March 2010 - Fractint - mailman.xmission.com

Re: [Fractint] Bad news from Old F.C.
by JackOfTradeZ＠comcast.net 19 Mar '10

19 Mar '10

. Sorry to hear that Jim. But 20 years is a long time for any cat? Be thankful for 20 long fractal years! I am going thru the same thing now with my White German Shepherd. It is heartbreaking. Only 9 years. Emotionally devastating. Only another animal lover could ever understand. :( But I am keeping hope alive for now. :) .

1 0

Bad news from Old F.C. (Not exactly fractal related)
by Jim Muth 18 Mar '10

18 Mar '10

Fractal fans: It's just after 11am Thursday, March 18 here at Fractal Central and I have just received a call from my sister back at Old Fractal Central. She told me that Thomas, the one remaining original fractal cat who is now 20 years old, is in very bad shape and unlikely to make it through the day. We have been worried about him for several weeks, and if my writing has been a bit sharp lately, it is because of my concern for Thomas. As for the global warming off-topic, John is right. There are simply too many of us on the planet, and we are unwilling to do the only thing that could possibly save us -- reduce our numbers. I think that deep inside we all realize this, yet are unwilling to accept and face it. Advanced technology will not save us. Colonizing other planets is a sci-fi fantasy. It looks like the grand experiment of intelligent life on earth will end up being a failure, and the last living man will ask the surrounding emptiness what it was all about. The regular FOTD will be posted in about 12 hours. Have a happy day. FRACTAL JIM, the currently somewhat depressed

1 0

Warming catastrophe (non-fractal topic)
by Jim Muth 18 Mar '10

18 Mar '10

At 11:38 AM 3/16/10 -0500, Maryetta Campbell wrote: >Jim Muth wrote: >> >> After watching one manmade-global-warming-doomsday >> program after another on Sunday, I am fast becoming >> convinced that the whole warming thing is more >> politics than fact. >> > >Then you should read some of the statistics on "Glacier Melting Rate", >or watch some better shows. > >Glaciers are shrinking not only in area but also in thickness. Some >are losing as much ice in one week as they used to surrender in a >whole year. And some are no longer there at all, because they have >completely melted over the past few decades, even though they had been >around for hundreds/thousands of years. > >The glaciers in the Himalayas are receding quicker than those in other >parts of the world and could disappear altogether by 2035. The >Himalayan rivers support a _VERY_ large portion of humanity. The rate >of retreat for the Gangotri glacier, which feeds the River Ganges >(India's holiest river), over the last three decades was more than >three times the rate during the preceding 200 years. . . . Etc. Etc. Etc. I have heard, seen and read all this stuff a hundred or more times. And I agree, it is true. But why do the warming alarmists continue repeating that glaciers and ice caps are melting when it is common knowledge? This melting has been known by climatologists for many years. The questions are how much of the melting is 'man-made' and how much is natural, what if anything can we do about it, and how much are we willing to sacrifice to reduce the part we are responsible for. For example, how many are ready to park their cars, the biggest greenhouse gas emitters, permanently and turn to public transportation? Do I hear replies about living too far to walk and public transportation not being available? It appears to me that these climate doomsday programs are trying to instill fear among the general public so that they will support legislation (cap and trade?) to fight the hyped-up dangers of the warming. Such legislation will surely bring great profits to some big corporations. Luckily, the public is starting to see through the big scare. You appear to be a liberal thinker. I'm sure you can see how the so-called dangers of a 'public option' in health care -- rationing, death squads, etc. -- are little more than political hyperbole stirred up by the right to frighten the public. Why is it so hard to see that the coming 'climate catastrophe' is similar hyperbole from the left based on misrepresented and questionable science. In my opinion, the most amazing thing in all of this is how easily the general public can be led like a flock of sheep to believe anything those who are actually running things (most likely the big corporations) want us to believe. If you care to debate, please include a workable solution to the so-called climate catastrophe that is looming just ahead of us. I would start by saying that if the Himalayan glaciers disappear, we would find a way to use some of that heavy monsoon rainfall to supply water to the subcontinent -- that is if the alarmists do not start claiming that the monsoon will disappear also. Remember that a warmer planet earth means a faster water cycle -- faster ocean evaporation and heavier rainfall, and not a global desert. As for spreading reflective sheets of foil over the glaciers, it would not work. The sheets would soon be covered by new snow and become ineffective. Fanally, to keep things a tiny bit on topic, perhaps we can use fractals in some way to solve the dilemma. Fractal Jim (politically questionable)

