010/1/172.5/0 params=0/0/0/0/0.01/0/7e-020/0 float=y maxiter=6200 inside=255 logmap=-1260 colors=000cgwcgwcgwcgwcgwcgwcgwcgwcgwcgwcgwcgwcgwc\ gwcgwcgucgtcgtcgtcgvchvcivcju`ksZlrWlrUmrRmrPmqMmq\ KoqHqqFsqHpmJmiLjfNhbPe_RbWT_TUYPWVMYSIbPFfNBhK8oH\ 4pF1mE5eD9bCDVBHSALP9PM8TJ7XG6`D5cFA_GEXIIUJMRLRNM\ VKOZHPbERgASkXUocVspTbuRMNP5XR7WS8WU9WVBWWCWYDWZFW\ `GVaHVbJVdKVeLVgNVhOViPVjSRkUOlWLmYIzzKzzLzmMwmNmc\ PcdQXfRUgSShUPiVNjWLkXQj6KmBEpG9rKSYRaTLkOGiNHhNHf\ MHeMHcLHbLHaKH_KHZJHXJHWIHUIHTHHSHHVJJXLL_NNaPPcRR\ fTThVVjXXmZZo``qabqb_qcYqdWqeTqfRqgPqhMqiKqjIqkGql\ DqmBqn9qo6qp4qq2qr0WZEBFSCHSDJSDLSEMSFOSFQSGSSHTSH\ VSIXSIYSJ_SKaSKcSLdSMfSMhSNjSOkSOmSPoSPpSMVWJ9ZLBX\ MDWOFUPHTRJRSLQUNOVPNXRLYSKZUJ`WHaYGc_EdaDkcBqeAxg\ 8zi7zj6zi5zi5zi5zh5zh5zh5zh5zg5vg5rg5mf5hf5hf5jf5f\ e5ce5ce5cd5cd5cd5Yd5Ub8MaA8`DB_FDZHGYKIXMLWONVRQUT\ STVVSYXR__QaaPddOffNhiMkkLmnKopNrsUtuUvpZjlc_ghOcm\ D_r2`v3`z3az4az4az4bz5UUc } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 26-01-08 (Pentagon Heptagon [8])
by Jim Muth 26 Jan '08

26 Jan '08

FOTD -- January 26, 2008 (Rating 8) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's image uses a new formula, which is simply yesterday's formula with initial 'b' generalized rather than set to 0,0. This might give a little more variety to the images it draws. I named the new formula HyperMandelbrot2. Today's image is named "Pentagon Heptagon" because of the very prominent pentagon. And there is also a heptagon, much smaller and closer to the center. And yes, the series of polygons with an odd number of sides does continue indefinitely. An outzoom will reveal a triangle, while a couple inzooms will reveal a nonagon, a hendecagon, and a tridecagon. (I think these are the right names for polygons of 9, 11 and 13 sides.) How far the series goes beyond this point is anybody's guess, but I suspect that, like so much else in the world of fractals, it continues without limit. I have made no effort to figure out the number series of the arms stretching between the polygons, though it probably has a logical order. But at the same time, I see that the arms within the pentagon are unevenly distributed. Two of the pentagon vertexes have arms connecting with them from within, while the other three are cut off from the center. Today's coordinates define a blank area in the classic Mandel- brot set. If real(p3) and real(p4) are set to zero, the result is a flat black screen. The area actually lies somewhat inside the main bay of the M-set. Even though I have no idea how today's image ranks among Sea- horse Valley images of the HyperMandelbrot set, I have rated it at an 8. Its mathematical interest is enough to be worth at least that rating. The calculation time of 4-1/4 minutes is fast enough to keep impatience at bay. And if it is not, the finished image will soon be available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday was bright and sunny here at Fractal Central, but it was also cold and blustery, making it a rather unpleasant day to be outside. The high temperature of 27F -3C fely cold even in the strongest sun. With numerous sources of heat inside F.C., the fractal cats had their problem deciding where to spend the day. I had no such problem however. I spent the day working, then searching for a FOTD. As today's image shows, I was successful. And the next FOTD image will be posted in 24 hours. Until then, take care, and where's it at? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pentagon-Heptagon { ; time=0:04:14.05-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=t center-mag=-0.749480813398176/+0.031703452082799/\ 3.321327e+010/1/89/0 params=0/0/0/0/0.2/0/1e-020/0 float=y maxiter=3600 inside=0 periodicity=0 colors=000mL6lM9lNBlODlPFlQIlRKlSMlTOlURlVTlWVlXXk\ `_lYZmWYnUXnSXoQWpOVpMVqKUrITtCTrGTqJToMTnPTlSTkVT\ iYTh`TfcTjcYecT`cPXcKScGNcBMc4Jc7HcAEcCCcF9cI7cK4d\ N2cQ0cSgcaXcZKcVNcXQcZSc`VcbYcc_cebdgefigikjklmnno\ pzrszuuzzzzvtzvrzupvunrtkmtihsgcse`sbYr`VrZTqXQqUN\ pSLpQIpOGrJPsFYuBev7nt9Bw3vu4ss5pq6mo7jm8gk9di9agA\ ZeBWcCTaDQ_ENa7GZEKWKOURSRXWzz_zzczzfzzbzzZzzVzzRz\ zOifKndGrcCva8z`5tb6oc7ie8df9ZhAUiBOkCJlDDnE8oEAnF\ CmFEmGGlGIlHKkHMkIOjIUiJZiJchKhhKmgLrgLvkMwkMwlRwq\ NwrJwwGwxCws8wt6vt5rp4mp3hq7cmAZmKUnUPmcKmmFlvAnz5\ oz3pz3qz4lz4gm4bc5ZZ5UZ6UY6dY7dY7dY5sa7nY9jVBfRDaO\ FYKDUFGUHJUILUKOULQUNTUOVUQYUR_UTbUUdUWgUXiUYkRalO\ dnLgoJjlMeiOagRYdTUaWP_YLX`HUbDPb8Sd9VeAXgB_hCbiDd\ kEglFjmBimFijIhgLhcOg`RgYVfUYfR`eOceKfdHjdEmcApc7s\ c4va5r`5o_6kY6hX6dW7aV7YT7VS8RR8OV4RQ8LLBGGFA8H2CI\ 5GI8KIBNJERJHVJKZJNaKQeKT } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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Image artifacts due to precision problems
by Hal Lane 25 Jan '08

