Russell, Thank you to present my gallery at the list. Triternions are attractive formulas. Gilles ----- Original Message ----- From: "Russell Walsmith" <russw@lycos.com> To: "Fractint and General Fractals Discussion" <fractint@mailman.xmission.com> Sent: Monday, November 07, 2005 18:29 Subject: Re: [Fractint] Triternions Ikenaga and Lambda Thanks for your interest in the triternion formulas, Gilles. List members may enjoy your elegant galleries at http://www.mathsong.com/casaraku/ Ciao, Russell ----- Original Message ----- From: "gilles nadeau" <gillesnadeau56@videotron.ca> To: fractint@mailman.xmission.com Subject: [Fractint] Triternions Ikenaga and Lambda Date: Sun, 06 Nov 2005 02:41:50 -0500
Hello all,
I am new on this list but I use Fractint since 1994. I have difficulty in include/understand English and I use a translator. I would like to propose two new models of "Triternion". T_Ikenaga and T_Lambda. The formulas triternion are mysterious. I read that those would be 6-d. I am not a mathematician and I does not know exactly what that means. Here two formulas.
Gilles Nadeau
T_Ikenaga-XZ {; 6-dimensional M-Set ; based on formulae by Russell Walsmith ; Gilles Nadeau, March, 2005 ; x=y=t=u=v=w=0 cx=real(pixel) cy=real(p1) ct=imag(pixel) cu=imag(p1) cv=real(p2) cw=imag(p2) : tx= x^3+t^3+v^3-3*(x*y^2+t*u^2+v*w^2)+6*(x*t*v-x*u*w-y*u*v-y*t*w) ty=-y^3-u^3-w^3+3*(y*x^2+u*t^2+w*v^2)+6*(y*v*t-y*w*u+x*w*t+x*v*u) tt= 3*(t*x^2-t*y^2+v*t^2-v*u^2+x*v^2-x*w^2)-6*(t*u*w+x*y*u+y*v*w) tu= 3*(u*x^2-u*y^2+w*t^2-w*u^2+y*v^2-y*w^2)+6*(x*v*w+x*y*t+t*u*v) tv= 3*(v*x^2-v*y^2+x*t^2-x*u^2+t*v^2-t*w^2)-6*(u*v*w+x*y*w+y*t*u) tw= 3*(w*x^2-w*y^2+y*t^2-y*u^2+u*v^2-u*w^2)+6*(t*v*w+x*y*v+x*t*u) dx=cx*x-cy*y+cv*t-cw*u+ct*v-cu*w dy=cy*x+cx*y+cw*t+cv*u+cu*v+ct*w dt=ct*x-cu*y+cx*t-cy*u+cv*v-cw*w du=cu*x+ct*y+cy*t+cx*u+cw*v+cv*w dv=cv*x-cw*y+ct*t-cu*u+cx*v-cy*w dw=cw*x+cv*y+cu*t+ct*u+cy*v+cx*w x=tx+dx-x-cx y=ty+dy-y-cy t=tt+dt-t-ct u=tu+du-u-cu v=tv+dv-v-cv w=tw+dw-w-cw z=x+flip(t) z2=y+flip(u) z3=v+flip(w) |z|+|z2|+|z3|<=64 }
T_Lambda-XZ {; 6-dimensional M-Set ; based on formulae by Russell Walsmith ; Gilles Nadeau, March, 2005 ; x=0.5 y=t=u=v=w=0 cx=real(pixel) cy=real(p1) ct=imag(pixel) cu=imag(p1) cv=real(p2) cw=imag(p2) : tx=x*x-y*y+v*t-w*u+t*v-u*w ty=y*x+x*y+w*t+v*u+u*v+t*w tt=t*x-u*y+x*t-y*u+v*v-w*w tu=u*x+t*y+y*t+x*u+w*v+v*w tv=v*x-w*y+t*t-u*u+x*v-y*w tw=w*x+v*y+u*t+t*u+y*v+x*w dx=x-tx dy=y-ty dt=t-tt du=u-tu dv=v-tv dw=w-tw x=cx*dx-cy*dy+cv*dt-cw*du+ct*dv-cu*dw y=cy*dx+cx*dy+cw*dt+cv*du+cu*dv+ct*dw t=ct*dx-cu*dy+cx*dt-cy*du+cv*dv-cw*dw u=cu*dx+ct*dy+cy*dt+cx*du+cw*dv+cv*dw v=cv*dx-cw*dy+ct*dt-cu*du+cx*dv-cy*dw w=cw*dx+cv*dy+cu*dt+ct*du+cy*dv+cx*dw z=x+flip(t) z2=y+flip(u) z3=v+flip(w) |z|+|z2|+|z3|<=128 }
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