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
}