25 Jan '08

************************************************* Jim Muth in his "FOTD -- January 24, 2008" text says: >some of the images appear so unlikely that I >cannot shake the impression that they are >artifacts of mathematical imprecision rather >than true fractals. My question is: Can one determine if a fractal's features are precision problem artifacts by computing the fractal twice -- with two different values of the number of arbitrary precision digits -- and then comparing the two images? <---<< My hypothesis is that if you compare the two images calculated in the above manner and they are the same, then problems of precision are not the cause of a fractal's unusual features. Is this the case? <---<< If this method does correctly determine whether an image has artifacts or not, is adding the following items to an image's parameter file a valid way to exactly set the number of digits of precision used in a calculation? 1st image calc: --------------- MATHTOLERANCE=-1/-1 BFDIGITS=14 2nd image calc: --------------- MATHTOLERANCE=-1/-1 BFDIGITS=15 I cannot find the email sent to me that tells how to compare two images. Here is what appears to work -- please correct me if I am wrong: To compare two images that are in files: - Run FRACTINT *without* the command line parameter debug=50 - Load the first image from its file using <r> - Type <g> and then: debug=50 - Load the second image from its file. (Note that the File List selection page title is now: "Select File for 3D Overlay") - The image on the screen is the difference between the two images. Identical pixels in the two images are shown as color zero. Different pixels are shown as non-zero. - If this 'difference image' has any non-zero pixels the two images are different. Is the above procedure to compare two images in files correct? <---<< It appears that the color map of the images is used to display the difference pixels. If there are extremely dim color map values in the image one could be fooled into thinking that there were no differences between two images when in fact there were if the difference pixels that were displayed happened to use dim color map values. If this is a problem for a particular image one could get around it by loading a garish color map, say, a color map of 15 bright colors and black like: GOODEGA.MAP This makes all non-zero pixels be easily visible against a black background. I calculated a default Mandelbrot image at 640 x 480 using both the default integer math and then putting float=yes in my SSTOOLS.INI file. (I had forgotten to do this when installing FRACTINT onto my recent computer.) I was surprised to see a significant number of differences between the integer and float images. I constructed a color map that would allow me to see the difference image pixel values as follows: 0 0 0 This file shows the pixel values 127 0 0 1-6 as distinct recognizable 255 0 0 colors. All other pixel values are 0 127 0 dim gray, except for pixel value 0 255 0 zero which is black. 0 0 255 - HHL 1/24/08 0 0 127 64 64 64 64 64 64 64 64 64 . . . 64 64 64 The difference image showed a few dozen pixels with values of 1 - 6 and a few hundred dim gray pixel values with values somewhere in the range of 7 - 255. All other pixels were black. Is it likely that I did this comparison and analysis incorrectly, or is this difference between integer and float expected? <---<< Does anyone know if the pixel values of the difference image represent the absolute value of the difference between the pixel values of the two compared images as I am conjecturing they do? <---<< Also, am I correct in assuming that arbitrary precision works for formula file fractals? <---<< - Hal Lane ######################### # hallane(a)earthlink.net # ######################### *************************************************

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Re: FOTD
by JackOfTradeZ＠comcast.net 25 Jan '08

25 Jan '08

. Jim Muth ponders: ""It seems very strange that a value as tiny as 0.00000000000000000000007 would produce such a big change in an everyday scene in Seahorse Valley"" Ever hear of "Chaos Theory" and "extreme sensitivity to initial conditions" ? <G> That's why fractals is way cool! .

