       3D Pascal's beta cube

• To: mathgroup at smc.vnet.net
• Subject: [mg49610] 3D Pascal's beta cube
• From: "Roger L. Bagula" <rlbtftn at netscape.net>
• Date: Sat, 24 Jul 2004 03:48:19 -0400 (EDT)
• References: <200407211814.i6LIELN23030@proapp.mathforum.org> <cdnq13\$l3v\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```(* 64*64*64 CUBE OF xy,yz,zx  beta triangle 3D *)
(* BY R. L. BAGULA 23 July 2004©*)

a=32;

b1=Beta[Abs[a-Abs[a-x]],Abs[a-Abs[a-y]]]
b2=Beta[Abs[a-Abs[a-y]],Abs[a-Abs[a-z]]]
b3=Beta[Abs[a-Abs[a-x]],Abs[a-Abs[a-z]]]

g=Flatten[Table[If[Mod[1/(b1*b2*b3),2]==1,
Cuboid[0.5*{x,y,z}],{}],
{x,0,2*a},{y,0,2*a},{z,0,2*a}]];

gg=Show[Graphics3D[g,Boxed->False,ViewPoint->{-3.059, 8.168, 2.221}]]

Notebook available by request.
Roger L. Bagula wrote:
> There is and old Visualization in Mathematica that
> gives a modulo 2 version of a Pascal's triangle.
> It is a right angle version of a tetrahedral 3d Sierpiski triangle.
> Here it is: ( copyright Mathematica):
>
> g=Flatten[Table[If
> Mod[Multinomial[x,y,x],2]==1,Cuboid[1.2*{x,y,-z}}],{}],{x,0,15},{y.0,15},{z,0,15}]
> Show[Graphics3D[g]]
>
> phil wrote:
>
>>Is there a three dimensional version of Pascal's
>>triangle? If so, I suppose it would be a cone (?).
>>Applications?
>>
>>phil
>>
>
>
>

--
Respectfully, Roger L. Bagula