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 Author Topic: split-complex ternary algebra xD  (Read 3736 times) Description: second attempt 0 Members and 1 Guest are viewing this topic.
kujonai
Forums Freshman

Posts: 16

 « on: January 04, 2010, 05:07:12 AM »

With a triplex  a + qb + pc   ←→  (a,b,c)   with a,b,c belong to z (complex)

q^1=+q      q^2=\$p      q^3=\$1
q^4=\$q      q^5=#p      q^6=#1
q^7=#q      q^8=+p      q^9=+1

and  \$1=(-1+i*sqrt(3))/2     #1=(-1-i*sqrt(3))/2

..example for the simple iteration F(n+1)=F(n)^3+k
with F(0)=0 and k belongs to z ....
or how and in what program can i to make this 3d fractal? some suggestions?

good luck to this new year
 « Last Edit: January 04, 2010, 05:08:46 AM by kujonai » Logged
David Makin
Global Moderator
Fractal Senior

Posts: 2286

 « Reply #1 on: January 04, 2010, 01:02:17 PM »

With a triplex  a + qb + pc   ←→  (a,b,c)   with a,b,c belong to z (complex)

q^1=+q      q^2=\$p      q^3=\$1
q^4=\$q      q^5=#p      q^6=#1
q^7=#q      q^8=+p      q^9=+1

and  \$1=(-1+i*sqrt(3))/2     #1=(-1-i*sqrt(3))/2

..example for the simple iteration F(n+1)=F(n)^3+k
with F(0)=0 and k belongs to z ....
or how and in what program can i to make this 3d fractal? some suggestions?

good luck to this new year

If you can write code yourself and use Windows then a free solution is write a formula for either Fractint or ChaosPro, alternatively use Ultra Fractal.
Fractint is also a solution under Linux, I'm not sure what you could use on a Mac.

Note that there are 3D/4D formulas publicly available for all three programs (for say Julibrots or quaternions etc.) that you should be able to adapt.
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The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
jehovajah
Global Moderator
Fractal Senior

Posts: 2749

May a trochoid in the void bring you peace

 « Reply #2 on: January 22, 2010, 08:55:13 PM »

The problem as i see it kujonai is that 3d fractal programmes are based on quaternions or some related set of algebra. So for example to use quaternions you will need to define your p in terms of j. This then may alter your mod (9) ring for q. Unless you can design a programme using a 3d plotter, you will have to adapt your vectors to quaternions with the appropriate scale factors.
 Logged

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!
Timeroot
Fractal Fertilizer

Posts: 362

The pwnge.

 « Reply #3 on: January 23, 2010, 03:04:31 AM »

With a triplex  a + qb + pc   ←→  (a,b,c)   with a,b,c belong to z (complex)

q^1=+q      q^2=\$p      q^3=\$1
q^4=\$q      q^5=#p      q^6=#1
q^7=#q      q^8=+p      q^9=+1

and  \$1=(-1+i*sqrt(3))/2     #1=(-1-i*sqrt(3))/2

..example for the simple iteration F(n+1)=F(n)^3+k
with F(0)=0 and k belongs to z ....
or how and in what program can i to make this 3d fractal? some suggestions?

good luck to this new year

If you can write code yourself and use Windows then a free solution is write a formula for either Fractint or ChaosPro, alternatively use Ultra Fractal.
Fractint is also a solution under Linux, I'm not sure what you could use on a Mac.

Note that there are 3D/4D formulas publicly available for all three programs (for say Julibrots or quaternions etc.) that you should be able to adapt.

Although there are built-in formulas for some 3D/4D fractals in FractInt, you cannot make your own 3D images of them - only 2D slices at a time.
 Logged

Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
David Makin
Global Moderator
Fractal Senior

Posts: 2286

 « Reply #4 on: January 23, 2010, 03:37:37 AM »

With a triplex  a + qb + pc   ←→  (a,b,c)   with a,b,c belong to z (complex)

q^1=+q      q^2=\$p      q^3=\$1
q^4=\$q      q^5=#p      q^6=#1
q^7=#q      q^8=+p      q^9=+1

and  \$1=(-1+i*sqrt(3))/2     #1=(-1-i*sqrt(3))/2

..example for the simple iteration F(n+1)=F(n)^3+k
with F(0)=0 and k belongs to z ....
or how and in what program can i to make this 3d fractal? some suggestions?

good luck to this new year

If you can write code yourself and use Windows then a free solution is write a formula for either Fractint or ChaosPro, alternatively use Ultra Fractal.
Fractint is also a solution under Linux, I'm not sure what you could use on a Mac.

Note that there are 3D/4D formulas publicly available for all three programs (for say Julibrots or quaternions etc.) that you should be able to adapt.

Although there are built-in formulas for some 3D/4D fractals in FractInt, you cannot make your own 3D images of them - only 2D slices at a time.

I thought Fractint's compiler was sophisticated enough to write your own 3D ray-tracing code, but it is a while since I used Fractint
 Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
Timeroot
Fractal Fertilizer

Posts: 362

The pwnge.

 « Reply #5 on: January 27, 2010, 01:53:42 AM »

Nope, the Fractint compiler is pretty weak. Doesn't even allow you to write your own ray-tracing code, because you can't include loops  It's too bad, because it calculates pretty fast.
 Logged

Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
jehovajah
Global Moderator
Fractal Senior

Posts: 2749

May a trochoid in the void bring you peace

 « Reply #6 on: October 08, 2010, 10:23:40 AM »

I wonder if Terry Gintz idynamasz might do the job?
 Logged

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!
jehovajah
Global Moderator
Fractal Senior

Posts: 2749

May a trochoid in the void bring you peace

 « Reply #7 on: January 19, 2011, 11:25:14 AM »

(a+q*b+c*p)^3  i get

a^3+4*a*b*c +2*b*c^2+b^3*(-1+i*sqrt(3))/2+c^3*(-1-i*sqrt(3))/2

(3*(a^2)*b+2*a*b*c +b*c^2)*p

(3*(a^2)*c +b^2*c+3*a*c^2*(-1-i*sqrt(3))/2+(3*(a)*b^2+2*b^2*c)*(-1+i*sqrt(3))/2)*q

Could somebody, or Kujonai check this please?
 Logged

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!
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