August 2006 - Fractint - mailman.xmission.com

FOTD 30-08-06 (Off on a Tangent [5])
by Jim Muth 30 Aug '06

30 Aug '06

FOTD -- August 30, 2006 (Rating 5) Fractal visionaries and enthusiasts: In today's image we check another midget of a very low order. The parent fractal is the Mandeloid that results when the expression Z^(1.1892)+C is calculated 49 turns down the logarithmic ladder. The central midget might be the last one for quite some time. I have a theme planned for the September FOTD's and midgets are not included. The rating of a 5 is all I could do for today's image, which mostly repeats things we have seen many times before. But one thing that has not been seen so many times is the huge discon- tinuity in the pattern surrounding the midget, one of the greatest I have yet seen. I named the image "Off on a Tangent". There is no logical reason for such a name. I simply felt like giving the image that name. The render time of 7 minutes is true on my 10-year-old fractal- dedicated P200 unit. On the current SOTA (State Of The Art) machines, the image will calculate in about 2 minutes. But some SOTA machines are over-qualified to run Fractint, which is still the world's best fractal generator. To avoid fractal frustra- tion, the owners of these handicapped units will need to down- load the finished GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A warm, muggy, lazy afternoon with a temperature of 86F 30C was interrupted by a heavy thunder-shower at 4pm. The new fractal cats went to the window long enough to see what all the outside commotion was about. Then they returned to their job of getting into trouble. My sister called from Old Fractal Central this morning to let me know that the old fractal cats, Thomas and Tippy, are in good health, and are doing the same things they did when we were there My day was slow, but in the evening we heard from a customer who informed us that he will send in a big job tomorrow morning. The rush might put tomorrow's FOTD in doubt, so be sure to check back here in 24 hours to see how it goes. Until tomorrow, or maybe the next day, take care, and life is the world's greatest mystery. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Off_on_a_Tangent { ; time=0:07:05.95--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 periodicity=10 center-mag=-2.75444535467781000/-0.095428023111382\ 43/3.412037e+009/1/-40/2.57163975737953465e-005 params=1.1892/0/-49/0 float=y maxiter=7500 inside=0 colors=000udJzdczfUvgKrm6qj8qhAqfCqdEqbFq`HqYJqWLq\ UNqSOqQQqOSqMUqJWqHXqFZqD`qBbq9dq7ep9goBhnDinEjmGk\ lImkKnkLojNpiPqyPuiQrURoDTpFRmHQjIPgKOdLMbNL_PKXQJ\ USIRTGPVFMWEJYDG_CD`ABb98c85e72f60h91iB1kD2lF2mH3o\ K3pM4qO4sQ5tS5uU6wX6xZ7z`7zb8zd8zg9zi9zkAzmAzoBzr6\ zq9zqBzqDzqGzqIzqKzqMzqPzqRyqTwqWvqYuq_sqarqdpqfoq\ hnqklqmkqopzymuujqqhmneijbef`acYY_WUXTQTQMPOIMLEIK\ 9DJAFJBGJCHJDIJEJJFKJFLJGMJHNJIOIJPIKQILRILSIMTINU\ IOVIPWIQXJMNIOTIQYISbIUgIWlIYqG`yI_vKZtMZrNYpPYnRX\ lSXjUWhWVeXVcZUa`U_aTYcTWeSUfSShUZjWdkYjvfXzoHznJz\ mLzlNzkOykQwjSuiTthVrhXpgYof_meakdbiddhcffbgdaibak\ a`l__nYZpXZqWIpWHoVCnVHnUFmUPlTOlTMkSLjSJjRIiRGhTG\ lSFjRFhREgQEeQDcPDbPC`OC_NCYNBWMBVMATLARL9YK9XK9dJ\ D_JGgIJeIMkF_zIUzKRzMNwOMkRKhTJfVIdXHb_F_aEYcDWWCU\ hARj9Pl8Nn7Lq5Is4GuYEvZDw2Ct2Dj2Ee2Fn2HpKFoLEoLDnM\ CmMBlNAlN9nQBoTDqWErZGtaH } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(p/(2*PI)) r=real(p2)-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 29-08-06 (They All Look the Same [NA])
by Jim Muth 29 Aug '06

