File:Relation 1000 0101 (cubic matrix).png
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Summary
[edit]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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I, the copyright holder of this work, hereby publish it under the following licenses:
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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
[edit].png&action=edit§ion=3){kind=link}
#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,-1>
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 = < 0, 0, 0>;
#declare v2 = < 0, 0,-1>;
#declare v3 = <-1,-1,-1>;
////////////////////////////////////////
declare unit1 =
union{
object{unit0 translate v1}
object{unit0 translate v2}
object{unit0 translate v3}
}
declare unit2 =
union{
object{unit1 translate 2*v1}
object{unit1 translate 2*v2}
object{unit1 translate 2*v3}
}
declare unit3 =
union{
object{unit2 translate 4*v1}
object{unit2 translate 4*v2}
object{unit2 translate 4*v3}
}
object{unit3 translate 8*v1}
object{unit3 translate 8*v2}
object{unit3 translate 8*v3}
#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,-1>
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 = < 0, 0, 0>;
#declare v2 = < 0, 0,-1>;
#declare v3 = <-1,-1,-1>;
////////////////////////////////////////
declare unit1 =
union{
object{unit0 translate v1}
object{unit0 translate v2}
object{unit0 translate v3}
}
declare unit2 =
union{
object{unit1 translate 2*v1}
object{unit1 translate 2*v2}
object{unit1 translate 2*v3}
}
declare unit3 =
union{
object{unit2 translate 4*v1}
object{unit2 translate 4*v2}
object{unit2 translate 4*v3}
}
object{unit3 translate 8*v1}
object{unit3 translate 8*v2}
object{unit3 translate 8*v3}
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 23:12, 6 July 2015 | | 2,048 × 2,048 (83 KB) | Cmdrjameson (talk | contribs) | Compressed with pngout. Reduced by 31kB (27% decrease). |
| 13:34, 27 January 2011 |  | 2,048 × 2,048 (115 KB) | Watchduck (talk | contribs) |
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