Studies of Euler diagrams/gapspots/hard and soft

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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   (cm1: C in A and B)
bazinga gapspots
EuDi; batch 5; 8 redrawn.svg
EuDi; batch 5; 10 redrawn.svg
EuDi; batch 5; 13 redrawn.svg

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.

EuDi; 3-ary xor even.svg
EuDi; 3-ary xor odd.svg

vanatu[edit | edit source]

This is a XOR including an OR:              It is a gap variant of bar and a filtrate of tomute.

EuDi; vanatu.svg EuDi; vanatu graph.svg

bunese (7 of 8 cells)[edit | edit source]

Below are three possible Euler diagrams of the same Boolean function. It is in logic, and in set theory.

  • left:   The false cell is shown as a gapspot.
  • middle:   An intersection of three borders is shown instead.
  • right:   With three straight lines the plane can be partitioned in seven areas.
EuDi; 3-ary Boolean function without cell 7; gap.svg EuDi; 3-ary Boolean function without cell 7; point.svg EuDi; 3-ary Boolean function without cell 7; flat.svg

Rdr.svg foravo (hexagon)[edit | edit source]


This function can reasonably be shown with two or no gapspots. The latter means, that the three borders intersect in one point.
This point could be enlarged into gapspot 0 or 7. But that would be a random choice, which should be avoided.

EuDi; foravo rings.svg
both gapspots
EuDi; foravo gap 0.svg
gapspot 0
EuDi; foravo gapless.svg
no gapspots
EuDi; foravo gap 7.svg
gapspot 7

2×3[edit | edit source]

EuDi; 2x3 potula.svg
EuDi; 2x3 kinide.svg
EuDi; 2x3 gilipi.svg
EuDi; 2x3 gelade.svg

kagusi (2×4)[edit | edit source]

If the gapspots were true, the red circle would vanish.

graph, Euler diagram
EuDi; batch 7; 3 grid.svg
EuDi; batch 7; 3 Euler.svg

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.)

gapspots bundles 3-2-2-1   cm2 gapspots 5×4   gufaro
EuDi; batch 3; cm2 redrawn.svg EuDi; batch 4; bu1 redrawn.svg
Distance between cells 37 and 32:   2 above, 4 below Distance between cells 10 and 24:   2 above, 6 below
EuDi; batch 3; cm2 redrawn linear.svg EuDi; batch 4; bu1 redrawn linear.svg

piferi[edit | edit source]

Like example putuki, but with spot 0 as gapspot.   (Compare logota, another octagon.)

matrix and circular graph
3×3 graph with gapspot
1-dimensional graph and Euler diagram closed to a circle

Rdrdo.svg 5×5 circles[edit | edit source]