29 Aug '06

FOTD -- August 29, 2006 (Not Rated) Fractal visionaries and enthusiasts: Today's harmless little scene appears in the Z^sqrt(sqrt(2))+C Mandeloid as it appears 59 levels up the complex logarithmic ladder. (The logarithmic ladder is explained below.) The scene is so harmless in fact that I did not bother giving it a rating. I did give it a name however. After not too much thought, I named it "They All Look the Same", which sounds a bit biased, but really is not. A quick glance at the image will reveal why I gave it that name. Indeed, all midgets in the Mandeloids with an exponent of Z between 1 and 2 do seem to look pretty much the same. They all resemble splashes, or starbursts as they are sometimes called. I spend countless hours searching, hoping that I will find a midget in this range that is truly different. So far I have had minimal success. The calculation time of today's parameter file is under 19 minutes on my machine. This is a bit slow for an image of such questionable worth. For relief, I recommend downloading the completed image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The 'complex logarithmic ladder' is a phrase I invented. I sometimes refer to the same thing by the name 'logarithmic hyperspiral'. Neither phrase will be found on the internet. I invented the phrases because the complex logarithmic function is multi-valued, and can have an infinity of solutions. Each solution gives a unique four-dimensional julibrot fractal, complete with both Mandelbrot and Julia slices. In my mind, I simply stacked these four-dimensional fractals onto one another until they formed a single many-layered hyper-object of 5 or so dimensions. It is the stack of all the julibrot fractals possible to create with a single exponent of Z that I call the logarithmic ladder. Today's parent fractal for example exists on the 59th level of this ladder. The ladder could perhaps be more conveniently thought of as the 59th floor of an infinitely tall skyscraper. In the MandelbrotBC2 formula, the p1 parameter determines the exponent of Z, while the p2 parameter determines the level of the ladder we wish to explore. Cloudy and muggy but dry weather prevailed here at New Fractal Central on Monday. The fractal cats seemed not to notice. They were too busy chasing each other up and down the hallway. The big event of their day came when I opened a bottle of soda. When Nico heard the hiss of the escaping gas, he hissed back at it. Cassie watched Nico make a fool of himself. The next FOTD is due in 24 hours. If all goes well, it will appear on schedule. Until then, take care, and mysteries just happen. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheyAllLookTheSame { ; time=0:18:51.96--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.13962249185463330/-0.000766113336763\ 77/5.149203e+007 params=1.1892/0/59/0 float=y maxiter=25000 inside=0 outside=tdis periodicity=10 colors=0000Gz0Gz0Gz0Gz0Hz0Hz0Hz0Hz0Jz0Jz0Jz0Jz0Jz0\ Lz0Lz0Lz0Lz0Nz0Nz0Nz0Nz0Pz0Pz0Pz0Pz0Nz0Pz4RzARzETz\ JVzNVzTXzXXxbVxeVxkVxoTxuTxxTxzRxuRsmRmeRg`PbTNXLN\ TEJN8HH0HC0J60L00L00N00U00V00W00X00Y00Z02_06`08a0C\ b0Ec0Hd2Ji2Nm2Pq2Tu2Vv2JuAAqH0oN0bV0Td0R`0RZ0PX0PV\ 0NR0NP0LN0LL0JH0JG0HE0HC0H80G60G40E20E00C02C04A04A\ 0680880A608806A04C04C02E00G00G00H00J00J20L40N60N80\ PA0RE0zG0TH0VJ0XL0XN0ZP0`T0`V0bX0dZ0d`0eb0gd0ge8uJ\ ez0gz2iz6kxAmvEmuGosJqoNsmRskVuiXvg`xedxbgz`kzZmzX\ qzVuzTxzPzfNzzLzzkzzHzzGzzkzzgzzEzzEzzEzzEzzEzxEzv\ EzuCzqCzoCzkCxiCueCsdCq`CoZAmzAkTAgRAezAdLAbHA`GAZ\ EAXzC`LEbPGeRGgTEeTEdzEdTEbTEbTE`TE`TEZTEXTEXTEVTE\ VTETTETTERTEPTEPTENTENTELTELTEJL0LTEJVdC`gHdkNgoRm\ sXqvbuzexzkzzqzzuzzzzzzzzvzzqzzizxdzsXzoRziJzeEudX\ kbo``zR`zTbzTdzVezVezXzzXizXizZkzZmz`ox`ovbqubsqbs\ odumdziexgexe0Ez0Ez0Ez0Ez } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(p/(2*PI)) r=real(p2)-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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I am not familiar with the term 'logarithmic ladder'...
by Hal Lane 28 Aug '06

28 Aug '06

Jim, In your FOTD -- August 28, 2006, Anatomy of a Midget you say "I calculated the Z^sqrt(2)+C Mandeloid as it appears 414 levels down the logarithmic ladder..." I am not familiar with the term 'logarithmic ladder' and would like to understand what it means and how it applies in the context of calculating fractal images. If you have previously explained or given a reference to this, would you please point me to it? Google was not helpful to me in this instance. Thanks! - Hal Lane ######################### # hallane(a)earthlink.net # ######################### -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.405 / Virus Database: 268.11.6/428 - Release Date: 8/25/06

