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<Brian>I like your logarithmic spiral made of logarithmic spirals!
by Hal Lane 04 Dec '13

04 Dec '13

Brian, Thanks for posting your two images. I especially like your BP_18_64.png -- the logarithmic spiral made up of logarithmic spirals! Your image reminds me of a fractal I was calculating overnight, but lost due to a Blue Screen of Death... Is BP_18_64.png a zoom into Jim's FOTD for Nov. 29th, 2013? <---<< - Hal Lane (\__/) ######################## (='.'=) # hallane(a)earthlink.net (")_(") ######################## ----------------- Author: Brian Prentice Date: 2013-12-03 08:50 -500 To: Fractint and General Fractals Discussion Subject: [Fractint] Two Details Two details from recent FOTD's: http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_64.png http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_65.png Brian Prentice ----------------- --- This email is free from viruses and malware because avast! Antivirus protection is active. http://www.avast.com

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FOTD 04-12-13 (Pseudo-Quadratic [A-9,M-9])
by Jim Muth 04 Dec '13

04 Dec '13

FOTD -- December 04, 2013 (Rating A-9,M-9) Fractal visionaries and enthusiasts: Today's superior image shows a minibrot in the parent fractal that results when the expression Z^(1.333)+C is iterated one level up the hyperladder with no function applied. This parent fractal rather resembles the eastern half of the main bay of the Mandelbrot set, complete with a quite convincing large quadratic bud on its northern side. Today's unusually brilliant scene features a minibrot lying on a tiny disconnected filament fragment near this almost-quadratic bud. >From a distance, the minibrot in today's image is shaped strikingly like the countless Minibrots found in the M-set, though a closer check reveals huge differences. The name "Pseudo Quadratic" refers to this false resemblance. In my opinion, both the art and the math aspects are worth the rating of a 9. The art rating reflects the extra effort required to achieve the brilliancy. The math rating is so high because I have never seen a minibrot so closely resembling a quadratic minibrot in a fractal with an exponent of Z as low as 1.333. The calculation time of 4-3/4 minutes is admittedly slow, but at least in today's case, the result is well worth the wait. The finished image is or soon will be available on the following FOTD web sites: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Fine early winter weather prevailed here at Fractal Central today. The day began with heavy fog, but the fog lifted in the morning and revealed a mostly sunny sky that remained that way through the afternoon. The ample sun raised the temperature to a high of 48F +9C. The fractal cats appeared too interested in each other to pay much attention to the sun on the window shelf. The fractal humans had other things to do. The next FOTD will be posted in the proper time. Until whenever, take care, and which is worse -- conservatives who want to pass laws to force everyone to obey the rules of behavior set down in their Bible or liberals who want to pass laws to eliminate the natural inequalities inherent in humanity? As I see it, neither of these goals is ever going to be achieved, but it sure is a lot of fun watching the two sides continue their futile squabbling. Jim (neither right nor left) Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Pseudo-Quadratic { ; time=0:04:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.3243347326496687/+1.081261598206034/\ 3.441011e+009/1/172.5/0 params=1.333/0/1/0 float=y maxiter=5000 inside=0 logmap=-305 periodicity=6 colors=00000B00C00D00E00F10G20H30I40J50K60L70M80N9\ 0OA0P50G50H50I50J50K50L50M50N50O50P50Q50R50S60T70U\ 80T80T71S72S63S64Q53P53O42M40J30H30D208204100zQKtJ\ KqAKn8Hj8Dh46g60hB0iH0jL0kP0lT0mX0ma0ne0oi0pm0qq0z\ zFzzcVbB7HL6KK6MJ6OI6RH5TG5VF5YE5_D5aC6eD7iD8lD9pE\ AsEBwEBzEIyKPyQWyWbyaiygoylmvjkthjrfhpdfnbel`ciZbg\ X`eVZcTYaRW_PVYNTWOSVORTOQSPPQPOPPNNQLMQKKQJJRIHRH\ GRGESFDSECSJJWOQ_TXcYcgbjk`il_hmZhmYgnXgoWfoVfpUeq\ TeqSdrRdrOZzMTzJOzHIzECzC7zDCzDGzEKzEOzFSzFXzG`zGd\ zHhzHlzHpzIqzJqzKqzLqzMrzMrzNrzOrzPszQsXQsVRsSStPT\ tNUtKctImmKzmMzmOzmQzmSzmUzmWzmYzmZzmZzmZzmZzmZzmZ\ zmZxmZymZtmWomTjzRezOczMczJczHczEmzCmzJmzQmzXmzcfz\ jmzgmzemzbmz`mzYozWqzUszRuzPwzMzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 03-12-13 (The Absolute Limit [A-5,M-7])
by Jim Muth 03 Dec '13

