File:Relation 0010 0001 (cubic matrix).png
Original file (2,048 × 2,048 pixels, file size: 61 KB, MIME type: image/png)
Captions
Captions
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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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 = <-1,-1, 0>;
////////////////////////////////////////
declare unit1 =
union{
object{unit0 translate v1}
object{unit0 translate v2}
}
declare unit2 =
union{
object{unit1 translate 2*v1}
object{unit1 translate 2*v2}
}
declare unit3 =
union{
object{unit2 translate 4*v1}
object{unit2 translate 4*v2}
}
object{unit3 translate 8*v1}
object{unit3 translate 8*v2}
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 22:43, 6 July 2015 | | 2,048 × 2,048 (61 KB) | Cmdrjameson (talk | contribs) | Compressed with pngout. Reduced by 27kB (30% decrease). |
| 13:33, 27 January 2011 |  | 2,048 × 2,048 (88 KB) | Watchduck (talk | contribs) |
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.png&oldid=470376343){kind=link}