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  

sarina 
futare 
geteso 
multibundle 3221  

sasunu 
nutite 
karafa 
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.
3ary  

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.  
selera 
pelele 
gap variants of manila  

linaki 
karifu 
gap variants of basiga  

kulika 
torova 
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 3ary 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.
variants  

foravo (hexagon)
[edit  edit source]2×3
[edit  edit source]grid  

potula 
kinide ⚒ 
gilipi ⚒ 
gelade 
redrawn  

ternary labels 

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 2dimensional
[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 0sphere) 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.)
multibundle 3221 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)  