03 Dec '13

FOTD -- December 03, 2013 (Rating A-5,M-7) Fractal visionaries and enthusiasts: How low can you go? No, we're not talking about the long-gone fad of limbo dancing, the lowness lies in today's exponent, which is the 128th root of 2 or 1.0054298, a value so close to unity that its graph is barely distinguishable from a straight line. But thanks to the MandelbrotBC3 formula, and also the multi-valued nature of the complex log function, we have dredged up something from almost nothing. True, today's image consists of nothing more than arcs filled with smaller arcs all the way down, but the screen is not filled with a flat pattern and a smooth-edged boundary. The art rating of a 5 is everyday average. The math aspect has more interest, and rates a 7, which is somewhat above average. The name "The Absolute Limit" refers to my present feelings about the low-exponent theme. It does not mean I will never try to find detail in a fractal with an exponent of 1.0027112, but it does mean that if I ever do go searching, it will not be for a while. With a running time of 4-1/4 minutes, the calculation is a bit on the slow side, so if time is a factor, check the web sites. To avoid calculation the image check the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> A mix of sun and clouds with a temperature of 46F +8C and a calm wind made today rather pleasant here at Fractal Central. The fractal cats spent their waking hours getting to know each other better and their sleeping hours asleep. The fractal humans, if that's what we are, spent the day doing routine things. The next FOTD will be posted in the near future. Until the near future arrives, take care, and have you heard the conspiracy theory about the existence of conspiracy theories? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Absolute_Limit { ; time=0:04:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-14.7101/1.17509/8.709171/1/19.25/0 params=1.0054298/0/0/2400 float=y maxiter=2000 inside=255 logmap=405 periodicity=8 colors=000D880000000000000000000000000000000050080\ 0800900900A00A00C00C00D00D00E00E00F00F00G00G00H00H\ 00I00I00I00I00I00J00J00J00J00L00L00L00L00M00M00M00\ M00O00O00O00O00P00P00P00P00R00R00R00R00Q00O00R00R0\ 0U00U01W02X04Z05_06a08c09d0Af0Ch0Di0Er0Eq0Gu1Hv4Jz\ 5Kz8Kz9MzCOzDPzGRzHRzKUzMXyO_tPaoRaiSadUa_WaWZaR_a\ MaaHcaDda9fa5ha1iZ0kW9mPMmESo5Zr0Sp0Mf0EX18O44G658\ 850A50D50E50J60M81P95UAAXCG_DMcERhGXkHcoJiwJhrKfmM\ dhOccPa_R_WSZRUXMWXJW_DUa9Sc4Rf0Ph0Oi0Of0Jc4Ea9AZG\ 8WO4UU0Ra0Ph0Ma2JWCGRKEKWGMdIMpKMzMMzOMzQMzSMwUMvW\ MtYMr_MpaMmcMkeMigMhiMfkNcmOaoQ_qSZsUXtWWuYZv_awad\ xchyekzgozirzkvzmyzozzqzzszzuzAaz0azXaz0azfazzazka\ zzaz0azzaz0azzaz0azhrzcrzZrzUrwRrrMrmHriardarZaraa\ rdarharkryorzwrzrrzmrzirzfrzarzZrzWrzPrzSrzUrzXvzZ\ yzazzczzfzzhzzizzZzzPzzMzzazzizzrzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Two Details
by Brian Prentice 03 Dec '13

