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Author Topic: True 3D mandelbrot fractal (search for the holy grail continues)  (Read 47513 times)
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jehovajah
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« Reply #240 on: October 07, 2010, 08:33:32 AM »

Fracmonk nobody is shunning you, i hope. The interest in this space is waned because we all have a surfeit of the mandlebulb, any of which are a lifetime study! Or rather a playing field.

I am enjoying your work but from afar and am busy on my own interests, so i am sorry if you have been feeling left out. Sometimes pioneering work means a lonely trail.

You say you have updated your paper so repost the link and i will have a look.
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
fracmonk
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« Reply #241 on: October 12, 2010, 07:12:49 PM »

Msg. 239 this thread, end of last page (16).  I feel that this space is a universe unto itself as well.  Maybe each of us will just wind up w. their own.  Hopefully not IN their own, though.  No prospect for mathematical explanations of Mandelbulb outside of "Oh, look what happens when you do this!"?
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fracmonk
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« Reply #242 on: October 14, 2010, 07:22:42 PM »

In the very beginning of my comments on this subject, I mentioned "designer dimensions".  Did a bit of research on the loathsome subject of math terminology, and found that my approach uses "binary arithmetic operations" w. a 2-arity consistent with how the original M-set is generated.  M-bulb & many others use a 1-arity unary math atop it somehow.  (Correct me if I'm wrong about that!)  I don't see consistency in such a dimensional mix. Don't get me wrong- M-bulb is a tremendous mathematical work of art, but is it really a proper extension of M?

Firing squad volunteers line up below.
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fracmonk
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« Reply #243 on: October 19, 2010, 04:38:51 PM »

Most everyone must be by now aware of the passing of our beloved Dr. M. on Thursday, as I heard it reported finally Sunday.  This was my first chance to get back to you.

Below is an account of my own, if you care to indulge me in my own grief.  They say it's better to share these things.

* Losing Dr M 1.doc (29.5 KB - downloaded 124 times.)
« Last Edit: October 19, 2010, 04:41:01 PM by fracmonk » Logged
fracmonk
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« Reply #244 on: October 26, 2010, 05:32:57 PM »

I've spent some time gathering my thoughts for this.  One of the reasons I got involved here was the perception that fractal art, with all its polish, was eclipsing fractal science.  Over the years, I saw the Spanky site fall victim to link rot as New Agers competed to dazzle you with, well, polish over substance.  Often I wonder whether I'm too late.  Looking around this site, I saw a comment that asked whether Dr. M could weigh in on Mandelbulb and give his thoughts on it, but everyone seemed afraid to ask.  I don't know if his health problems were what might have prevented him, but he apparently never did.  If you're one of few who downloaded my own account from the last post, you will see that I also have cause for extra grief for the same lost opportunity.  I would have been greatly honored to get his critique on my own work.  He was primarily a scientist, and I feel that I must be true to the same spirit that drove him.  I tell myself to be patient, and they will come around, as they did for him.

Because of the univerality of M, it shows up easily in odd places, and lends itself to many kinds of extensions.  The one I've been describing to you relies on the behavior of the numbers themselves in iteration, and is more consistent with the original complex dimensions that produce M than any others suggest.  That seems to have gotten yawns so far, and let me tell you, I JUST DON'T GET IT!  Is there something in the water?  I hope that eventually others will realize the significance of this.

Anyway, if I've missed some key thing here, have the decency to let me know.  Everyone has blind spots, and I can face up to mine.  I think I've made a fair case, though.  Again, correct me if I'm wrong.  I can take it.
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miner49er
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« Reply #245 on: October 27, 2010, 01:00:15 PM »

Most everyone must be by now aware of the passing of our beloved Dr. M. on Thursday, as I heard it reported finally Sunday.  This was my first chance to get back to you.

Below is an account of my own, if you care to indulge me in my own grief.  They say it's better to share these things.

Lovely read, thanks :-)

Amazing that you actually get to talk to the fella. He presented a lecture at the University I went to, annoyingly the year before I started.

Sad to see him go but what a legacy he's left us!

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Tglad
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« Reply #246 on: October 27, 2010, 02:03:00 PM »

post #234 made me laugh too.
Narrated narrated narrated
NARRATED

hey I can say it
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fracmonk
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« Reply #247 on: October 28, 2010, 07:20:16 PM »

Tglad & miner49er-  As they say, that was then, this is now.  Narrated.  It seems to work...it may have had something to do w. pix being overposted then.  Why that symptom?  Still beats me!  Glad U got it, though.

Still need more serious and genuine feedback for the math, and plain english about how Mbulb works, since I REALLY want to deal w. the powerful feeling I have that somehow I'm missing something!

Also, colder weather will force me back to more limited internet access, where I will seldom get my hands on equipment that can do uploads and downloads, and I will be forced into verbal-only messages like this one again.

On public computers in some places, they impose this handicap for fear of (shudder) terrorists and hackers (and bears, oh my!)
« Last Edit: October 28, 2010, 07:22:40 PM by fracmonk » Logged
fracmonk
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« Reply #248 on: November 04, 2010, 06:22:40 PM »

The last line of my last post, for those too young or otherwise unfamiliar, is a takeoff of one of Dorothy's lines in the Wizard of Oz.  Another goes something like: "Toto, I don't think we're in Kansas anymore."  I really love that one...

For newcomers to my "notquat" formula, my comments in this thread begin at p.12.  The .frm file to use w. FractInt for 2-d slice images is in p.15, reply# 222, and the most concise version of the paper, again, is @ end of p.16.