3 2

FOTD 18-03-10 (Lucky Sevens [6])
by Jim Muth 18 Mar '10

18 Mar '10

FOTD -- March 18, 2010 (Rating 6) Fractal visionaries and enthusiasts: With a busy day Wednesday cutting into the fractal time, today's discussion will have to be brief. The parent fractal is a classic Mandelbrot set with order-7 characterists in its depths. Today's scene is located in a radical star on the northwest shore line of the main bay of the parent. The minibrot at the center is pure Z^7 stuff, while the surrounding elements appear to be classic Mandelbrot stuff. The resulting mixture rates a modest 6. The name "Lucky Sevens" refers to the order-7 nature of the image. The calculation time of 3-1/2 minutes is pretty speedy, though the trip to view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> should be even speedier. Another near-perfect day passed peacefully here at Fractal Central on Wednesday. The fractal cats thoroughly enjoyed the unbroken sun on their window shelf, while the humans enjoyed the temperature of 63F 17C. This human was a bit too busy to enjoy the weather, but he did enjoy the savings in heating fuel. The next FOTD will be posted in 24 hours. Until then, take care, and look toward the light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Lucky_Sevens { ; time=0:03:36.81-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=AllNewDivideBrot3 function=recip passes=1 center-mag=-0.550996203572/+0.50282992259\ 48/6.52779e+008/1/-12.5/0 params=7/10000000 float=y maxiter=2500 inside=0 logmap=304 periodicity=6 colors=000FA0FA0FA0FA0FA0FA0FA0FA0FA0FA0FA0FA0FA0F\ A0FA06A07A08A09A5AAACAFEAKHAKKAKKAMKAOKAQKASKAUKAW\ KAXKAVKAUKAUKAUKAUKAUKAUKAUKAUKAUKAUKAUKAUKAULAUMA\ ULAUFAU9BUBDUCEUDFUEGUFIUGJUHKUILUJMUKOULPUMQUNRUP\ TVQUWRVXSWYTXZUZ_V_aW`bXacYceZdg_ei`fkagmciodjqekr\ flrgnrhosipsjqskrslttmutnvtowtpxtqwsrwsrvrsvrsvqtu\ qtuzuuzzzzzzzzzzzzzzzziKfdKc`K`XKYSKVOKSKKPFKMBKJ7\ KG8KF8KF9KF9KE9KEAGEADDBADB7DB5DDIjHOfMVaQ`YVfUzlQ\ zjQzzQzgQzeQ`dQW_NSWKORH473KNEFJBBE87A5faw_WmTRcNM\ VGGL9BBT4gK5UB6Gn`ofVfZQZRLRJGIBBApMViKRcINYGKSEGL\ CCFA9985HcNCSG7H94zz3XQFMODJKBGG9EDPB9S85_0Ic3Am5B\ r68w66z64zzmmqcciUUaKCUA9M26E2WRsMKaCDKUDNPBJLAGG9\ CC89775rXh`OUKFGpsbhkXadSVYNORHHKCcAUcAUcAUcAzzUzm\ UUqmzrUUsmztUUumzsURrmzpZLomzmhFlmzkrAjvzjzDizzizF\ hzzhzHzzzzzJzzzzzMzzzzzOzzzzzQzzRzzSzzUzzVzzWzzXzz\ YzzZzz_zz`zzbzzczzdzzezzf } frm:AllNewDivideBrot3 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < 1000000 } END PARAMETER FILE=========================================