03 Dec '13

Two details from recent FOTD's: http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_64.png http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_65.png Brian Prentice

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FOTD 02-12-13 (Thirty-Second_Root [A-7,M-8])
by Jim Muth 02 Dec '13

02 Dec '13

FOTD -- December 02, 2013 (Rating A-7,M-8) Fractal visionaries and enthusiasts: Today's image is a scene in the parent fractal that results when Z to the power of 1.021897 is iterated at ground level of the hyperladder with no function applied. Not coincidentally, this value is the square root of the exponent of yesterday's image, and also the 32nd root of 2. The parent fractal of today's image closely resembles the parent of yesterday's image, though with less chaos along the edges of the large bay, which is shaped much like an elephant seal with a large pendulous nose. Today's image is located in the chaos near the straight southern shore line of the large bay. The amount of semi-organized detail in the scene is unexpected in a fractal created by an exponent of 1.02..., but images do not lie, and the stuff in today's image did not come from nowhere. (Or did it?) The name "Thirty-Second Root" refers to the exponent of Z. The art rating of a 7 indicates that the image is worthwhile, though perhaps not as striking as some past fractal scenes. The math rating of an 8 shows that the amount of detail in the image is quite unexpected. The calculation time of 1-3/4 minutes will pass quickly enough. For convenience, the image has already been calculated and posted to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Variations are available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> A cloudy sky and temperature of 41F +5C made today entirely un-notable here at Fractal Central. The fractal cats, who are not quite ready to share the window shelf, took turns watching the outside scene. The fractal humans, who wonder what the world is coming to, kept their wonder alive by watching the TV news at lunch time. The next FOTD will be posted soon. Until whenever that might be, take care, and when people dislike a big corporation, they usually fight it by organizing a boycott against the corporation's products. The big oil corporations certainly are disliked, even hated, so where are the cries for a boycott of products derived from petroleum Jim (they got us hooked) Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Thirty-Second_Root { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-7.97709/-0.623008/9.910814/1/33/0 params=1.021897/0/0/1500 float=y maxiter=3500 inside=255 logmap=106 periodicity=8 colors=000A0HA0JA0LA0NA0PA0RA0TA0RA0PA0NA0LA0JA0HA\ 0FA0DA0CA0D00C00C00I00I00I00I00J00J00J00J00L00L00L\ 00L00M00M00M00M00O00O00O00O00P00P00P00P00R00R00R00\ R00M00O00P00R00S00U01W02X04Z05_06a08c09d0Af0Ch0Di0\ Er0Et0Gu1Hw4Jz5Kz8Kz9MzCOzDPzGRzHRzKUzMXyO_tPaoRai\ SadUa_WaWZaR_aMaaHcaDda9fa5ha1iZ0kW9mPMmESo5Zr0Sp0\ Mf0EX18O44G658850A50D50E50J60M81P95UAAXCG_DMcERhGX\ kHcoJiwJhrKfmMdhOccPa_R_WSZRUXMWXJW_DUa9Sc4Rf0Ph0O\ i0Of0Jc4Ea9AZG8WO4UU0Ra0Ph0Ma2JWCGRKDKWrMdrMprMzrM\ zrMzrMzrMwrMvrMtrMrrMprMmrMkrMirMhrMfzaczaaza_zaZz\ aXzaWzaZzaazadzahzakzaozarzavzayzazzazzazzazzazzaz\ zazzazzazzazzazzazzazzazzazzazzazhrzcrzZrzUrwRrrMr\ mHriardarZaraardarharkryorzwrzrrzmrzirzfrzarzZrzWr\ zPrzSrzUrzXvzZyzazzczzfzzhzzizzZzzPzzMzzazzizzrzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzaaa } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 01-12-13 (Alien Sea Creature [A-6,M-6])
by Jim Muth 01 Dec '13