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FOTD 28-08-06 (Anatomy of a Midget [8])
by Jim Muth 28 Aug '06

28 Aug '06

FOTD -- August 28, 2006 (Rating 8) Fractal visionaries and enthusiasts: I have always wondered what a midget in the Z^sqrt(2)+C fractal looks like up close and personal. Today I decided to find out. I calculated the Z^sqrt(2)+C Mandeloid as it appears 414 levels down the logarithmic ladder, and found the smallest midget I could that was within range of resolution. I set the maxiter at a very high 50000 and let the image rip. The unusually high maxiter is necessary to show all the detail in the more chaotic areas surrounding the main bay. Surprisingly, or perhaps not so surprisingly, the midget mirrors the appearance of its parent fractal. The sharp, jagged elements radiating from the midget have divided and sub-divided until they have lost definition. I would like to more closely examine the chaotic areas of the image, but sadly, these lie beyond resolution. I named the image "Anatomy of a Midget". After all, the picture is basically a study of a midget. I rated it at an 8, perhaps a bit high but not beyond reason. The render time of 27-1/2 minutes is true when the parameter file is run on my fastest machine, a P4-2300, with the passes set to 1. On my usual P200 unit, the image takes about 1/1-2 hours, not nearly the 11-1/2 times as long as might be expected. All this concern about render times may be avoided by download- ing the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy rain fell all day Sunday here at New Fractal Central on the banks of the Susquehanna River in Central Pennsylvania. By the time the day ended, near 4 inches, that is 10cm, of rain had fallen, causing some flooding of small streams and streets. The fractal cats stopped chasing each other long enough to glance out the window once or twice to watch the rain. But they are not outside cats, and they don't worry about wet weather. My day started slow and finished slow. The next FOTD will appear in 24 hours. Until then, take care, and what is more unreal, a dream or a fractal? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AnatomyOf_A_Midget { ; time=0:27:30.35-SF5 on P4-2300 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 inside=0 center-mag=-0.35216497790502230/+0.096774058667879\ 18/2.68731e+011/1/117.5/-0.000214201607454139742 params=1.4142/0/-414/0 float=y maxiter=50000 logmap=650 periodicity=10 mathtolerance=0.05/1 colors=000kwUlvSmuQnsNorLpqJqoGrnEsmCokDljDhhDegDb\ eDZdDWbDSaDP_DMZDIXDFWDBUD8TD5SDFWGOZIYbLfeNohPmeN\ kcMiaKh_JfYIdWGbUFaSE_PCYNBWL9VJ8TH7RF5PD4OB3SDDVF\ NZGXaIfdJpZZeTmVSnXRnZRn_QoaPobPodOoeNpgNpiMpjLqlL\ qmKqoKqpOmlRiiUffXbb`__cWXfTTiPQlMNjLPiKRgJTfJVdIX\ cHZaG``GbZFdYEfWDhVDjTClSBnQApPArREoTHlULiWOfYScZV\ ``ZYbaVceSehPglMhoJjsGkvEnoOqhXtafwVozPxlYp_fiddbh\ cXlaRq`LuZFyY9`XBsbCpeDngEkjFhlGfnHclGakFksFYiEVhE\ TgDRTCPXCMXBKbBIaAG`AKbEOdHReKVgNZiQajUelXin_lobpq\ esrhpofnmdkjbih`ffZdcXaaV__TXXRVVPSSNQQLNOJLLHIJFG\ HEEPCCXABc99k78r6AnCCkHDhMFdRGaWIZ`JVeLSjMPoi0gfJi\ dakbtm`tYZtIYt3_kA`cHaWObOV_QSYRQWSOUTMSUJQVHOWFMX\ DKYBJXFJXIJWMIWPIVTIVWIU_HUbHTfHTiHSmGSpGRtGRwGRzG\ UyGWxGYxG_wGawGcvGewGgxGiyGkzGmzGozGqzGszPnzXizedz\ m_zuVzW0zX2zX4zX6zX8zYAzYCzYEzYGzYIz_LzaOzcQzdTzfV\ zhYzi_zkbzmezngzpjzrlzjyz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(p/(2*PI)) r=real(p2)-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 27-08-06 (Imperfect Perfection [7])
by Jim Muth 27 Aug '06