1 0

FOTD 15-03-10 (Blades of Passion [7.5])
by Jim Muth 17 Mar '10

17 Mar '10

FOTD -- March 15, 2010 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is titled "Blades of Passion". But do not expect anything connected with a hot backstage romance at the figure- skating competition. The name refers to the windmill-like blades in the lower half of the image. (Fine-Tooth Comb" might be a good name for the upper half of the image.) The parent fractal is an almost-Julia set of a tiny spurious valley on the positive X-axis of the Z^(2.07)+C Mandeloid, with the grossly enlarged mandel part rotated 90 degrees. Today's image is located where the mandel stuff intersects the northern edge of the almost-Julia set. In the image, the upper half is made of the mandel stuff, while the 'blades' in the lower half are made of the almost-Julia stuff. The rating of a 7.5 includes 1/2 point for the coloring, which makes the top half almost look like a net. The calculation time of just over 5 minutes is well within reason for such a complex image. Those who become mentally congested at the thought of complexity may make things simple by viewing the finished image on the new FOTD web site at: <http://www.Nahee.com/FOTD/> I will no longer include the address of the old web site, which will soon be discontinued, though the address is still readily available in the back-dated FOTD discussions. After watching one manmade-global-warming-doomsday program after another on Sunday, I am fast becoming convinced that the whole warming thing is more politics than fact. I doubt that I have ever seen so much mis-represented stock film footage. (I should keep a list of the misleading statements.) Almost certainly someone has much to profit if we are led to take panicky actions to fight this grossly-overblown threat, but who is behind the big scare, hoping to make the huge profits? Maybe the phone companies are behind it. As long as we're so occupied with global warming, we'll have less time to be con- cerned about more immediate threats such as the non-ionizing radiation given off by the toy-like and now absolutely neces- sary 'wireless' devices that are overwhelming our culture. Yes I know that no study sponsored by a phone company or wire- less-device manufacturer has ever found a harmful effect of the radiation. But the devices have also never been demonstrated to be safe, and what about those studies sponsored by independent sources, which do find harmful effects? Now on to the weather report. Heavy clouds with occasional periods of rain prevailed here at Fractal Central on Sunday. The temperature of 48F +9C was fair enough, but the fractal cats still complained about the lack of sun. My day was about average. In the evening I got a phone call from my sister back at Old Fractal Central, who told me that Thomas the one remaining original fractal cat is in failing health. Thomas is over 20 years old, so we'll have to see how it goes with him. Tippy, the other original fractal cat, went to the eternal lap two years ago. The next FOTD will be posted in 24 hours. And who knows, it might even rate an 8 or 9. Until then, take care, and wait patiently. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Blades_of_Passion { ; time=0:05:05.72-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 float=y center-mag=0.11405/0.89808/12.43585/1/82.5/0 params=89.999/0/89.999/90/0.2627/0/0/0/2.07/0 maxiter=1220 inside=0 logmap=-7 periodicity=10 colors=000hAwiAujAskAqlAomAmoAkp9iq8er6bt5_u3Xv2Uw\ 1Rn8PfFNiKOlPPoUPrZPtcPvhPwhRvgSvfUudWucXtbZta_rWZ\ pRZnMZmHZkCZi7Zh2Za6YVAXPEWIIVCLVDMXDMZDN_DNaDNcEO\ dEOfEOgEPiEPkFQlFQnFQpFRqFRsFRtDNlCJdAFX9BQIHRRMS_\ RTgWUhWUiWTiWTjWTkVTkVTlVSmVSmVSnVSoVRoVRpURqU0qUR\ zUQsZQs0QtUmcNklR`pJDrPKnKhoUgocfo0ep0zpNcpNbkUFmV\ EnXEpYDqZDoXEmWEkVEiTEgSEeRFcQFaOF_NFYMFXLFVMHUNIS\ OJRPKQQLORNNSOLTPKUQJVRHVTGWUFXVDYWCZXA_Z9`_8a`6ba\ 5cb4ccIVeVMfgDgfCffCffCefCefCdfCdfBcfBcfBcfBbfBbfB\ afAafA`fA`fA_fA_fA_hDYiEXjFXkHWmJVnMUmOUhNYcMaZLeU\ KiPKmKKmJJmLIlOHkQIiSIhUJgVKeXLdZMc`MbbN`dO_fPZhQX\ jQWlRVnSTpTSrURyiZxfXwdWvbVv_TuYStWRJPdNQbQQaTR`WR\ _ZSYaSXeSWhTVkTTnUSqURMGRQIQUKQYLQaNQeOQiQQmRQqTQY\ CO`EPbGPdIPgKPiLPkNQnPQpRQrTQ6N5AO7EP9IPAMQCQQEURF\ YRHaSIeSKiTMmTNqUP4v_7tZxrYuqYqoXmnWjlVfkUbiT_gSWd\ RU`QRXPNTOKPNDLM6HLFDKO9K } frm:SliceJulibrot5 {; draws all 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=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

