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
}