27 Aug '06

FOTD -- August 27, 2006 (Rating 7) Fractal visionaries and enthusiasts: Today's FOTD image takes us to the Z^1.95+C Mandeloid as it appears at ground level of the logarithmic ladder. At this level the parent fractal resembles a chopped-up Mandelbrot set. Today's scene is located in the East Valley area of its parent. It's an unusually attractive image for a fractal with an exponent of Z less than 2. The 'passes=b' option works quite well with today's image, and it is by far the fastest. I named the image "Imperfect Perfection" and rated it at a 7. The rating could have been a 7 or an 8. Being in a conservative mood, I decided on the rating of 7. The 6-1/2 minute render time may be avoided by downloading the completed GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds and a temperature of 73F 23C kept the sun worship- pers indoors here at New Fractal Central on Saturday. It stayed dry however, making conditions perfect for checking one of the local antique emporiums, which, with a little coaxing from fractal lady, is what I spent the afternoon doing. The fractal cats spent the day looking for trouble. Nico worried himself silly trying to get into the basement, but the basement still needs to be cleaned before he will be permitted to explore it. The work is still slow, which means there should be no trouble finding and preparing the next FOTD, due to appear in 24 hours. Until then, take care, look for the bright side and be enlight- ened. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ImperfectPerfecton { ; time=0:06:25.24--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=b center-mag=+0.26576286572368590/+0.007295698873062\ 91/5.409258e+009/1/-77.5/7.83611996738736716e-006 params=1.95/0/0/0 float=y maxiter=2000 inside=001 logmap=264 periodicity=10 colors=000000XRKQKKJEKGGKDHKAIK7JL9NMAQNCTODWQE_TG\ bVHeYIh_HcWG_TFVPERMDMJCIFBDCB99GGGLMMPTSUZYZddbkj\ gqpkwvgrqcmm`iiXdeT_`QWXMRTJNPKIQKERKARK6SK2SKJ7XF\ LiBYu8jsDlrHnpMpoQqiNadLN_J8HPmFNmDLmCJmAHm9FmBKkC\ OiDTgEXeFacGghcu_crZHlWGdTFXQERNEMKJLVNKdME_L9WL4S\ Q5NV6J_7Ed8Ah86kDBmKGoQKqWPsYVuZ_w`dxbiycnzcs`_YTZ\ WKXTCWQ4VOLYN``NRMLI8JDSN8jQ7gP6eP5cP4`O3ZO2XO1VOA\ QLJMISHF_DDh8Aq47y05u27q38m5Ai6Be8Da9EbECcJBdOAeT9\ fY7gb6hg5xk4w0AjBGZMLNXRBfWe2nd8gcE`bJUaPNaUHYXNU_\ TRbZNdcKgiGjoDltXPap1JY7HGDGmE59_kGZfNYaUXX`WTgVOn\ UJuTFnUJhUNaVRWVVQVZUXWYZUa`SebQidOmfMptKleKiUKfNK\ bFK_8KX1KT3NP5PM7RI8UFAWBCY8D_g2he7fcBdbFb`J`ZOZYS\ XWWVV_USdPPhKMmEJr9Gv4HnHHgTH`dHUpGZoFbnEfmDklCokB\ sjFknIhrLmuYmhimW1nX3qW4tV5wU6zT7zS8zR9zQAzQPzYcze\ rzmlzffz`mzVrzOvzIzzCzzDzzEzzFzzGzzHzzWzzizzwzzqzz\ lzzgzzbzzYzzTzzOzzJzzQzzf } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(p/(2*PI)) r=real(p2)-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 26-08-06 (Total Reality [7])
by Jim Muth 26 Aug '06

