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fracmonk
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« Reply #15 on: December 14, 2010, 02:32:55 PM » |
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(via bunneemail)
To continue last post, a couple more views of -1+0i+0j+.25ij, and the M equivalent and its julia, converted to complex.
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« Last Edit: December 15, 2010, 05:01:11 PM by fracmonk, Reason: no infringement »
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fracmonk
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« Reply #16 on: December 20, 2010, 07:46:45 PM » |
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Jesse recently informed me of his intension to make these formulae available in the Mbulb collection as "CommQuat", if I've got it right, and if it turns out right, I think. Look for it, as I myself suffer from limited access, as you may know. I'd love to see results from it! Thanx in advance...
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fracmonk
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« Reply #17 on: January 04, 2011, 07:22:45 PM » |
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Has the search expired?
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fracmonk
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« Reply #18 on: January 26, 2011, 04:41:09 PM » |
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For those interested, I've done some curious work that can be found on this site under: Theories and Research->Is there anything novel left...which has 3d & 4d application potentials.
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fracmonk
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« Reply #19 on: March 09, 2011, 04:29:25 PM » |
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Found a new approach based on 4-param constant, 2 real, 2 imag, anyone interested?
In case there are any Python fans present, it's "...something completely different." ...
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« Last Edit: March 09, 2011, 04:32:54 PM by fracmonk »
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fracmonk
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« Reply #20 on: March 18, 2011, 03:24:03 PM » |
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Since I do everything in 2-d anyway, I've decided to post this new bit in the "New Theories and Research" section, under "Is there anything novel..." -look at all the cobwebs!
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fracmonk
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« Reply #21 on: September 01, 2011, 07:18:12 PM » |
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So I was wondering- is there anything in the voluminous fractalforums "grail"-related archives about initial z value providing a 3rd and 4th dim. if you know offhand?
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David Makin
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« Reply #22 on: September 02, 2011, 03:34:56 AM » |
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So I was wondering- is there anything in the voluminous fractalforums "grail"-related archives about initial z value providing a 3rd and 4th dim. if you know offhand?
If you mean complex fractals with 2 dimensions as start z and 2 as c then that object (and related ones other than z^2+c) has been around since the early days of Fractint i.e. at least 15 years (probably a lot longer - I started late, only 1999) and is generally referred to as a Julibrot. Here's an animation displaying 3D slices of the said 4 dimensions - in each case two are "fixed" as the correct axes and the third visual dimension taken as a line in the plane of the remaining two, the animation is produced by rotating the line from matching one of the spare dimensions around to the other e.g. x = real(starz), y = imag(startz), initial frame z = rea(c) intermediate frames z = line in plane of c at angle a (going from 0 to 90), final frame z = imag(c). Unfortunately the results have as much or even more "whipped cream" than quaternions, in fact I personally suspect that the surface is only ever fractal in one given direction. Here's the animation:
<![CDATA[<a href="http://www.youtube.com/v/gr-ul7sZDwc&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/gr-ul7sZDwc&rel=1&fs=1&hd=1</a>]]> |
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KRAFTWERK
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« Reply #23 on: September 03, 2011, 10:42:34 AM » |
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Jesse recently informed me of his intension to make these formulae available in the Mbulb collection as "CommQuat", if I've got it right, and if it turns out right, I think. Look for it, as I myself suffer from limited access, as you may know. I'd love to see results from it! Thanx in advance...
Hello Fracmonc Just want to inform you that your CommQuat is one important third of my mug-awarded Fractal Wasp Troll.  Thank you for your great work! Johan |
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fracmonk
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« Reply #24 on: September 06, 2011, 05:20:16 PM » |
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David- I had wrote my own formula q+d & made a series of 2-slices (as I do) for a range of incremented real z0. Off z0=0, I found that a distance for real z0 yielded the same for pos or neg, so that those 3d had the corresponding symmetry. I thought that Julibrots might be a bit different, but, I guess, no...
Kraftwerk- I didn't know it was a source of your prizewinner, and am that much happier 4 U. That you could make it look that inviting is satisfying to me in the extreme! And thanx!
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KRAFTWERK
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« Reply #25 on: September 07, 2011, 11:48:13 AM » |
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...
Kraftwerk- I didn't know it was a source of your prizewinner, and am that much happier 4 U. That you could make it look that inviting is satisfying to me in the extreme! And thanx!
I thought about mentioning it to you before, sorry about me being so late. Glad you appreciate it, I for sure appreciate your work even if I have some problems following the maths!  This is why I did my series "The Mathematician", "The Programmer" and "The Artist", this is what fractalforums are all about, a beautiful symbiosis! I have used the CommQuat in some more of my images, I will send you all links if you are interested... You are welcome, and again, thank you! |
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fracmonk
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« Reply #26 on: September 14, 2011, 12:10:21 AM » |
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Kraftwerk- I'm sorry for not answering your last post sooner. Yes, I'd love to see more, naturally. I understand about not being prompt, but we have to meet other demands...the math is not so bad, for + &-, very simple, for x, a bit complicated, but div. is a bear, and needs review.
Later!
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KRAFTWERK
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« Reply #27 on: September 14, 2011, 08:55:56 AM » |
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Kraftwerk- I'm sorry for not answering your last post sooner. Yes, I'd love to see more, naturally. I understand about not being prompt, but we have to meet other demands...the math is not so bad, for + &-, very simple, for x, a bit complicated, but div. is a bear, and needs review.
Later!
No problem fracmonk, if I do not follow the math all the time, but that is my problem, I am a novice learning more for every day here.  Links to more images including the CommQuat: http://MANDELWERK.deviantart.com/art/Royal-Monstrous-Coagulation-211226065http://MANDELWERK.deviantart.com/art/The-Rose-with-the-Pearl-253973564http://MANDELWERK.deviantart.com/art/The-burden-of-intellect-256020712http://MANDELWERK.deviantart.com/art/Fighting-Fractal-Gods-201017720Now I will not hijack your thread any more! |
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fracmonk
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« Reply #28 on: September 14, 2011, 06:16:36 PM » |
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K- I'm only peeking in here on the run- thanx 4 the linx, & perish the thought of "hijacking" the thread, (it's not "mine"). Anyone with something to say should ALWAYS feel free to make a contribution to the "cause"...
Take care, O.K.?
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Alef
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« Reply #29 on: December 08, 2011, 04:53:16 PM » |
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fractal catalisator
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True 3D mandelbrot fractal (search for the holy grail continues)
The 3D Mandelbulb
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November 25, 2010, 12:57:55 AM
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