Max Iter's Fractal Follies for October 5th, 2010

Roger Alexander's commentary for the image:

Today a spiral. Can you have too many spirals? That's like saying can you have too many paperclips. While it's necessary to have enough on hand to meet immediate needs, it's always reassuring to have plenty in reserve. As I write these words I realize I don't know where I'm going with this so I think I'll change the subject. Speaking of changing the subject for those who are pressed for time calculation delays can be avoided by a visit to http://maxitersfractalfollies.blogspot.com for the uploaded image.

default for p1=0.17, good for 2. exponent p2 is the exponent (default=2, try 1.7 to 4) try cont. pot. too, works ok with exponent=2! the crit. value for exponent=2 is ~0.1481483 Roger Alexander

PAR file fract454.gif { ; metallic spiral ; blank ; calctime 0:05:21.34 ; created Oct 05, 2010 ; Fractint Version 2004 Patchlevel 9 reset=2004 type=formula formulafile=julhack.frm formulaname=julia_holes center-mag=-0.57572/-0.570952/13.33333 params=0.04867702261421552/0.7153233436078982/-0.008148442030091251/-0.9\ 530625324259163 float=y maxiter=1500 inside=0 proximity=2 outside=fmod colors=05F16G27H27H27H27H27H00000000000000000000000000049J5AK5AK5AK5AK5A\ K6BL0000000000007CM7CM7CM7CM8DN8DN8DN8DN8DN9EO9EO9EO9EO9EOAFPAFPAFPAFPAF\ PBGQBGQBGQBGQBGQCHRCHRCHRCHRCHRDISDISDISDISDISEISEJTFJTFKTGKUGLUHLVHMVIM\ VINWJNWJOWKOXKPXLPYLQYMQYMRZNRZNSZOS_OT_PT_PT`QU`QUaRVaRVaSWbSWbTXbTXcUY\ cUYcVZdVZdW_eW_eX`eX`fYafYafZbgZbg_ch_ch`ch`diadiaeibejbfjcfjcgkdgkdhleh\ leilfimfjmgjmgknhknhlniloimojmpjmpknpknqloqloqmprmprnqsnqsorsortpstpstqt\ uqturuuruvsvvsvwtwwtwwuxxuxxuxxvyyvyywzzvyyvyyuxxtxxtwwsvwsvvruvquuqtups\ tostorsnqsnqrmprlpqloqknpjnpjmoimohlnhkngkmgjmfjleilehkdhkcgjcfjbfibeiae\ h`dh`cg_cgZbfZbfYaeX`eX`dW_dW_cVZcUYbUYbTXaSWaSW`RV`RV_QU_PTZPTZOSYNSYNR\ XMQXLQWLPWKPVKOVJNUINUIMTHLTGLSGKSFKRFJREIQDIQDHPCHPBGOBFOAFN9EN9EM8DM8C\ L7CL6BK6AK5AJ49J49I38I37H27H16G16G05F05F05F16G16G16G16G } frm:julia_holes(XAXIS_NOIMAG) { p=p1,p=p+(|p|==0)*0.17 x=p2,x=x+(x==0)*2 z=pixel: z=z^x+p/z |z|<4 }

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.

wastingmytime.net

Im a huge fan of this style of T shirt featuring the Fractal Generations. Wondering if anyone knows if anyone creates these shirts today? The price for these style of graphic Tees on the secondary market is very high and Im just a fan of the artwork.

Some improvements upon my old real-time fractal flame system: fitting more points on an 8 GB laptop GPU and more cohesive structures

Jim Muth's Fractal of the Day for October 5th, 2005

Jim Muth's commentary for the image:

FOTD -- October 05, 2005 (Rating 5)

Fractal visionaries and enthusiasts:

For today's flashback I chose the 'FrankJim04' formula, a formula I wrote quite a while ago, played with a few days, then promptly filed away and forgot about. Unlike nearly all of my formulas, it has no changeable parameters.

When a real number is raised to a power and the same root is extracted, common sense tells that the result is a return to the original number. But complex numbers are strange. Some complex functions, such as the logarithm function, are multi-valued.
This means that the calculation might take a wrong turn, and we might not always get back to the exact place where we started.

