# No subject

Sat Mar 19 21:51:29 CET 2011

```(guess this explains my bad grammar)

A*B=3DC
where
A:[x1,y1,z1]
B:[x2,y2,z2]
C:[x,y,z]

[x1,y1,z1] * [x2,y2,z2] =3D [x,y,z]

x =3D (x1*x2) - (y1*y2) - (z1*z2)
y =3D (x1*y2) + (y1*x2)
z =3D (x1*z2) + (z1*x2)

Correct only if A and B are the same
Or if x1,y1,z1 are the same and
x2,y2,z2 are the same
and a few other cases
otherwize magnitude of x,y,z
is slightly different than A * B
********************************************END OF HISTORY

START OF CODE SNIPET*******************************************************=
**************
void mandelbrot::iterate(void)
{

int vtxi;

long int p,q,r;
int n;
double k,l,x,y,z,newx,newy,newz;
double m;

vtxi=3D0;

for(r=3D1; r<depth; r++)
{
for (p=3D1; p<width; p++)
{
for (q=3D1; q<height; q++)
{
if(julia=3D=3D0){
k=3D(double)x1+(x2-x1)*p /(width);
l=3D(double)y1+(y2-y1)*q /(height);
m=3D(double)z1+(z2-z1)*r /(depth);

x=3Drealp;
y=3Dimagp;
z=3Dkapap;
}else{

x=3D(double)x1+(x2-x1)*p /(width);
y=3D(double)y1+(y2-y1)*q /(height);
z=3D(double)z1+(z2-z1)*r /(depth);

k=3Drealp;
l=3Dimagp;
m=3Dkapap;
}

for (n=3D1; n<numits; n++)
{
//newx=3Dx*x-y*y+k;
//newy=3D2*x*y+l;

//6-9-2002 equation

newx=3D((y*z)+(z*y))+k;
newy=3D((x*z)+(z*x))+l;
newz=3D((x*y)+(y*x))+m;

/*
*  2000 equation
*/

/*
*   newx=3D((x*x)-(y*y)-(z*z))+k;
*   newy=3D((y*x)-(z*y)+(x*z))+l;
*   newz=3D((z*x)+(x*y)-(y*z))+m;
*/

/*
*  1996 equation - see history
*/

/*
* newx=3D((x*x)-(y*y)-(z*z))+k;
* newy=3D((x*y)+(x*y))+l;
* newz=3D(x*z)+(x*z)+m;
*/

x=3Dnewx;
y=3Dnewy;
z=3Dnewz;

//putpixel(surface, p+startx-1,q+starty-1,n);

//putpixel(surface,(int)(x*10+160),(int)(y*10+100),(unsigned char)n);

if (x*x+y*y+z*z>magnitude)
{
if((n>lowcolor)&&(n<highcolor))
{
vtx[vtxi].x=3D(p/scaledivisor);
vtx[vtxi].y=3D(q/scaledivisor);
vtx[vtxi].z=3D(r/scaledivisor);
vtx[vtxi].r=3DcMap[n].r;
vtx[vtxi].g=3DcMap[n].g;
vtx[vtxi].b=3DcMap[n].b;

if(alphamode=3D=3D0)
{
vtx[vtxi].a=3D16;
}else{
vtx[vtxi].a=3D(unsigned
char)((0.9375*n)+16);//((256/(256-16)) * n)+16
}
vtx[vtxi].n=3Dn;
vtxi++;
}

// putpixel(surface, p+startx-1,q+starty-1,n);
//SDL_UpdateRect(screen, p+startx-1,
q+starty-1, 1, 1);

n=3Dnumits;

}//mag check

}//n

}//q
}//p
}//r
nvertexes=3Dvtxi;
}

*******************************************************************END
OF CODE SNIPPET

>
> Complex numbers have 2 dimensions. The logic that originally led to
> finding them doesn't work for more dimensions. Looking at complex numbers
> in different ways (as modified vectors or as modified polynomials) leads
> to other structures that are interesting, in 2 or 4 or more dimensions,
> but fail to be as nice as complex numbers are. Complex numbers are very,
> very similar to real numbers.

> I don't know of any 3-dimensional number system that is sufficiently
> similar to complex numbers to be comparable.
>
>> a: [x1,y1,z1]
>> b: [x2,y2,z2]
>> a*b=3D(y1 * z2 - z1 * y2)i + (x1 * z2 - z1 * x2)j + (x1 * y2 - y1 * x2)k
>
> this is almost like cross-product, but the j part has the wrong sign.
> anyway. cross product is weird because a*a =3D 0, and this is also the ca=
se

I have visited this perplexing search for the 3 dimensional equivalent
Elusive it is.

> I get the following error message :
>
>    :-\ Cette vid=E9o est priv=E9e.
>        Op=E9ration impossible
>
>   _______________________________________________________________________
> | Mathieu Bouchard ---- t=E9l: +1.514.383.3801 ---- Villeray, Montr=E9al,=
QC

Appologies. You should be able to view it now. I had it set to private