01 Dec '13

FOTD -- December 01, 2013 (Rating A-6,M-6) Fractal visionaries and enthusiasts: There is little to be said about today's image, which is simply the parent fractal that results when the expression Z^(1.044274)+C or Z^(sqrt(sqrt(sqrt(sqrt(2)))))+C is iterated at ground level of the complex hyperladder with no function applied. The image reminded me of a scene in the sea of a hypothetical water world, where a sea creature is swimming toward the surface. The name "Alien Sea Creature" soon followed. The amount of smaller detail in the fractal is striking, especially in the area of the little 'flipper' just below the sea creature's head. This area is most likely to hold minibrots, though due to the slowness, I have not yet checked there. The art and math aspects of the image both rate a 6, which is at least a little above average. The calculation time is a rather slow 3-1/4 minutes, most of which can be saved by checking the FOTD web sites. Save a few minutes by checking the finished image at: <http://www.crosscanpuzzles.com/Archives.html> with curious and interesting variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Heavy clouds and chilly temperatures made today an unpleasant one here at Fractal Central. The fractal cats, who are learning fast how to co-exist in peace, had a day of playing and resting, while the fractal humans did the things humans do on days unfit for outside activity. The next FOTD, most likely another venture into the world of ultra-low exponents, will be posted in the near future. Until we see how near, take care, and keep those drugs and those new electronic gadgets coming. They keep us distracted from the pathetic condition of present-day humanity, and the even worse future that awaits both us and our children. (And I wonder when, if ever, high technology will ride to the rescue.) Jim (negative but blunt) Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Alien_Sea_Creature { ; time=0:03:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident inside=0 center-mag=-10.4062/0.743786/0.1168224/1/40/0 params=1.044274/0/0/525 float=y maxiter=22000 logmap=2 periodicity=10 colors=00000F00G00H00I00J00J00K00K00K00L00L00L00M0\ 0M00M00N00N00N00N00O00O00O00O00P00P00P00P01Q01Q02Q\ 02Q03R03R04R04R05S05S06S06S07T07T08T08T09U09U0AU0A\ U0BU0BV0CW0CX0DY0EZ0F_0G`1Ha2Ib3Jc4Kd5Le6Mf8Ng9OhB\ PjCPkEQlFRmHSoITpKTqLUrNVtOWuQXvRXwTZtU`qVbnWckXch\ YceZcb_c_acXbcUccRdcOecLfcIgcFhcCicLjWUjPwkIarAGlC\ HfEH`FHVHHQJIKKIEMI8OI3PI7SJBUKFWLIZMM`NQbOUdPXgQ`\ iRdkShpSgmTfjUegVddWcbXb_YaXZ`U_`S_bOZcLYdHXfEWgAV\ h7VfCSdHPcLMaQK_VHZZEXcBWg9UcGS_NQXTOT_mUemUlmUrmU\ rmUrmUrmUpmUomUnmUmmUlmUjmUimUhmUgmUfzcdzcczcbzcaz\ c`zc_zcazcczcezcgzcizckzcmzcozcqzcszcszctzctzctzct\ zctzctzctzctzcuzcuzcuzcuzcuzcuzcugmxdmuamrZmpXmmUm\ jRmhcmecmacmccmecmgcmimqkmspmummwjmyhmzfmzcmzamz_m\ zWmzYmzZmz`mzamzcmzdmzfmzgmzhzzazzWzzQzzJzzDzz7zzA\ zzCzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 29-11-13 (Winged Minibrot [A-7,M-7])
by Jim Muth 29 Nov '13