26 Aug '06

FOTD -- August 26, 2006 (Rating 7) Fractal visionaries and enthusiasts: I see in the news that the planet Pluto has been demoted to the ignominious status of a dwarf. This means that what I learned in school is no longer valid. There are no longer nine planets in the solar system, but only eight. I should not be too upset about learning the wrong thing however. I also recall being taught that Piltdown Man was the missing link, and the solar system is a unique thing which formed when the gravity of a passing star pulled blobs of material from the body of the sun. I'm not sure what the astrologers, who need Pluto to make their charts work, will do now that they have lost one of their planets. Maybe I'll check the internet to see what they make of it. My own view is that we might have lost a planet, but we have gained the world of fractals. Today's image would have remained forever undiscovered if I had not calculated the fractal that results when Z^(1.1) is subtrac- ted from Z^(-1.1) and (C) is added. The odds of this particular scene ever seeing the light of day are infinitesimal, yet here it is -- today's FOTD. How could such an unlikely thing possibly have come to pass? The answer of course is that there are an infinity of almost- impossible things that can happen in the world of fractals. And unless I am mistaken, which I often am, infinity multiplied by an infinitesimal equals unity. Today's image rates a 7, and it is worth it. The scene was rendered in the traditional manner, with outside=iter and inside=0. The unusually decorative effect is a natural part of the scene, not a result of program trickery. I named the image "Total Reality" because it is totally real. The render time of the included parameter file is just over 4 minutes, but the wait may be avoided by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and downloading the completed GIF image from there. The temperature on Friday reached only 82F 28C, but the day was a bit too humid for perfection. The fractal cats didn't mind however. Their big excitement came when Nico leaped onto the table and knocked over a lamp. We forgave him. After all, it's a cat's duty to get into trouble. The day ended peacefully with tuna and cheese in the cats' food dishes. My day was reasonably relaxing. The work was finished before noon, leaving me with nothing to do in the afternoon but search for fractals. With only a few exceptions, nothing in the world is more interesting than searching for fractals. The next FOTD will appear in 24 hours. Until then, take care, and for your answers, look beneath the surface. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Total_Reality { ; time=0:04:11.42--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.72855285500812400/-1.644842873009020\ 00/1039023/1/152.5/-1.05321999605001437e-006 params=1/-1.1/-1/1.1/0/0 float=y maxiter=750 inside=0 logmap=73 periodicity=10 colors=00058d35R12DM4BA27513lVM_NGOFBC75fa1yA6V53h\ OKMCAOX`GMOe`CAVBmcW29GMmUBMF8w`wQmzjAi0fY0AH05X7f\ O5WG3L81AGrpCdb8RQYTSKe`7riBkkFelJZmMTn_oaRbSIQJ9D\ 9vHgbBTJ5EvGvbAbJ5Jn5VP2FsfS`SIIE9ju0Va0FJ0uIyhJh5\ wR2UDuXopBvsdNeUHSKBEA5DDc0ekq93_62I31qh0cX0RM0DB0\ XNCMF8B74zZXVHGJs7Ee59S34E1YxdHUKQ0FDSf8IS49EaxF81\ cElb9WQ4GDA1_50I0Cm08X04GxAZh7QU5HF28CkuUhEKU9AF4c\ 2GLc3EQ27D1EsFAeB7S73E3d79K34Dw7VzjFVNsEB3PH4kj3_Z\ 2ON1CBPY5IP3CH2681BS`l`n_RaOIPC9Ct2De19S16E03deGKL\ 8U9WP06gWFOE0PF3GA28511eY0LHdO3RG2D816v_4bO2JCcMFU\ GBKB7A532_P1RI1IC096xjEhZAUN7FB3ZiUHUFrUu_UaIUJ3Ui\ 1UNkw_OTIdUXUUOKUGAU8ccbUUTKUJAU9jbFNU7xt2ca1KU0Ia\ ZDUQ9UH4U8DrQ8_H4U8gUBTU7EU38WZ6YQ4_H2a8HcPBeG5h8T\ koOn9Cq4RtwIwc9zK9zh6zX4zM2zBzzdzzUzzKzzAzz4zzjzzr\ zzRzzuzzzzz7zz5zz3zz1zzozzdzzUzzKzzAzz0zz0zz0zzjzz\ VzzFzz0zz0Ez07z0izrNzRnz6 } frm:MandelbrotMix4 {; 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, 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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FOTD 25-08-06 (Sub-Atomic Mystery [7])
by Jim Muth 25 Aug '06