6 most basic 2-d views are available in replies 21&22 in "Implementation: 3d Mandelbrot type fractal" thread.

Schlega did some 3-d views in July that can be found in reply 6 in the "Programming" section, under "A Great Need...
He's got some code there, too.  Not familiar w. ChaosPro, I don't know if it's right.  The pix may be, but I think they're under-iterated, and less detailed than optimum.  Can anyone: verify/provide orientation info/elaborate upon/improve, these "possibly historic" images?

That should gather up available info a bit tidier.
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fracmonk
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« Reply #249 on: November 10, 2010, 07:12:50 PM »

There is an observation I'm very fond of, I think from Zen, that says that everything you can see is in the way of something then that you can't.

We still have serious problems, that I earlier bemoaned, with how dimensions are defined, and whether they should be somehow better classified.  Do we speak of directions and distances, on one hand, or of qualities or properties, on the other?

In the former sense, I think most of us here are usually concerned, rather than the latter.  I've talked of 2d & 3d slices of a 4d object, one based on square roots of i.  I often wonder if most dimensions we experience in this world are unseen.

Would anyone be mildly interested in a new thread concerned with CUBE roots of i, (which HAS to be very different somehow, w. my best guess) so that if the M formula were used, one would get a 6d object to look at?  According to Hurwitz, thankfully, there's no division possible.  Please let me know...
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cKleinhuis
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« Reply #250 on: November 10, 2010, 11:06:15 PM »

people, this thread is growing too large, are you ok if i close it, with notice for next thread ?
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divide and conquer - iterate and rule - chaos is No random!
fracmonk
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« Reply #251 on: November 12, 2010, 04:28:22 PM »

Trifox- Glad you're here for this:    It's a serious NEED TO KNOW!

In the core code for the square root of i object I've done, I made a profoundly WRONG 2-character mistake that, copied into all view formulas, makes most of them give WRONG results most of the time.  I only discovered this at the 11th hour of the 11th day of the 11th month, and could not notify til now.  That means that MOST but not all of the pix I posted on this site are WRONG if pretty artifacts, and MANY but not most observations I made based on them are erroneous as well.

I'm posting the corrected version of the .frm with MY DEEPEST APOLOGIES below.  The wonder is that in the previous version, ANY of it turned out basically right.  Up to now, I have become inadvertently guilty of promoting the "designer dimensions" I was so busy complaining about.  There are the same symmetries, though the character of edges, and presumably surfaces in 3d will be different.  I'm also adding sample 2d pix done w the correct version.

* 4dExtsR.frm (5.16 KB - downloaded 70 times.)

* ADR.GIF (7.97 KB, 320x200 - viewed 286 times.)

* BCR.GIF (7.14 KB, 320x200 - viewed 286 times.)

* CDR.GIF (7.19 KB, 320x200 - viewed 286 times.)
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fracmonk
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« Reply #252 on: November 12, 2010, 04:46:10 PM »

To continue,
Oddly, most of the info in the paper I wrote on the subject is still accurate, but I have to review and correct that too.  I've done THOUSANDS of time-consuming pix w that bad code, so as bad as you may feel, being responsible for it makes it that much worse for me.  I will fix this, no matter what it takes.  For those few who have followed my work, I apologize once again.  They say you only hurt the ones you love...

For chaos theory, it seems that small errors can turn into systematic ones.  (see?)

Because of my access problems and other commitments, I won't be able to fix this mess as quickly as I would like.  I will use every moment I can, however, to do so.  I only wish anyone using it might have found it sooner.  The .frm is prefaced w a comment giving the specifics.  I hope no one interested becomes discouraged as a result.  I'm really trying not to myself!

Trifox, in this light, do you have any suggestions?
« Last Edit: November 12, 2010, 04:48:36 PM by fracmonk » Logged
fracmonk
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« Reply #253 on: November 15, 2010, 07:18:04 PM »

More details:

For those interested, it is truly remarkable that my paper will need very little amendment.  The problem is with the code and the pix it creates, not with the theory, concepts, or the math.  Locations cited in earlier posts naturally correspond to a wrong-shaped object and the Julias that are then consistent with IT, and the correct object is apparently completely M-like in its features, now that I've taken a better look at it, having Julias consistent with a correct formulation.

I cannot upload anything right now, and I will be very cautious in future- once burned, twice shy.  This is good advice for anyone.  Check and understand what the code is supposed to do, if you're as serious about it as I am.  If you're not, enjoy the pretty pix, (the OLD ones) even if they're not meaningful in the least.

The paper will be corrected and posted accordingly post haste.  (When it's absolutely right!)
« Last Edit: November 19, 2010, 06:14:42 PM by fracmonk, Reason: (clarification) » Logged
fracmonk
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« Reply #254 on: November 16, 2010, 07:21:11 PM »

Reflecting a bit:
Using the corrected code, you will find that ABR.gif (not shown in post 251) would be the standard M, that ACR & ADR are identical, & that BCR & BDR are in a left-hand, right-hand relationship w. each other.  So it may be the canonical extension of M that eluded us all this time after all.
Despite my being (up to only very lately) the most terrible ambassador for this object, I am sure it can stand on its own now.
I firmly believe that this thread, in all its tortured history, will be judged to have finally found its salvation before the end...

So Trifox, if it makes everything easier, I have no objections to your putting it out of its misery now!

You agree?

Probably better to start again fresh.  Very little will need repeating.
« Last Edit: November 16, 2010, 07:25:50 PM by fracmonk » Logged
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