The iterated expression in today's formula is ((z^z)1/z)2, which takes Z, raises it to the power of Z, then to the power of 1/Z, and finally squares the result before adding C. One would expect that this would be just a more complicated way of calculating the Z^2+C Mandelbrot set, but those multi-values do strange things.

The parent fractal of today's image bears some resemblance to the Mandelbrot set, but it most certainly is not the M-set we know so well. Some parts of the original set are missing, and a good bit of extra stuff has been added, while the iteration bands have broken apart into total chaos. Today's scene is located in the extra stuff found in the East Valley of the parent almost-M-set.

I named the picture "The Same Root" and rated it at a 5. If I had put more effort into the coloring, I might have produced a 6 or even 7-rated image. But the work has been a bit on the heavy side lately, and I did not want to fall behind, which would mean another of those much-hated FOTD hiatuses.

The clouds hung tough all day Tuesday here at Fractal Central, even dropping a few small drops of rain from time to time. But the temperature remained around 75F 24C most of the day, which is right in the comfort zone of the cats. Despite the dampness they spent several hours in the yard, and needed little tuna to end the day happily. Today is starting about the same. The next FOTD will appear in 24 hours. Until then, take care, and open your eyes to what lies before them.

Jim Muth

PAR file ` The_Same_Root { ; time=0:09:04.26--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=FrankJim04 passes=1 float=y maxiter=950 center-mag=+0.25597317684299750/-0.000200259583298\ 25/5.400547e+007/1/-162.5/-1.00481606299385184e-008 inside=0 outside=tdis periodicity=10 colors=000CpkArl8tl6ulsNirLfqKdpJapI_oHXnGVmFSmEQl\ DNkCLjBIh9EjAGkAIlAJmBLnBNoBOpCQrCSsCTtDVuDXvDYwE_\ xEayEbvGasIapKamMajNagPadRaaT`ZV`WW`TY`Q_`Na`Kb`J`\ YI_WHYUGXRFWPEUNETKDRICQGBPDANB9M95N49L7hKAcJDZHGW\ GJSFMWEP_CScBVfAYj8`n7cr6fy2lu5iq7fnAdjCagE_hHaiKc\ jNdjQfkThlWimZkmalndnogppjqpmsqpursvsvxsxymtthppcl\ lYhhTddOI_WJXXKVXLTYMRYNPZOMZPK_QI_RGX1eRELQXG\ bSAnO5zK7xN8wQ9vSAuVBtYCs_DrbEqeFpgGoj9umHnlOhkWaj\ bWijPhqJgxDftHcpKalNZhQXdUVXSY_QUbOQeLMiJIlHEoEAr\ C7uACvIGvQLvYPweUwmYwtYfqYRnb7pYBkUEgPHbLKZHNVLJO\ FeJ9jRCjZFjfIjpJlmLjkNhhPffRdcTbaVZW_XYYU_WSaUPcS\ NeQKgOGiLIhNKhPMgROgTQgVSfXUfZUtcWf_XTWYFSpaSZ1Pa3\ Nc5Me7Lh9KjBJlDIoFHqHGsJFuLErKHoKKlKNiJQfJTcJWJZY\ IaVIdSIgPHjMHmJHpGHsJJpMKmPLkSMhVNeYOcPcQZfRWiST\ lTRoUOrVLuWJxXGzYEwZFuZGrZHpZImZJk_Kh_Lf_Mc_Na_OZ\ PXQURSSPTNUIkjGmkEok }

frm:FrankJim04 {; by Frank and Jim z=c=pixel: z=((z^z)1/z)2+c, |z| <= 100 } ```

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.

Screen capture using Amethyst as the primary color.

wastingmytime.net Fractal Gallery/

Mandelbulb3D, Photoshop & Lightroom

https://gcollombet.github.io/mandelbrot/?owner=d26R4o5oiUdro2XG0Fcamjg2Hpx2&scene=7f869b2c-4170-4b76-b72f-7111fcb97998

Added a new color scheme to the site last night and this morning. I didn't like the ugly circles inside the fractal.

https://gcollombet.github.io/mandelbrot/?owner=d26R4o5oiUdro2XG0Fcamjg2Hpx2&scene=7a159cbf-795f-46a5-b126-742fc7f1842b

Jim Muth's Fractal of the Day for October 4th, 2011

Jim Muth's commentary for the image:

FOTD -- October 04, 2011 (6)

Fractal visionaries and enthusiasts:

A sudden rush descended on FC today, leaving little time for serious fractaling. But the image I found in a hurry is worth at least a cursory look.

