File:Relation 0111 1110 (cubic matrix).png
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.png){kind=small}
Summary
This file shows a 16×16×16 "logical tensor" representing a 3-ary Boolean relation. (white 0, red 1)
In the following example calculation the 3-ary relations are represented by their logical tensor,
their Venn diagrams and cubes dual to the Venn diagrams.
As the used operation is and the resulting tensor shows all ones that are both in the fist and in the second input.
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The dimension 3 is necesseary because 3-ary relations are to be represented.
The 24=16 is a random power of two. Tensors like this one represent the relations in a four element universe.
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This file was created with POV-Ray, and uploaded with Commonist. | 
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Published by Watchduck under the following licences:
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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POV-Ray source
#include "colors.inc"
background {color White}
camera { angle 8
location <65,45,-150>
look_at <7.6, 7.5, 8>
up < 0, 1, 0>
right < 1, 0, 0>
}
light_source { <50,30,20>
color White
shadowless
}
light_source { <-1,20,-2>
color White
shadowless
}
difference{
box {
< -0.1,-0.1,-0.1>,
< 16.1,16.1,16.1>
pigment{color Black}
}
union{
box{
< -8,-8,-8>,
< 8,8,8>
pigment{color Black}
scale <1.02,0.995,0.995>
}
box{
< -8,-8,-8>,
< 8,8,8>
pigment{color Black}
scale <0.995,1.02,0.995>
}
box{
< -8,-8,-8>,
< 8,8,8>
pigment{color Black}
scale <0.995,0.995,1.02>
}
translate<8,8,8>
}
no_reflection
}
sphere{<0,0,0>,0.3
pigment{color Black}
}
/////////////////////////////////////////////////////// red
#declare unit0 =
box{
< 15.98,15.98,15.98>,
< 15.02,15.02,15.02>
pigment{color Red}
};
#declare v1 = <-1, 0, 0>;
#declare v2 = < 0,-1, 0>;
#declare v3 = < 0, 0,-1>;
#declare v4 = <-1,-1, 0>;
#declare v5 = <-1, 0,-1>;
#declare v6 = < 0,-1,-1>;
////////////////////////////////////////
declare unit1 =
union{
object{unit0 translate v1}
object{unit0 translate v2}
object{unit0 translate v3}
object{unit0 translate v4}
object{unit0 translate v5}
object{unit0 translate v6}
}
declare unit2 =
union{
object{unit1 translate 2*v1}
object{unit1 translate 2*v2}
object{unit1 translate 2*v3}
object{unit1 translate 2*v4}
object{unit1 translate 2*v5}
object{unit1 translate 2*v6}
}
declare unit3 =
union{
object{unit2 translate 4*v1}
object{unit2 translate 4*v2}
object{unit2 translate 4*v3}
object{unit2 translate 4*v4}
object{unit2 translate 4*v5}
object{unit2 translate 4*v6}
}
object{unit3 translate 8*v1}
object{unit3 translate 8*v2}
object{unit3 translate 8*v3}
object{unit3 translate 8*v4}
object{unit3 translate 8*v5}
object{unit3 translate 8*v6}
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 13:34, 27 January 2011 | | 2,048 × 2,048 (243 KB) | Watchduck |
File usage
The following page uses this file:
.png){kind=link}