March 2004 - Fractint - mailman.xmission.com

[Fractint] the cubic mandelbrot cubic connectedness map has views in six planes of wxyz space
by David Lowenstein 08 Mar '04

08 Mar '04

they are, wx, xy, yz, wz, wy, and xz. in terms of rudy rucker's abuv they are ab, bu, uv, av, au and bv. -david http://www.mathcs.sjsu.edu/faculty/rucker/cubic_mandel.htm 3D cross sections are wxy, xyz, wyz, wxz. --------------------------------------------------------------------------------

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cubic mandebrots
by David Lowenstein 05 Mar '04

05 Mar '04

http://www.hypercomplex.org/quats.htm http://www.mathcs.sjsu.edu/faculty/rucker/cubic_mandel.htm

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FOTD 05-03-04 (Cubic Mandelbrot [4])
by Jim Muth 05 Mar '04

05 Mar '04

FOTD -- March 05, 2004 (Rating 4) Fractal visionaries and enthusiasts: Today there is some good news and some bad news. The good news is that I will take steps to assure the unbroken continuity of the daily FOTD's. I will put several images and discussions into a spare directory and hold them for use on the days when I lack the time to find a new image and write a new discussion. The bad news is that it will take several days to create the backup supply of FOTD's. As a result, today's FOTD will be the last until March 9th. On the Fractint list, Tony Hanmer wrote: >In a formula such as MandelbrotMix4, are there enough midgets >to make very tiny jumps from one to the next, such that each >midget stays the same size and orientation but only its surroun- >ding detail changes slightly? This would lead to animations >with a stable midget, which would be amazing to see. The answer is yes. The number of midgets that could be created with the MandelbtotMix4 formula is one of the higher infinities, and animations such as you describe would be fascinating to watch. But making animations with the M-Mix4 formula raises problems. When the parameters are changed, the detail around the midgets does indeed change. And the size and orientation of the midgets remains nearly unchanged. But the midgets jump around in a totally unpredictable manner, and are quickly lost beyond the edges of the screen. As a result, it becomes neces- sary to track the midgets down, and when they are finally found, sometimes with much difficulty, it is nearly impossible to posi- tion them in exactly the same spot on the screen. The resulting animations are jerky and very unpleasant to watch. Not much need be said about today's image. It is a scene in a remote valley in the northwest quadrant of the cubic Mandelbrot set. The image has been running for the last hour while I have been busy at other tasks. The rating of a 4 hardly makes the render time of over 1-1/4 hours worth the effort. The overall value comes in at a nominal 5. The image may be seen with much less effort by viewing it on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But before going there, give Paul a chance to render and post the image. The light rain on Thursday morning ended before noon, leading to a cloudy and mild afternoon. Before venturing outdoors, the dynamic duo checked the temperature and found it was 52F 11C. They decided this was acceptable, and spent several hours in the yard, nibbling the new grass. This morning is starting with similar weather. We shall see what the duo decides. My decision is to attack the pile of work still before me, so until next time, which will not be until March 9th, take care, enjoy fractals while you have them, and be certain you will always have them. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Cubic_Mandelbrot { ; time=1:16:36.22--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotCube passes=1 center-mag=-0.25362329215568170/+1.276686610281370\ 00/2.409843e+009/1/2.49999017136973389/7.615552049\ 72785837e-006 params=0/0/0/0 float=y maxiter=75000 inside=0 logmap=-4088 periodicity=10 colors=000TKUSKVRKWQKXPKYOKZNK_MK`LKaKKcKKeKKgKKjK\ KmMKpOJpQIrWLtUOvWRxYUy_Xza_zcbzeezghzhkzgnzgqzcry\ _sxWtwSuwOvwKwwGxwXywOzwFzw6zu8zs9wqAuoCsmDqkEoiFm\ gFkeGicGgcHedHcfHaiI_kIYmJWoJWmJVkPWhTVcOU`MSZLPVK\ JAJMAIOBHRBGTBISCJSDKSEMRFNRGORHQQIRQJSQKTQL`VJh_I\ odHl_MiVRgRWcTU_VSYXQWZOX`MYbKZdI_fG`hEagIbfLceOdd\ RecVfbYga`h`ci_gjZjkYmlYpmXnmWlmVjmUhmTfmSdmRbmQ`m\ PZmOXmNVmMTmLRmKPmJNmIMmESmAXmDUmFRmHOmJLmLJmNGmPD\ mRAmT8mQ7mO7mM6mK9mICmGFmEImCLmAOmERmIUmMXmQ_mUbmY\ em`hmdkmhnmlqmptmtwmwzmvzmuzmtzmszmrzmqzmpzmozmnzm\ mzmlzmkzmjzmizmhzmhzm`zmUzmNzmGzm9zmBzmDzmFzmHzmJz\ mLzmNzmOzmRzmOzmMzmJzmHzmEzmCzmAzmCzmEzmGzmIzmKzmM\ zmOzmPzmRzmTzmVzmXzmZzm`zmazmZzmXzmVzmTzmUzmUzmUzm\ UzmUzmUzmUzmUzmUzmRzmNzmJzmEzmAzm6zm9zmCzmFzmIzmLz\ mNzmQzmTzmWzmZzmazmczmXzmQzmJzmCzm6zm8zm9zmAzmCzmD\ zmEzmGzmHzmIzmKzmLzmMzmMz } frm:MandelbrotCube {; Jim Muth real(c),imag(c) z=p1, c=pixel+p2: z=z*(sqr(z))+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

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FOTD & Midgets
by Tony (Anthony) Hanmer 05 Mar '04