25 Aug '06

FOTD -- August 25, 2006 (Rating 7) Fractal visionaries and enthusiasts: I checked the electron spin web page earlier today and found a reasonable explanation of what is known about the topic, which apparently is not too much. One thing for certain is that electron spin is far different than the spin of a toy top or the earth on its axis. All we really know is that electrons, what- ever they are, are involved in some kind of abstract action, which we have arbitrarily named spin. I saw mentioned somewhere that this mysterious spin might in- volve higher dimensions. I wonder about this myself. In a higher dimension as near as the fourth, there is an entirely new kind of motion known as double rotation. An object subject to double rotation must undergo any number of 360-degree turns before it returns to its starting position. The points of an object under double rotation generally trace the surface of a four-dimensional donut. But if both rotations are equal, all points except the point at the center trace circles. In dimen- sions higher than the fourth, even stranger motions are possible. In the last book I read, space, down at the level of superstrings and supermembranes, is supposed to have 11 or so dimensions, allowing for a mind-boggling variety of motions. Maybe this has something to do with electron spin. But deep inside, I feel we are missing something of immense profundity, which is staring us in the face. We are like deep sea fish who don't recognize the existence of water. The quantum world is just too strange, too alien to be a part of the intuitive reality we observe and assume exists around us. The realities conflict. I feel that something is not as real as we take it to be. What all this means is open to debate. Today's fractal however is undebatable. It is an evaporated scene in the parent fractal that results when various negative portions of Z^(-1.7) and Z^(-7.1) are combined and (1/C) is added. Being evaporated, the fractal consists entirely of trapped 'inside' points made visible by the 'bof61' inside fill. The magnitude of the scene is beyond the point where breakdown begins, making the mathtolerance entry in the parameter file necessary to assure the image is rendered at the correct magnitude. I named the image "Sub-atomic Mystery". The magnitude of 3x10^12 is great enough to enlarge atoms to everyday size. The rating of a 7 might be a bit inflated, but the 9-1/4 minutes spent running the parameter file will not be wasted. The easiest way to view the scene is to download it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it has been posted for convenience. The weather was less than perfect here at New Fractal Central on Thursday. The temperature of 79F 26C was ideal, but the sky was filled with too many clouds to call the day perfect. Since the new fractal cats, Cassie and Nico, do not go outside, they do not concern themselves with weather. But this does not mean their day was without problems. For some reason they spent most of the afternoon sulking at each other. An evening treat of tuna for Cassie and cheddar cheese for Nico took their minds off their quarrel. The work is still caught up, which made my day better than average. I expect today to be the same. The next FOTD will apepar in 24 hours or so. Until then, take care, and where does it all come from? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sub-Atomic_Mystery { ; time=0:09:15.58--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.7456499103062/-2.77869068561652/3.04\ 4087e+012/1/17.5/0.1010712207165 params=-1/-1.7/-0\ .25/-7.1/0/1e+100 float=y maxiter=5000 inside=bof61 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=0009CI9C99C0MQ6ZcBjpGbbzhWvnPstJpRniRlZRjPR\ hERf4Vd4Zb4a`4eZ4iX4lV4pT4sS4mMBhHHcBOZ6U`8Wb9XdBY\ fCZhE_eGRZEUSDXMC_OLcPTgQ`kRioSqsTyvuX5qVNmUdiTvga\ ZfiC2SBCUHLVNVWTcXZP_`AbbMJdJKbHLaFKYDJUBIQ9HM7GI5\ FE3EA1D64E77E79F7CF8EG8HG8JG8MECODGQBKTAOV8SX7WZ6_\ h5dq4hz3lt5fn7ah9XbBRXDMSEHXCFaADe8Cj6An49s27w06s5\ 7oA8kF8bLEURJLXPCbU4gZJXXXMVjBUeJX`QZWX`RccMjeHqgM\ ijQbmUWpZOsbHvfAxbGt_MqWSnTYkPcgMidIoaFuZOsYWqXcoW\ knWhhUebSbXQ`ROYLMVFKTAJP9KL8KH7LE6L15F64O34N58U6B\ W7Fa8Ic9MhAPlBTpCWsgzjizdwzZmuTguRauPXiNRkLMcJGaH4\ gHBVGIXGOUGVRGum8zmCzmGzNKLPSGQOCQK8_G4_CkJf`KcQLa\ 5FVBJSGMQMQTRTQXXTa_RYNDfbPwzTruXnq`imheil`epXasSY\ wOUzPXxQ_wRauSdtTfrUiqTnzUlqUkkUjeUhZUgTZzJjRIhQHg\ OHeNGdMGhPIlRKpTMtVOxXQmYUcZXT_`J`c9`fP_aL`WHaREaM\ AbG7bB3c60c12VK4Ma6Ds7Jk7Pd7VY8`R8fK8lD8q6DnFIkOMh\ XReeGRhBKq7Dz8Cq8Ch8C_9CR } frm:MandelbrotMix4 {; 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, 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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FOTD 24-08-06 (Atomic Nucleus [6])
by Jim Muth 24 Aug '06