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FOTD 25-01-08 (Goodbye Minibrot [?])
by Jim Muth 24 Jan '08

24 Jan '08

FOTD -- January 25, 2008 (Rating ?) Fractal visionaries and enthusiasts: When I first saw today's image, all I could say was 'wow'. I have never seen this happen to a minibrot before. But in the world of fractals, the unexpected can only be expected. The image shows what happens to midgets in the 4-dimensional HyperMandelbrot set when the view is skewed in some unimaginable direction. I named it "Goodbye Minibrot" in memory of the minibrot that once was there but now is gone, and leaves its outline to carry on. Actually, I have no idea what's happening in the image, but what- ever it is, it is quite curious. Nor do I know how or why the HyperMandelbrot formula works as it does. It seems very strange that a value as tiny as 0.00000000000000000000007 would produce such a big change in an everyday scene in Seahorse Valley. But the details in today's image are consistent with those in the Seahorse Valley Julia fractals created by the type=hypercomplexj formula, when the value of C is very critical. To see the original Seahorse Valley scene, change the real(p3) parameter in today's image to zero, then sit back and be filled with awe and wonder. Since I have no idea where to rank today's image in a world that is virtually unexplored, I could give it no rating. The whole thing is a mystery, as made evident by the question-mark rating. The calculation time of 3-1/3 minutes is well within reason, especially considering that the periodicity checking is turned off, as it must always be when using this formula. The simplest and most convenient way to see the image is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it there in solid comfort. Thursday was fair enough here at Fractal Central even though occasional heavy clouds and several snow showers spoiled the perfection. The high temperature of freezing was just about right for the coldest time of year. The fractal cats watched the big fluffy snowflakes for a half hour or so, then decided it was better to have a bit of fun by sitting on the work. After moving the sitting cats, I finished the day's real work with plenty time to look for fractals. The next FOTD, which will be a further exploration of the HyperMandelbrot set, will appear in 24 hours. Until then, take care, and reason it out. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Goodbye_Minibrot { ; time=0:03:19.54-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot passes=1 center-mag=-0.74984503749226/+0.03360828961391/\ 155571.8/1/92.5/0 params=0/0/0.2/0/7e-023/0 float=y maxiter=1200 inside=0 periodicity=0 sound=off colors=000bWFmR6cWFV`OMeXDje4nm5nl6nk7nj8nj8ni9nhA\ ngBngBnfCneDoeEpdFqcFsbGubHtaIs`Ir`JqbJpdJofJngJmi\ JlkJkmJjnJipJhrJgtJfuKevLdvMcvNbvNavO`vP_vQZvRYvRX\ vrZut`ewaRubQscPqdOoeNmfMkgLihKgiJejIckHalG`lGZmFX\ nEVoDTpCRqBPrANs9Lt8Ju7Hv6Gv6Ep5Cj5Bd49Z47T46N34H3\ 3C36D68D8BEADECFEFIFHKFJMFLPGORGQUHSWHUYHX`IZbI`dI\ bgJeiJglKinKkpKnsLpuLrwLtvKruJptIosHmrGkqFjpEhoDfn\ CemBclBakA`j9Zi8Xh7Wg6Uf5Se4Rd3Pc2Nb1La2M`3M_4MZ5M\ Y6MX7MW8NW9NXANYBNZCN`AL_CNZEOYGPXIQXJRWLSVNTUPVUQ\ WTSXSUYRWZQY_QZ`P`bObcNddNeeMgfLigKkhHnkKliNkhPifS\ heUgdXeb_daab_daZkWTf`YadaXieTmiOrmJvqFzuGyrHypHxn\ IxlJxjJwhKwfKvcLvaMv_MuYNuWNtUOtSQtQSsNUsLWrJYrH_r\ FaqDcqBes8gq9io9kn9ml9mk9ni9oh9pg9qg9rfArfApdAnbAk\ _AhXFeUKbRP_OUYMUWKUULUSLUQMUOMPMNKKNFINAGM6FM5EL5\ DL5BK4AK49J38J37J37K0HXGRiW_uk`oe`j`adVa_QaUKbPFbJ\ 9bE4aI8aLBaOEaRHaUKaXOa_R } 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=========================================

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