05 Mar '04

Greetings Jim, I admit to being fascinated by the endless supply of regular midgets from which you feed us, each with its own entirely novel surrounding! For a while, long ago, I found myself lazily wishing that you'd apply such creativity to other fractal types; but then I got into the rhythm of the FOTD and reached the above conclusion. Which leads me to my question. In a formula such as MandelbrotMix4, are there enough midgets on hand to make very tiny jumps from one to the next, such that each midget stays the same size and orientation but only its surrounding detail changes slightly? This would lead to animations with a stable midget, which would be amazing to see. Tony Hanmer Tbilisi, Republic of Georgia _________________________________________________________________ Tired of spam? Get advanced junk mail protection with MSN 8. http://join.msn.com/?page=features/junkmail

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FOTD 04-03-04 (High-Order Valley [3.5])
by Jim Muth 04 Mar '04

04 Mar '04

FOTD -- March 04, 2004 (Rating 3.5) Fractal visionaries and enthusiasts: With the work still backed up, I had time for only an almost- automatic trip into the Mandelbrot set. My destination was the eighth valley out the negative X-axis, where I stopped and found a midget near the surface of a spiral. The broken, chaotic nature of the scene is typical of the area, which is one of the most difficult to explore in the M-set. The maxiter of the image is an immense 250,000, and even this fails to fully resolve the midget at the center. The logmap of close to a negative 34,000 confirms the difficulty of the area. Since I put almost no effort into the image, and because such fractals have been seen often, I could rate the image no higher than a 3.5. I gave the image a fractional rating to spare it the indignity of a rating of a shameful 3. When the render time of 39 minutes is considered, the overall value comes in at a not very impressive 8.9. I named the image "High-Order Valley" because it is located in a valley of high order. The best way to see the image is to download it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday and Wednesday were quite pleasant here at Fractal Central, and the cats enjoyed the conditions to the utmost. But this morning is starting with a light rain. The cats already look unhappy. I'll be unhappy until I finish the pile of work before me. Until next time and next fractal, take care, and things will get better. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= High-Order_Valley { ; time=0:39:23.39--SF5 on a P200 reset=2003 type=mandel passes=1 center-mag=-1.40114016879128400/+0.000003334519280\ 19/1.183764e+011/1/132.500439777237176/-0.00037265\ 1854078746847 params=0/0 float=y maxiter=250000 bailout=9 inside=0 logmap=-33650 periodicity=10 colors=00060R00U00W00Z03a06d09g0Bj0Em0Hp3Ks6Nv9RyB\ UzEWzHWzKUzNUyRRvURsWNpZNmaKjdKggKgjHmmEpmBspBvp9z\ s6zv3zv3zy0zy0zz0zz0zzBzzUzzgzztzztzzszzrzyqzsrzjs\ zdtzZuzRvzKszEmz6iv0dp0Zj0Wd0RZ0KU0HN0BH09E0djazzm\ zzmzzdzyKza3vH0m00d00R00U00W00Z00Z00a00d00g00g00j0\ 0m00p00p00s00v00y00y00z00z00z00z00v00m00d03WBENRUE\ dg6ps0zz0zz0zz0zz0zz0zz0zz0zz0zz0vz0mz0dz0Uz0Kz0Bz\ 03z00z00z00z00z00z00z00z00z30z60zB0yH0pN0zmHza0jR0\ U90RB0NE0NH0KK0KK0HN0HR0EU0BW0BW09Z09a06d06d0Bd0Hg\ 0Kj0Rm0Up0Zs0av0gy0mz0pz0vz0yz0zz0zz0zz0vz0jz0Zz6N\ zEBzR0zZ0zj0zp0zs0zv0zy0zz0zz3zz6zzBzzHzzNzzRzzWzz\ azzdzzjzzpzzvzzyzzzzzzzzzzzzzzzzzzzzzzzzzzyzsvzjsz\ amzUjzKgzBdz3az0Zz0Wz0Uz0RzKWzNZzNdzNgzNmzRpzRvzRy\ zRzzUzzUzzUzzUzzWzzWzzWzzKzzWzzdzzmzzvzzzzzzzzzvzz\ pzzmzzjzzgzzdzzazzZzzZzzWzzUzzRzzNzzKzzKzyHzsEzpBz\ j9zgBzZ9zd9zg6zj6zm3zp3zs } END PARAMETER FILE=========================================

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just a question
by David Lowenstein 03 Mar '04

03 Mar '04

what is the 32-bit color version of a map? http://spanky.triumf.ca/pub/fractals/formulas/noel1.frm http://www.mathcs.sjsu.edu/faculty/rucker/cubic_mandel.htm I think Noel giffin should call his inductive fractals rudt sets since they both come from the same diagonalization. -david

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chaos download and rudy set
by David Lowenstein 03 Mar '04

03 Mar '04

http://www.mathcs.sjsu.edu/faculty/rucker/chaos.htm

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[Fractint] you can get the chaos soucecode and program at rudy rucker's website.
by David Lowenstein 03 Mar '04

03 Mar '04

It also has info on cubic mandelbrots and the rudy sets. -david

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No FOTD for 03-03-04
by Jim Muth 03 Mar '04

03 Mar '04

Fractal fans: Due to the non-fractal work load, there will be no FOTD for March 3. This time I will not unexpectedly post a FOTD at a later hour. The next fractal will appear on schedule on March 4. As soon as I can get around to it, I will put aside a couple extra images and discussions to post in a hurry on very busy days like today. Take care and see you in 24 hours. Jim M.

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multifractals?
by David Lowenstein 03 Mar '04

03 Mar '04

http://www.angelfire.com/nc/HUMMINGBIRD1/images/multifractal.jpg http://munin.hsh.no/home/gw/public_html/proj/two_phase_flow2.html http://bg.mypagesonline.com/multi/ http://www.physionet.org/tutorials/multifractal/dimension.htm when several different distorted fractals appear in the same object, is this a multifractal? -david

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