24 Aug '06

FOTD -- August 24, 2006 (Rating 6) Fractal visionaries and enthusiasts: Back in my naive teen-age years, when I was just becoming familiar with the scientific world of astronomy, weather, and atoms in particular, I often wondered what an atom looks like. I soon formed a picture of the atom as a miniature solar system, with electrons orbiting the nucleus like planets orbit their stars. The nucleus seemed to me to be a boiling mass of protons and neutrons somewhat resembling a pot of boiling liquid. It all made a kind of sense. When a radioactive atom decayed, it was because a proton had escaped the surface of the boiling nuclear liquid. I felt that if I could shrink myself small enough, I could actually observe these atomic things taking place. I wondered whether atoms actually might be miniature solar systems with galaxies, stars and planets, like in the story about a shrinking man which I read about that time. Then I started reading more serious books about the sub-atomic world and the quantum. I came to realize that whatever is actually down there is so far removed from our everyday experi- ence that it can be best described only approximately by math- ematical expressions. To attempt to picture a physical reality corresponding to the quantum math is a futile endeavor. I now know that protons and electrons are not 'things' in the sense that tables and chairs are things. They are ideas, mental models that happen to work reasonably well. In a sense, we create them along with their attributes when we describe them. This is well illustrated in the case of an electron, which is said to be both a potential wave and a potential particle with a spin of 1/2. Such a spin means it would need to undergo two complete 360-degree rotations before it would present the same face to a hypothetical observer. Unless an electron is some kind of single-sided Mobius object, which must be turned 720 degrees before it returns to its original position, the elec- tron's attributes would appear to be impossible. Electrons may appear impossible, but it would be interesting to see what a person would observe if an electron were enlarged to the size of a basketball. Of course, if electrons are mere points, enlargement is meaningless. By contrast, fractals most certainly are not only possible, but have actually been observed in full graphic representation. Unfortunately, so far at least, fractals such as the Mandelbrot set have been seen only as computer-generated photographs. Today's photographic image of a fractal has been named "Atomic Nucleus". The central midget reminds me of a nucleus, while the surrounding elements could be seen as electrons. The image is a scene in the parent fractal that results when Z^(-1.75) is subtracted from Z^(1.75) and (1/C) is added. In this case the parent fractal could more accurately be called the parent debris field. It is little more than a scattering of fractal debris. But that debris is filled with countless midgets, one of which lies peacefully at the center of today's frame. The rating of a 6 seems appropriate. Rendered as it is with the outside set to 'iter', the image does look a bit under-detailed, but in this case the under-detailed version is the best. The other outside options give so much detail that the result is more chaos than fractal semi-order. The image is a fast one, which renders in 2-1/2 minutes on my P200 machine. Equally brief if not briefer is the time spent downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> What a waste! We had another absolutely perfect day here at New Fractal Central on Wednesday and the new fractal cats didn't even care. They spent the day chasing each other up and down the hall and getting into other various and sundry trouble. My day was spent doing various odd jobs between the times I was doing fractals. If all goes well, and why should it not, the next FOTD will appear in 24 hours. Until then, take care, and don't be nucular, be nuclear. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Atomic_Nucleus { ; time=0:02:30.66--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.39532679744866780/+0.594877164365430\ 40/3.945085e+007/1/40/-1.05442878494538261e-006 params=1/1.75/-1/-1.75/0/0 float=y maxiter=500 inside=0 periodicity=10 colors=000sh2th2th2rg3qf3pe3od3mc3lb3ka3j`3h_3gZ3f\ Y3eY3eY3dX3bW3aV3`U3_T3YS3XR3WQ3VP3TO3SN3RN3QM3PL3\ NK3MJ3LI3KH3IG3HF3GE3FD3djKbhJagI`eH_dHZbGYaFX`FWZ\ EUYDPAmPAjPAgPAdKAaHAZDAWBAQAAMBAICBEDCAED5FE3k7tf\ 8mb9fZA_VAUQBNMCGID9GzzFxxFvvFutFsrFqpFpnFnlFljFkh\ FifFgdFfbFd`FbZFaXE_VEYTEXREVPETNESLEQJEOHENFELDEJ\ BEI9EG7EE5q`jmZfjXcgV_dTXaRUZPQWONTMJQKGNIDKG9HE6s\ rVrqUqpTpoTonSnmRmlRlkQkjQjiPihOhgOhgNgfNfeMedLdcL\ cbKbaKa`J`_I_ZIZYHZYHYXGXWFWVFVUEUTDTSDSRCRQCQPBPO\ AONAON9NM9ML8LK7KJ7JI6IH6HG5GF4FE4ED3zjYvgVrdTnbQj\ _OgXMcVJ_SHWQETNCPKALI7HF5s`7r_6q_6pZ6oZ6oY6nY6mX6\ lX6lX6kW6jW6iV6iV6hU5gU5fU5fT5eT5dS5cS5bR5bR5aQ5`Q\ 5_Q5_P5ZP5YO4XO4XN4WN4VN4UM4UM4TL4SL4RK4QK4QJ4PJ4O\ J4NI3NI3MH3LH3KG3KG3JG3IF3HF3HE3GE3FD3ED3YK7XJ6XJ6\ WJ6WJ6VJ6VJ6UI6UI6TI6TI6SI5SI5RH5RH5RH5QH5QH5PH5PG\ 5OG5OG5NG4NG4MG4MF4LF4LF4 } frm:MandelbrotMix4 {; 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, 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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FOTD 23-08-06 (Garden of Rings [6])
by Jim Muth 23 Aug '06