6 5

FOTD 17-03-10 (Epsilon to Patrick [6])
by Jim Muth 17 Mar '10

17 Mar '10

FOTD -- March 17, 2010 (Rating 6) Fractal visionaries and enthusiasts: The parent fractal of today's image is an everyday Mandelbrot set. This is true only on the surfaqce however. In its depths, this M-set takes on the characteristics of the Zexpe fractal, which has the formula (Z^(2.718...)+C). Today's image lies deep enough that the Zexpe characteristics are fully developed. The image is located on the northeast shore line of the main bud of its parent M-set. The minibrot at the center displays the full Zexpe shape, though the surrounding elements, while numbering around 5, show Mandelbrot-set characteristics. I named the image "Epsilon to Patrick". The Epsilon shape and the fact that March 17 is Saint Patrick's Day inspired the name. The rating of a 6 indicates that I consider the image to be only slightly better than FOTD average. The calculation time of 2-3/4 minutes may be avoided by surfing to the new FOTD web site at: <http://www.Nahee.com/FOTD/> and viewing the completed image there. Absolutely perfect weather prevailed here at Fractal Central on Tuesday, with clear skies and a temperature of 61 F 16C. The fractal cats approved wholeheartedly. My day was on the busy side, but not so busy as to keep me from finding an average fractal image. The next in the endless series of fractals will be posted in 24 hours. Until then, take care, and don't fall for the manmade-global-warming scam. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Epsilon_to_Patrick { ; time=0:02:44.69-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinalDivideBrot function=recip float=y center-mag=-0.7909685423430249/+0.1464022856501517\ /1.376139e+009/1/10/0 params=2.718281828459/100/0/0 maxiter=2400 inside=0 logmap=358 periodicity=6 colors=000r_VuZTsYRrXPqWNpULoSKnQImOGlMEkKCjIBfIDb\ IEZIFWIGSIHOIILIJKHMKGPJFSJEUIDXIC_IJaHNdHSgGYjGel\ FmoFrrFvt8wr7tq7pq7lq6gp6cp6_p5Vo5Ro5No4In4En4An8F\ jCKgGOdKTaOXZRaVVfSZkPboMfrJisGhsHgqHfnHckHahH_eIZ\ bIY_IXXIWUIVRJUOJSLJQIJOFJPEIQEIREHSEHTEGUEGVEGVEF\ WEFXEEYEEZEE_ED`EDaECbECcECeEBgEBiEAkEAmEAkGBjIBhJ\ CgLCeMDdODbQDaRE_TEZUFXWFWXGUZGT`GRaHQcHOdINfIMgIO\ fFQfDSfBUf9Wf7Yf5_f3`f1ag3ah4ai5aj6bk7bl8bm9bnAcoB\ cpCcpEcqFdrGdsHdtIduJevKewLexMeyNeyOimRmbUqRWuGZy5\ `xI7uJ9sJAqKBoKCmLDkLEiMFgMGdNHbNI`OJZOKXPLVPMTQNR\ QOOQORTMUWKXZJ_aHbdGefKhiUplczzbqmpsoprmprlprkpqjp\ qimqmczlUzkTzzWzzZzhaogcnffneindlncneUcXKUOAKPDLPG\ MQINQLOQOPRQQRTRSVSSYTS`UTbVTeWzgXzdWzbWz`WzYVzXVz\ _VzbUzeUzhUzkTznTeqTftSgwShzSzzUzzWzzXzzZzz`zzazzc\ zzezzfzzhzzizzepzFrzHtzKvzMxzOzzQXzf4zw8ztCzrGzpKz\ nOzkSziVzgZzebzcfz`jzZnzX } frm:FinalDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < esc } END PARAMETER FILE=========================================