29 Nov '13

FOTD -- November 29, 2013 (Rating A-7,M-7) Fractal visionaries and enthusiasts: Today's venture into the realm of ultra-low exponents takes us down to the world of Z^(1.07071)+C, where we check no farther than ground level of the hyperladder as it appears with no function applied. 0.7071 is the square root of 0.5, though this is of no significance in the appearance of today's fractal. The parent fractal resembles an unbalanced boomerang, with today's image located in the western part of the chaos between the two arms. There actually is a minibrot at the center of the chaos filling the screen, which justifies the name, though it is too small to show up at today's magnitude. This unseen minibrot is shaped like a torpedo and surrounded by patches of chaos of the most chaotic kind. The name "Winged Minibrot" came about when the two large amber elements in the upper part of the frame reminded me of a pair of wings. The art and math aspects both rate a 7, meaning they are worth a look, but nothing that might win a prize. The calculation time of 1-3/4 minutes seems a fair price for the image, though the FOTD web sites can make the price much more fair. In all fairness, the finished image may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Clouds and cold temperatures made today feel like a day from midwinter here at Fractal Central, with a high temperature of 34F +1C that was barely far enough above freezing to make the ice damp. The fractal cats spent the afternoon sleeping and playing, while the fractal humans spent the day recovering from Thanksgiving. The next FOTD will be delayed until at least December 1st. Until whenever, take care, and we must seek out the latest trendy electronic gadgets that we simply must have for Christmas. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Winged_Minibrot { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-7.3593914824083/-1.9453641284373/2.906\ 568e+007/1/171.250 params=1.07071/0/0/525 float=y maxiter=4000 inside=0 logmap=194 periodicity=6 colors=000zbDz`CzbCwZBtaBqWBrYAnTAjOAiT9iQ9cP8hK8f\ J7cH7bF600051665B79G7DL8HQ8LV9P_9SdPQOQVMQ_LQdJQiI\ QnGUsFcwEhrGmnHrjIvfJzaLzYMzUNzQOzLQzHRzDSz9Tz5Uz6\ Sf6Rd6Pa6O_6NX6LV6KS6JQ6HN6GL6FP5GT5HX5I`5Jc5Jg5Kk\ 5Lo5Mr5Mp9LoCKnFJlIIkLHjOGhSFgVEfYDd`CccBbfAai9VkG\ PmMIoSCqYUe_kVagUWdTQaTLZSFWSAYTCZTE_TGaTIbTKcTMeT\ OfUPgURiUTjUVkUXmUZnU`oUapV_qVYrWWsWUsXStXQuYOvYMv\ ZKwZIx_Gy_Ey_DeVTNQgRNhVKhYIiaFieCihAjl7jo5jl9hjCf\ hFdfIbdL`aO__RYYUWWXUU_SSbRVZSYWS_TSbQSeNSgKSjHSmE\ SoBSpH_pNgpToQljShiUdhW`gZWf`SebOddKdVNoMPyLRxKTwJ\ VvIXuHZtG`sFbrFdrEfqDhpCjoBlnAnm9pl9ql8km8en8_n8Uo\ 7Po7Jp7Dp77q72qLP4JLBIHIHDPF9WE5bD1iFEbGRWHcQK`PMY\ POVPRTPTQPVNPXLP_IPaFPcCPfAPh7Pj4Pl2P1_L4ZK7YJAYJD\ XIGWHJWHMVGPVGSUFVTEYTE`SDcRCfRCiQBkQBfO9bM8YK7UI5\ PG4LE3KD4JD4ID4IC5HC5GC5GC5IF9JICLKFMNIOPLPSORVRSX\ UU_XVa_XdbYge_ih`lkannKeW } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 27-11-13 (Moonrise on Vega-4 [A-8,M-9])
by Jim Muth 27 Nov '13