23 Aug '06

FOTD -- August 23, 2006 (Rating 6) Fractal visionaries and enthusiasts: The big job went out on schedule this morning, and the customer is happy. The most recent rush has ended and the FOTD has returned. I would like to guarantee that this interruption will be the last in the FOTD series of images and discussions, but I have not yet learned to see the future. To celebrate the re-appearance of the FOTD we have gone to the fractal that results when Z^(-1.5) is subtracted from Z^(1.5) before (1/C) is added. This fractal is little more than a single small Mandeloid surrounded by scattered bits and pieces of fractal debris. Today's image is located in a rudimentary valley of one of these tiny bits. I rated the image at a 6, though I could easily have chosen a rating of 7. I settled on the 6 because much of the image's effect was achieved by rendering the scene with the outside set to 'fmod'. The basic scene is really quite bland. I named the image "Garden of Rings". The rings were created by the 'fmod' option, which draws a series of overlapping bands and rings, usually centered on points of interest. This option is also the simplest way to find hidden midgets, especially in the Mandeloids with exponents of Z between 1 and 2. IMO, the render time of 6-1/2 minutes is reasonable enough, but individual opinions of what is reasonable may vary, so in addi- tion to rendering the image from the included parameter file, the image may be seen by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> My philosophical ideas are taking shape, but are not quite ready to be made public. After all, radical ideas demand radical thought and preparation. Very pleasant but very dry weather continued all day Tuesday here at New Fractal Central. Conditions are approaching drought status, but the new fractal cats did not even notice. They spent the day playing under an old afghan which I spread on the living room floor for them. My day was pretty much occupied with cleaning up after the big rush of the past week or so. Hopefully, such rush jobs will not arrive too often, though I certainly do not want them to totally vanish. The next FOTD will arrive in 24 hours. That is almost but not quite guaranteed. Until then, take care, and how would it be possible to prove that the universe is not real? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Garden_of_Rings { ; time=0:06:27.12--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.18116619808723830/+0.390853245407780\ 80/1.034841e+007/1/162.5/3.31205395526223967e-007 params=-1/-1.5/1/1.5/0/0 float=y maxiter=1200 inside=0 proximity=0.8 outside=fmod logmap=yes periodicity=10 colors=000zzzwyvtvrqwmnvhkuhkshjqhjoijmjikjiikigli\ flhemhgmhhngjogkogmpfnqfpqfqressetsevtfwsgxshyrizq\ jzqkyvjwtivrhupgtnfsleqjdohcmfbkdajc`ha_g_ZeYYcWXa\ UW_SVYQUWOTUNSTLRSJPRHNQFLPDJOBHN9FM7FL3FK6GJ5HI6I\ H7JG7IF8GE8FD9EC9CBABAA99B88B87C76C75D64D63E72B61C\ 62D64E66F88GAAHCCIEEIGGJIGKJHLLIMMJNNJOOKOPLPPLQPM\ RPNSPNTPOUOPUOQVOQWORXOSYOSZOT_OU_OU`OVaOWbNXcNXdN\ YeNZeNZfN_gN`hN`iNajNbkMcmNblNbkNbjNbiNbhNbgNbgNbf\ NbeObdObcObbObbObaOb`Ob_ObZObYObYPbXPbWPcVPcUPcTPc\ SPcSPcRPcQQcPQcOQcNQcNQcMQcLQcKQcJQcIQcIRcHRcGRcFR\ cERcDRcCRcCRcBRcASc9Sc8Sc7Tc7Tc6Uc5Uc4Vc3Vc2Xc1Wc2\ Xc3Xc3Xc4Xc5Xc5Xc6Xc6Wc7Wd8We8Wf9Wg9YhAZiBbjBhkCol\ DumDznEzoESRFSRGSRGSQHSQHSPISPJSOJSOKSNLSNLSMMSMMS\ LNSLOSKOSKPSJPSJQSIRSIRSHSSHTSGTSGUSFUSFVSEWSEWSDX\ c3l`5hZ7eX9bVB_SDXQFUOHRK9JLCLLEMLGNMIOMKPMNQMPRNR\ SNTTNVUNXVO_XOaYmGbmHcmJc } frm:MandelbrotMix4 {; 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, 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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The FOTD is coming
by JimMuth＠aol.com 20 Aug '06

20 Aug '06

Frantic Fractal and Philosophy Fans: Do not lose faith. I have not burned out; I have merely been very busy. But the job that is causing the rush will be delivered the morning of Tuesday the 22nd, giving me ample time to settle down and prepare the FOTD for August 23. So praises be to the powers that be. The FOTD will resume in only three days, on Wednesday. As for the consciousness thread currently threading its way around the philofractal list, I will have much to say. I find the topic of self-awareness one of the most interesting topics facing man. Not only do we have no idea where it comes from, we don't even know what it is, and we can't even agree on how to define it. Maybe self-awareness is a great illusion -- nothing that comes from nowhere. And if this is so, we may define it any way we wish. Jim (the probably conscious) Muth

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