1 0

FOTD 16-03-10 (A Phantom Minibrot [5])
by Jim Muth 16 Mar '10

16 Mar '10

FOTD -- March 16, 2010 (Rating 5) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's formula, the MandAutoCritMinZ, is one I worked up when I finalized the MandAutoCritInZ formula. It is the same as the MandAutoCritInZ formula except that it combines powers of (-z) rather than (+z). I have done very little with it because it virtually duplicates the images created by the original formula, and often fails to find a critical value of initial (z). But now and then it comes up with some new stuff. Today's image is one of the more interesting images it has produced. I named the image "A Phantom Minibrot" because of the brilliant white Mandelbrot shape left of center. The Mandelbrot effect is a totally random illusion. There is no minibrot lying just beneath the surface. The minibrot is a phantom. Ghostly specter or not, I could give the image a rating of no more than a 5. It's still an interesting scene however, well worth the 5 minutes required to calculate it from the included parameter file or the minute or so required to view the image in finished form on the FOTD web site at: <http://www.Nahee.com/FOTD/> Monday brought heavy clouds but dry weather to Fractal Central, with a temperature of 48F +9C. The fractal cats disapproved. My day was rather busy; tomorrow will likely be a repeat. The next FOTD will be posted in 24 hours. Until then, take care, and conspiracies are everywhere. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Phantom_Minibrot { ; time=0:05:05.76-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritMinZ function=ident float=y center-mag=+0.585989628/+0.00007827/4751.262/1/\ -117.5/0 params=2.76/-1.4/0.36/-4.4/0/0/0/0 passes=1 maxiter=1600 inside=255 outside=tdis logmap=140 periodicity=6 colors=000iQPjRPjSPjTQkUQkVRlWRlXRmYSmZSm_Tn`TnaTo\ bUocUodVpeVpfVqgWqhWqhWoeVmbVl_VjXViVVgSVePVdMVbJV\ aHV_EVYBVX8VV5VR1UU3VW4VY5V_6Va7Vc9VeAVhBVjCVlDVnF\ VpGVrHVtIVwJWvJVvJVvJVvJVvJVvJVvJVuJVuJVuJVuJUuJUu\ JUuJUuJUtJUtJUtJUtJUtJUtJTtJTsJTsJTsJTsJTsJTsJTsJT\ sJTqLUpMVoNWnOXlPYkQZjR_iS`hT`fUaeVbdWccXdbYe`Zf__\ gZ`gYahWbiVcjUdkTelSfmQgnPhnOioNjpMkqKlrJmsIntHouD\ qvEpuFpuGpuHpuHptIptJptKptKptLpsMpsNosNosOorPorQor\ QorRorSoqToqToqUoqVnpWnpWnpXnpYnpZnoZno_no`noannan\ nbmncmndmndmmemmfmmgmmgmlhmlimljmllnokmmjmljmjimii\ mhhmfhmegmcfmbfmaem_emZdmYdmWcmVbmTbmSamRamP`mOaoM\ `mN`lN_kN_jNZiNZhNYgNYfNXeOXdOXcOWaOW`OV_OVZOUYOUX\ OTWPTVPSUPSTPSSPRQPRPPQOPQNPPMQPLQOKQOJQNIQNHQNGQM\ EQMDQLCRLBRKARK9RJ8RJ7RI6RI5RJ3SI4RH5RH6RG7RG8RF9R\ FAREAQEBQDCQDDQCEQBFQBGQAGPAHP9IP9JP8KP8LP7MP2NN4M\ O5MO7MP8MPAMQBMQDMRELRzzz } frm:MandAutoCritMinZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*((-z)^b))+(d*((-z)^f)))+c, |z| < l } END PARAMETER FILE=========================================

1 0

Re: [Fractint] FOTD
by JackOfTradeZ＠comcast.net 16 Mar '10

16 Mar '10

. Is the new FOTD site up yet, and if so what is URL? . Not to get off track, but if history teaches anything, it is that it DOES repeat itself over and over ad infinitum. People never learn. This is the oldest tactic in the book. If people are kept worried and occupied with non-issues like climate change, cholesterol, and race (class warfare, setting the people at each other's throats), they will never be aware of the REAL issues, like the plunder of our children's heritage and the selling out of the country to internationalists. But perhaps there's some glimmer of hope in them thar tea bags ..... .

