Title: split-complex ternary algebra xD Post by: kujonai 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 $1=(-1+i*sqrt(3))/2 #1=(-1-i*sqrt(3))/2 ..example for the simple iteration F(n+1)=F(n)^3+k with F(0)=0 and k belongs to z .... or how and in what program can i to make this 3d fractal? some suggestions? good luck to this new year :D Title: Re: split-complex ternary algebra xD Post by: David Makin on January 04, 2010, 01:02:17 PM With a triplex a + qb + pc ←→ (a,b,c) with a,b,c belong to z (complex) ;) q^1=+q q^2=$p q^3=$1 q^4=$q q^5=#p q^6=#1 q^7=#q q^8=+p q^9=+1 and $1=(-1+i*sqrt(3))/2 #1=(-1-i*sqrt(3))/2 ..example for the simple iteration F(n+1)=F(n)^3+k with F(0)=0 and k belongs to z .... or how and in what program can i to make this 3d fractal? some suggestions? good luck to this new year :D If you can write code yourself and use Windows then a free solution is write a formula for either Fractint or ChaosPro, alternatively use Ultra Fractal. Fractint is also a solution under Linux, I'm not sure what you could use on a Mac. Note that there are 3D/4D formulas publicly available for all three programs (for say Julibrots or quaternions etc.) that you should be able to adapt. Title: Re: split-complex ternary algebra xD Post by: jehovajah on January 22, 2010, 08:55:13 PM The problem as i see it kujonai is that 3d fractal programmes are based on quaternions or some related set of algebra. So for example to use quaternions you will need to define your p in terms of j. This then may alter your mod (9) ring for q. Unless you can design a programme using a 3d plotter, you will have to adapt your vectors to quaternions with the appropriate scale factors.
Title: Re: split-complex ternary algebra xD Post by: Timeroot on January 23, 2010, 03:04:31 AM With a triplex a + qb + pc ←→ (a,b,c) with a,b,c belong to z (complex) ;) q^1=+q q^2=$p q^3=$1 q^4=$q q^5=#p q^6=#1 q^7=#q q^8=+p q^9=+1 and $1=(-1+i*sqrt(3))/2 #1=(-1-i*sqrt(3))/2 ..example for the simple iteration F(n+1)=F(n)^3+k with F(0)=0 and k belongs to z .... or how and in what program can i to make this 3d fractal? some suggestions? good luck to this new year :D If you can write code yourself and use Windows then a free solution is write a formula for either Fractint or ChaosPro, alternatively use Ultra Fractal. Fractint is also a solution under Linux, I'm not sure what you could use on a Mac. Note that there are 3D/4D formulas publicly available for all three programs (for say Julibrots or quaternions etc.) that you should be able to adapt. Although there are built-in formulas for some 3D/4D fractals in FractInt, you cannot make your own 3D images of them - only 2D slices at a time. Title: Re: split-complex ternary algebra xD Post by: David Makin on January 23, 2010, 03:37:37 AM With a triplex a + qb + pc ←→ (a,b,c) with a,b,c belong to z (complex) ;) q^1=+q q^2=$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 :D 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 :) Title: Re: split-complex ternary algebra xD Post by: Timeroot 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.
Title: Re: split-complex ternary algebra xD Post by: jehovajah on October 08, 2010, 10:23:40 AM I wonder if Terry Gintz idynamasz (http://www.mysticfractal.com/iDynaMaSZ.html) might do the job?
Title: Re: split-complex ternary algebra xD Post by: jehovajah 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? |