27 Nov '13

FOTD -- November 27, 2013 (Rating A-8, M-9) Fractal visionaries and enthusiasts: Today's image has a math rating of a 9. This is because I have finally checked a world that I long knew existed but have never looked into. Today, for probably the first time, we have a fractal created by iterating an expression with an exponent of Z between zero and +1. In today's image, the iterated expression is Z^(0.7)+C. When rendered in the default manner the parent fractal is a hopeless looking blank screen consisting totally of black inside stuff. But sometimes a hopeless mass of 'inside' stuff can be brought to life by rendering it with an active inside fill such as the 'bof61' I used in today's image. (I believe this fill colors the points according to which iteration comes closest to the origin.) When I did this with today's hopeless parent fractal, I was greeted by perhaps the most chaotic mass of fractal junk I have ever turned up. I can find no themes whatever in the patches scattered about the frame of today's image. The only thing that stood out when I first saw the image was a near perfect circle in the background. I colored this circle a brilliant white and subdued the other colors until I finally had what I saw as a scene on an alien planet. With no particular planet in mind, I named the image "Moonrise on Vega-4", which is a hypothetical world that probably does not exist. The artistic rating of an 8 is a humble reference to the coloring. The exceptional math rating of a 9 indicates that this is my first venture into the world of exponents between zero and +1. The calculation time of 2-1/2 minutes seems about right for an image that rates an 8. But bargain day is here! The wait may be avoided by checking the finished image on one of the FOTD web sites. Take advantage of the bargain. View the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And check the variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Today was a big improvement over yesterday here at Fractal Central, but still nothing to enjoy. The heavy clouds hung around all day, with a raw north wind and a temperature of 39F +4C. A few light sprinkles of rain and flurries of snow were of no consequence. Jasmine, the new fractal cat, began the day with a visit to the doctor, which spoiled her day. Nicholas, the old fractal cat, was thankful that it was not him. The humans spent the day preparing for the thanksgiving feast tomorrow. The next FOTD will be posted when it is ready. Most FOTD's take 24 hours to cook, so I would not be surprised if the next one were to appear in that time. But until whenever, take care, and if a future scientist were to create intelligent life in the laboratory, would it prove that God is not needed to explain man's existence or that intelligent design is necessary to create intelligent life? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Moonrise_on_Vega-4 { ; time=0:02:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=round passes=1 center-mag=+0.422913203/+0.291279598/1388/1/10/0 params=0.7/0/5/0 float=y maxiter=300 inside=bof61 logmap=yes periodicity=6 colors=000ebedcecdebeeafe_geZheYieXjer5Wr6Us6Ts7Ss\ 7Qt8Pt8Nt9Mt9Ln8Oh7Qb7SY6US6WM5ZH4`B4b53d03f24e35e\ 46e57d67d78d89cAAcBAcCBbDCbEDbFEaGEaHFaJG`KH`LH`MI\ _NJ_OK_PLZQLZSMZTNYUOYVOYWPXXQXYRXdZMZRXTKgODq_Hmj\ LiwOeuPeKQesRerSeqTepUeoVenWemXelYejZei_eh`egaefae\ 000PjdOidNgdMfcMdcLccKacJ`bJZbIYbHWaGVaGTa7J`EQ`DP\ `DN`CM_BK_VleUmeTneSoeSqfRoeQmePlezxzVdPVdPVeOWeOW\ fNWfNHJMXgMXgLYgLYhKYhKZhJ5CJZiIZiIYfJXdKWaKV_LJFM\ UVMTTNSQOSOORMPQJQKHQOEROCSNASM7TL5UL3UCAIM6WM7XN8\ XN9YNAZOCZJG_OE`PF`PGaPHbQJbQKcQLdQMdRNeROfRPgSRgS\ ShSTiTUiTVjTWkUYkUZlU_mV`mVanVboWep0KoUboTaoS`oR_o\ RZoQXoPWoOVoNUoNToMSoLRoKPoJOoINoIMoHLoGKoFJoEHoEG\ oDFoCEoBDoACo99nABoBDoBEoCGpCHpDJpDKqEMqFNqFPrGQrG\ SrHTsHVsIWsJYtJZtK`tKauLcuMfvLduLctKatK`sKZsJYrJWr\ IVqITqISpHQpHPoGNoGMnHNpGLnGKlGJjGIhGHfGGdGFbGE`GD\ ZGCXGBVGATG9RG8PG7NG6LI7N } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 26-11-13 (Dying Butterfly [A-9,M-8])
by Brian Prentice 26 Nov '13

26 Nov '13

Here is another view of Jim's extraordinary fractal: http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_62d.png This version is colored a little differently and zoomed out to show more of the detail surrounding the minibrot. Brian Prentice