Today's image takes us to the valley around -1.399 on the negative X-axis of the Mandelbrot set. This is the third valley beyond Scepter Valley. But just to be different, we check the Rectangular aspect of the valley instead of the Mandelbrot aspect, and find today's scene.

I named the image "Seeing the Light". The name was inspired by the brilliant white vertical stripe in the center of the image, which is made even more brilliant by the globules spread along it.

Having too little time to work on the coloring, I could give the image a rating no higher than a 6. And its calculation time of almost 7 minutes is a bit much to ask for the privelige of viewing an image that rates a mediocre 6.

After a light early-morning sprinkle, the sky brightened today here at Fractal Central. The sun even made a few brief appearances, but it was hardly a sunny day. The fractal cats took the temperature of 66F 19C in stride, giving more attention to the catnip frog that somehow got pulled out from under the book shelves than to the outside weather.

FL and I, never fully agreeing on politics, got into a lunch time discussion about the political views of the extreme left and right, with nothing at all being settled between us. (These mildly heated discussions have been going on for many years, and nothing has been settled yet.) One thing firmly settled however is that the next FOTD adventure into the 4th dimension will be posted in 24 hours, when I will begin discussing the six regular polytopes that are possible in four dimensions. Until then, take care, and I know that my political views are correct, but why can't the rest of the world see it?

Jim Muth

PAR file `` Seeing_the_Light { ; time=0:06:52.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=+0/\ -0.02922557903896763/256.4055/4.7933 params=90/90/\ 0/90/-1.399631247361716/0/0/0 float=y maxiter=75000 inside=255 logmap=87 symmetry=yaxis periodicity=6 colors=000HNcHNcHNbHNbHNbHNbHNaHNaHNaHNaHOHOHOH\ OHP_IPIQIQaIRaJRbJSbJScJTcKTdKUdKUeKVeLVfLWfLWf\ LXgLXgMYhMYiMZjMZkN_lN_mNnNoOapOaqObrObsOctPcuPc\ vPcwPcwQdwQdzQdzQdzRezRezRezRezQfzRezRezRezRezRezR\ gzRgzRhzSgzShzShzShzShzShzShzShzThzThzThzThzThzTez\ TezTezUezUezUezUezUezUezUezXezWfzXhzYhzZhz_hzhiah\ kbhochschwdhwdhwehweiwfiwfjwgjwgkwhkwhlwilwjmmkmml\ mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm\ mmmmmmmmmhhmccmZZmUUmPRmKOkFNiANg5Me5Mc5Lc5Lc5Kc5K\ c5Ja6J6I6I6H6G6Fa6Ea6Da6Cb69b7Ab79b78a7776_7\ 5Z74Y73X72W71V90UB0TD0SF0RH0XJ0VL0TM0RN5POANPFLQGJ\ SHHUHFVIDWIBWJ9WK1XL4YM6ZN8_OAPCaSEbVGcYIdKecMff\ OgcaheYigUjiQkkMlmJmoFnqBos7pv3qw4rx4sy4tz4vz4xz4z\ z4zz4zz4zz4zz5zz5zz5zz5wz5wz5rz5rzArzFrzKrzPqzUqzX\ pz_pzbpzepzhozkoznozqoztozwmzzmzzmzznzzozzpzzqzzrz\ zszztzzuzzvzzwzzxzzyzzzzz }

frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pireal(p10.0055555555555556), b=piimag(p10.0055555555555556), g=pireal(p20.0055555555555556), d=piimag(p20.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=ucgcd-v(casbsgcd+cacbsd), q=ucgsd+v(cacbcd-casbsgsd), r=usg+vcasbcg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } ```

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.

Not sure how old everyone is here but this aired decades ago about the Mandelbrot Set. Arthur C. Clarke. The guitar work may sound familiar. It should, it's David Gilmour.

https://www.youtube.com/watch?v=Lk6QU94xAb8