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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > Mandelbrot & Julia Set > The 3D Mandelbulb > Theory > Triplex algebra
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Author Topic: Triplex algebra  (Read 46123 times)
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Tglad
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« Reply #120 on: September 22, 2010, 03:11:26 AM »
"I have extended this idea to give 48 different polar forms"
I think you could say there are an infinity of polar forms, and I think it is right to say there is one for each rotation, which is equivalent to rotating the point by this rotation each iteration.

* Mandelbulb.gif (75.09 KB, 70x70 - viewed 1257 times.)
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Softology
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« Reply #121 on: September 26, 2010, 07:25:52 AM »
Have a look at Soler's PDF.  It does show variations that do cover 48 possible variations.  Some of them do match the orginal +SIN -SIN COS etc variations, but the rest are new and do give unique bulb types.  I have included Phase, Theta and Phi scaling/shifting in all the existing bulb formulas and these 48 do give new/unique variations.

Anyway, I hope the next 3D fractal that gets as much publicity as the Mandelbulb comes from these forums.  Keep going guys.  The Mandelbulb and Kaleidoscopic IFS were great examples of someone thinking "what if" outside the scientific community.

Jason.
« Last Edit: September 26, 2010, 07:36:20 AM by Softology » Logged
Nahee_Enterprises
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« Reply #122 on: September 27, 2010, 02:23:11 PM »
Quote from: soler on September 19, 2010, 04:15:35 AM
    Bugman has defined a triplex polar form using a particular matrix product.
    I have extended this idea to give 48 different polar forms.  If you are
    interested then please have a look at:
        http://soler7.com/Fractals/Matrices%20to%20Triplex.pdf

Quote from: soler on September 22, 2010, 02:33:45 AM
    Here is an image from one of the 48 variations:
        //soler7.com/Fractals/3D17/Mandelbulb1585.JPG
    Many more are at:  http://soler7.com/Fractals/3D0.html
    All were made using Visins of Chaos.

Greetings, and Welcome to this particular Forum !!!    smiley

Some nice work you have there.  Looking forward to your future contributions.
 
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KRAFTWERK
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« Reply #123 on: November 23, 2010, 10:45:23 AM »
Quote from: soler on September 22, 2010, 02:33:45 AM
Here is an image from one of the 48 variations:
<Quoted Image Removed>
Many more are at
http://soler7.com/Fractals/3D0.html
All were made using Visins of Chaos.

Wow, nice image! Very interesting!
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Softology
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« Reply #124 on: July 23, 2011, 07:05:41 AM »
Here are another 20 new variations.

http://softologyblog.wordpress.com/2011/07/21/new-mandelbulb-variations/

A few sample images...





Jason.
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Softology
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« Reply #125 on: July 27, 2011, 12:00:11 AM »
27 more new variations
http://softologyblog.wordpress.com/2011/07/27/more-new-mandelbulb-variations/







Jason.
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jehovajah
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« Reply #126 on: July 27, 2011, 01:57:16 PM »
Very nice! Paticularly like the plant analogue. Elvis Presley
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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!
Softology
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« Reply #127 on: August 01, 2011, 02:59:45 AM »
And yet another 16 new varieties.
http://softologyblog.wordpress.com/2011/08/01/even-more-new-mandelbulb-variations/

Jason.
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DarkBeam
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« Reply #128 on: February 26, 2017, 11:34:25 AM »
Note:
For usability sake I merged "Cosine power expansions", "Sine power expansions" and "Triplex algebra" posts and topics because it's incredibly useful to have it all in one topic. Thanks bugman A Beer Cup

Also, the multiplication rule for Cosine formula should be like that;

Code:
a = (z1/r1 + z2/r2); or a = (z1/r2 + z2/r1) ???
r1 = sqrt (x1*x1 + y1*y1); r2 = sqrt (x2*x2 + y2*y2);
xsq = a * (x1*x2 - y1*y2);
ysq = a * (x1*y2+x2*y1);
zsq = z1 * r2 + z2 * r1; or zsq = z1 * r1 + z2 * r2 ???
« Last Edit: February 26, 2017, 05:17:30 PM by DarkBeam » Logged
No sweat, guardian of wisdom!
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