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FOTD 26-11-13 (Dying Butterfly [A-9,M-8])
by Jim Muth 26 Nov '13

26 Nov '13

FOTD -- November 26, 2013 (Rating A-9,M-8) Fractal visionaries and enthusiasts: In yesterday's discussion I said that the day's fractal was filled with hard to find minibrots. But difficulty is no put-off for me when it comes to finding fractals. Using the 'fmod' method, I found a minibrot on the first inzoom. Today's image shows that minibrot. In the upcoming FOTD's I will show several more minibrots that are equally unlikely. The minibrot lies in the large field of debris extending southwest from the tooth-shaped open area of yesterday's fractal. The fuzziness is partly due to the inherent fuzzy nature of the minibrot itself and partly due to a curious breakdown of resolution in the area immediately surrounding the minibrot. Those using fractal programs with better resolution might be able to clear away part or perhaps all of the fuzziness. In my opinion, the art rating of a 9 is justified. And due to the unexpected complexity of the minibrot, the math rating of an 8 is also justified. The name "Dying Butterfly" describes the first thing I saw in the image. The calculation time of 4 minutes is on the slow side. But the web sites are always there to speed things up to instantly. The finished image is posted online at: <http://www.crosscanpuzzles.com/Archives.html> with various variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Today was unpleasant from dawn to dusk here at Fractal Central. The day began with light snow, which piled up about 3cm before changing to rain in the afternoon, while the temperature slowly rose from 30F -1C to 34F +1C. The fractal cats took a few peeks at the slush outside but spent most of the day sleeping and playing. The new fractal cat Jasmine, (we call her Jazzy), is developing into quite an athletic little feline, leaping a meter (3 feet) into the air after her dragonfly toy. The old fractal cat Nicholas, (we call him Nico), wonders where she gets all her energy. The fractal people spent the day watching the ice come and go. The next FOTD will be posted in the proper time. Since I have no idea what time might be proper, I can give no exact time. Until whenever the proper time arrives, take care, and no one is perfect. People should expect only lies and disappointment from the politicians they choose to be leaders. So to avoid future disappointment, expect nothing, as I did 5 years ago. A nega- tive attitude might be unpleasant, but it is all too often correct. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Dying_Butterfly { ; time=0:04:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-6.362700179650554/-2.356504276722922/\ 1.2e+011/1/45/0 params=1.09/0/0/525 float=y maxiter=16384 inside=0 logmap=373 periodicity=6 mathtolerance=0.05/1 colors=000KchKchKchKaiKaiKaiK`kK`kK`kK`kK_lK_lK_lK\ YnKYnKYnKYnKXoKXoKXoKWqKWqKWqKWqKWqH_kFbdLX_D_T5VO\ 0YJ1ZL2_O4XQ5XT8_U9fXAZ_C_aDddFceHahJ_kKYnNYrLXoKW\ lJUkIThHSgFQdEPcDO`CN_BLXALW9LT8LS6LP5KO4JL3IK2HI1\ GH1FE0ED0DB0BA0A809608A18C48E67H97JC6NE5PI3SK2UN1X\ Q1`T1cW1e_1ha0ke0oh0rk0uo0xr0zu0zs1zs1zr2zr3zr4zq5\ zq6zq9zoAzoBzoCznDzdEynFybIylJylKvkLskNqiOniPkiQhh\ TehUchW`gXYgYWg_Te`Qe`Oe`Ng`Lh`Ki`Jk`Il`HocFocDqXA\ qN8qW4oW3pW2of6nZAlVDkWHhWLebPccT`iXYk`WkeUliWnnYo\ r`ovcrnesghuakv`nx`qy_sz_vzCyzFzzIzzIzzIzzIzzIzzIz\ zOzzOzzOzzOzz`zz`zz`zz`zz`zz`zz`zz`zznzznzznzznzzn\ zznzznzznzznzznzznzznzznzznzznzznzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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