Studies of Euler diagrams/gapspots/hard and soft
Some gapspots can not be avoided, while others are a design choice. They could be called hard and soft. On this page functions with hard gapspots are marked with ⚒.
between different bundles ⚒ [edit | edit source]
There is no way to avoid gapspots between different bundles. The simplest examples are:
- two sets in an otherwise empty set (sarina: H and F in G)
- one set in an otherwise empty intersection (karafa: C in A∩B)
|gap variants of basiga|
XOR ⚒[edit | edit source]
Functions in the same box are complements. Those on the left (right) are true in cells with even (odd) digit sum.
One could choose an Euler diagram with 7 cells (compare bunese), which would remove one of the gapspots. But that would be a random choice, which should be avoided.
|gap variants of manila|
|gap variants of basiga|
vanatu ⚒[edit | edit source]
This is a XOR including an OR: It is a gap variant of vidita and a filtrate of tomute. The gapspots 2, 4, 6 are hard; 1 and 8 are optional.
|with optional gapspots|
|only hard gapspots|
bunese (7 of 8 cells)[edit | edit source]
Below are different Euler diagrams of the 3-ary Boolean function .
dagoro ⚒[edit | edit source]
The gaps 2 and 6 are hard. Gap 0 is optional. Without C this bundle falls apart in two bundles with a gap cell between them.
foravo (hexagon)[edit | edit source]
2×3[edit | edit source]
kagusi (2×4) ⚒[edit | edit source]
If the gapspots were true, the red circle would vanish.
|graph, Euler diagram|
|rather bad 1D Euler diagram|
|The problem with this representation is, that it was chosen to remove gapspot 0 rather than 9. But random choices should be avoided.|
1- or 2-dimensional[edit | edit source]
Euler diagrams can be drawn with gapspots in a higher dimension, or without in a lower. Generally one should prefer the lowest possible dimension. But it is reasonable to demand from an Euler diagram, that the set borders be contiguous - which a circle in one dimension (a 0-sphere) is not. So in this case, one might prefer the 2D diagrams, and consider the gapspots necessary. (The disconnected left and right parts are easier seen in this version of the 1D diagram on the right.)
|multi-bundle 3-2-2-1 todeda||5×4 gufaro|
|Distance between cells 37 and 32: 2 above, 4 below||Distance between cells 10 and 24: 2 above, 6 below|
piferi[edit | edit source]
Like example putuki, but with spot 0 as gapspot. (Compare logota, another octagon.)
|matrix and circular graph|
|Euler diagram (matrix and cylinder)|