1 0

FOTD 14-03-10 (Zexpe Below Zero [6])
by Jim Muth 14 Mar '10

14 Mar '10

FOTD -- March 14, 2010 (Rating 6) Fractal visionaries and enthusiasts: Today's scene lies in the northernmost of the two East Valleys of the (-Z)^(e)+C Mandelbrot fractal, otherwise known as the Minus-Zexpe Fractal. The parent fractal has two East Valleys, which are the remnants of the single Z^2 East Valley, which has now split apart and has been caught in today's image two-thinds of the way through the process of morphing into the northern Seahorse Valley of the (-Z)^3 Mandeloid. There is nothing exceptional in the scene. All I can say about it is look and enjoy. The way to look is to run the parameter file and wait about 1-1/4 minutes, or to surf to the new FOTD web site at: <http://www.Nahee.com/FOTD/> Saturday here at Fractal Central was marked by heavy clouds and high winds. Some rain fell, though the flooding rains failed to materialize. All the while the temperature hovered around 48F +9C. Fractal cats generally do not like rain, and the resident fractal cats are no exception. They spent the day in sulk mode, with their tempers showing. My day was uneventful, which means no antiquing expedition took place and the FOTD fractal was ready on time. The next FOTD will be posted in 24 hours, unless the world ends before then, that is. Until next time, take care, and now that the future has arrived, where are the wonders of the future? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Zexpe_Below_Zero { ; time=0:01:16.57-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 center-mag=+0.104839627\ 4699141/+0.3670053590720084/3.969899e+008/1/67.5/0 params=0/0/0/0/0/0/0/0/2.71828182845905/0 float=y maxiter=6400 inside=0 logmap=158 periodicity=6 colors=000SPVQPWOPXMPYKPZIP_GP`APaCPbEPcFPdHPeJPdK\ P`MQYNQUPQQRQMSRIUSEZT8cUBhVDmWFrVHsWFtUEsRDqPCoNB\ nKAlH8jE7iB6gG5fI4eK3eM4eO5eR5eU6fX7f_7fb8fe9gh9gk\ AgnAgpAgrBgpDfnFfkIeiKefMedOdaRd_TcXVcVXbT_bSabSca\ TeaUh`Vj`Wl`XnaYo_ZoY_hW`aUaVSbOQcCOdHMeMKfQIgVFhZ\ GhcIhhKhlMhqNhsOhuCkw0ky4jv8htCfrGcpKanO_lSXiWVg_T\ ecQcgOakM_qL`oKYmKWkJTjJRhJOfIMeIKcIHaHF_HCZHAXG7V\ G5TE0UG3UI5UJ7VL9VMCVOEWPGWRIWSKRNWMIgGCuHErHGoHHl\ HJiHKfIMcIN`IPYIRVISSJUPJVMJXJJYGJ_DGa8J`AL_COmEQn\ FTcHVYJYcL_XMbWOdWQgVXzcziVZUK_EA`GBaIBbJCcLCdNCeO\ DfQDgRDhOEiMFjKGkIHlFImDJnBKo9Lp2Jq7Mr5LsCOtJRuQUv\ XXwc_xjbypdzqTzlWzgZzbazWezYdzZdz`dzaezbfzdgyehxgi\ whjvikukltlmsnnrooqpppiqocrnYsmStlMukGvj9wiAxfAycA\ zaBzZBzWBzUBzRCzOCzMCzJCzGDzEDzBDz8gzJhzLizMizOjzP\ kzRkzTlzUlzWmzXnzZnz`ozapzcpzdqzfvzeszfqzgozgmzhkz\ hizigzidzjbzj`zkZzkXzlVzl } frm:SliceJulibrot5 {; draws all 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=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

