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heart rendering

• To: mathgroup at smc.vnet.net
• Subject: [mg28954] heart rendering
• From: "Clifford J. Nelson" <cnelson9 at gte.net>
• Date: Mon, 21 May 2001 00:43:40 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

What is the best way to render the graphics to show the heart of
the matter in this notebook?


CMYKColor is a four coordinate color directive: Cyan, Magenta,
Yellow, and Black. Each coordinate can represent the outward
movement of one of the planes that define a tetrahedron. So, all
of the subsets of four things have a color code and a geometrical
representation (in the Synergetics coordinate system). It is a
four dimensional tetrahedral Venn-like diagram. The larger subsets

(tetrahedra) contain the other representations of the smaller
subsets.

Graphic at:

http://homepage.mac.com/cnelson9/PhotoAlbum1.html

And see:

http://forum.swarthmore.edu/epigone/geometry-research/brydilyum

In[1]:=
StoP[x_List] :=
  Module[{an = {},w = x},
    Do[an=Prepend[an,- Last[w]/i Sqrt[i(i+1)/2]];
      w = Drop[w,-1]+ Last[w]/i, {i,Length[x]-1,1,-1}];an]

In[2]:=
Vertexes[x_List] :=
  Insert[Delete[x,- #],-Plus @@ Delete[x,-#],-#]& /@
Range[Length[x]]

In[3]:=
<<DiscreteMath`Combinatorica`

In[4]:=
ColorTet[x_] := {CMYKColor @@ x,Thickness[(1/(x. x)^1.2)/55],
    Line /@ KSubsets[StoP /@ Vertexes[x],2]}

In[5]:=
ggr[x_] :=  ColorTet /@ x

In[6]:=
gg =ggr[ Sort[IntegerDigits[Range[1,15],2,4],(Plus @@ #1)>=(Plus
@@ #2)&]];

In[7]:=
Show[Graphics3D[gg],Axes -> True ]