1 0

FOTD 13-03-10 (Misplaced Surprise [?])
by Jim Muth 13 Mar '10

13 Mar '10

FOTD -- March 13, 2010 (Rating ?) Fractal visionaries and enthusiasts: Today's image holds not only the promised surprise but a mystery as well. I named it "Misplaced Surprise" because the minibrot in the upper right seems strangely out of place. Yesterday's image is an East-Valley-type Julia set. This is evident by its appearance. Today's image shows the same scene from a viewpoint double-rotated only 0.001,0.001 degree from the Julia direction. (Double rotation is another story.) Despite such a tiny rotation, the resulting image has lost all resem- blance to a Julia set, and more closely resembles a non-critical Mandelbrot scene. But wait! This is impossible! What is a near-perfect Mandelbrot minibrot doing in a fractal that is so close to being a Julia set? Actually, the minibrot is far from perfect. A closer examina- tion will reveal that it is perturbed, but the fact that it is there at all makes the image so exceptional. When I began rotating the scene toward the Mandelbrot orienta- tion, I had one of the biggest surprises of my fractal career. A near-perfect Mandelbrot midget unexpectedly appeared amidst the degenerating Julia features. This is striking because, due to the four-dimensional shape of Mandelbrot elements in the Julibrot, with 2 infinitely extended dimensions and 2 compact dimensions, Mandelbrot features supposedly cannot appear in a Julia set. Another thing I notice in the image is the missing elements. In the pure Julia version, 32 striped red elements surround the cen- ter. In today's almost-Julia version I see only 24. I have no idea what happened to the missing elements, though I suspect a second radiant center lies off the screen some distance to the left. I have no answers to these fractal paradoxes, nor do I expect to think of any. I guess it will forever remain one of those unex- pected things that make fractals so interesting. Since the image is of purely mathematical interest, and would have little artistic worth to the 'look ma I'm an artist' type of fractalist, I rated it at a question mark. The calculation time of 1-2/3 minutes for all this surprise and mystery is quite a bargain. Those who are not bargain hunters may view the image on the new FOTD web site at: <http://www.Nahee.com/FOTD/> The weather here at Fractal Central took a turn for the worse Thursday night, and Friday dawned with cloudy skies and light rain. Friday brought continued clouds, intermittent rain and a temperature of 50F 10C. These conditions did not please the fractal cats, who wanted more sun. Unfortunately, with rain forecast for at least 3 more days, the cats will remain unhappy. My day was fair enough. If all goes well and no antiquing expedition arises on Saturday, the next FOTD will be posted in 24 hours. Until then, take care, and be with the fractal elite. P.S. My almost-useless AOL e-mail address may be discontinued in a month or so. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Misplaced_Surprise { ; time=0:01:39.89-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t float=y center-mag=-0.00021870072691744/-0.000080784627994\ 88/3194.472/1/-7.5/0 params=89.999/0/89.999/0/0.27\ 58107881858941/-0.006746958379780152/0/0/2.003/0 maxiter=6000 inside=255 logmap=310 periodicity=0 colors=000000XJaMCPB6CvGeFMQ7BDz82S51E20zEPS9GE48T\ UqJK_9AIaFgPATC5E8maeqz2`q1Rc1IR09DrtxdehRSUDUzVKz\ F6Sry4di3RV2DF1kisWU`GFIlxG_hCOU8CF4ixpNUQdz0zO0KG\ 0A80Ah06U03F0WvEGT7e08BrglGwZVoLih8xaGmRObGWT5faAz\ zFzzKe_DMj7LI6qU`_KOIACoqTQREURYKIMA9BdIQUDJK9DA46\ tZoqHX_BMI5B`xpvuDgf9TT6EE3aRzJDVBmg7XT3GE1Ul0M_0F\ O07CkPQWGHG88pONbIHQCBD65UuzaT1SL0JE0970EyqAic7VR3\ FDaQxSJhJDU96FwXTUGEhnyNwFFcA7K5peXQLGDB08704304Db\ 8z94V4LjGEVA7F5EVK9KD4A6jZRCZq9Qc6HR38D`8qI4R6_gtH\ FS87pD9Z86H43fYHWPCLH8A842Ly1AVig6UT4FE2q4M9Ib6DT4\ 9J2499vL6gF4TA2E5NTBHL8BE5572Q82J61D41620tg4SM2L2H\ E1B705gtaMSJte1eV0SL0EA02Rg1IT09ECMO6BCEOMp_BZO7HC\ 3itOYeINSCBE6upGfbCTQ8ED41g9hzz0MUzr2jqK0fFzOABC57\ bdUEQhAJU7Dc36_RLOIEC970`50O30C1Da_8PO4CCZG6NA4B52\ _MgRGXIBM95Bk7oW4YG2HhheSDDI88944vlOi_RNIDt2fa1SJ0\ Es78e56S34E12ZunAgH7XCzzz } frm:SliceJulibrot4 {; draws all 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

2 1