Studies of Euler diagrams/vidita

dummy

This 4-ary Boolean function has 10 of 16 true spots. It is a gap variant of medusa (see here).

3D Euler diagram

2D Euler diagram with duplicates of cell 6

symmetry
This code uses the Python library discrete helpers. from discretehelpers.boolf.examples import vidita assert vidita.symmetric_spots.blocks_with_singletons() == [[0], [2, 4], [3, 5, 10, 12], [6], [7, 14]]

2D Euler diagrams
multicrossings degenerated into gapspots 1 and 8   (making it a gap variant of inflated barogi) multicrossings multicrossings degenerated into duplicates of cell 6

vidute   (similar diagram with 3 pills)

The following example shows, that the approaches shown above are too rigidly geometric to be generally useful. The same kind of rigid diagram would have to be 3-dimensional, and the pills would have to be arranged in an equilateral triangle. A more generally useful approach is to say, that the pills are sort of in the same place, and permutable among each other. symmetry This code uses the Python library discrete helpers. from discretehelpers.boolf.examples import vidute assert vidute.symmetric_spots.blocks_with_singletons() == [[0], [1, 2], [3], [4, 8, 16], [5, 6, 9, 10, 17, 18]]

filtrates

Each of the 6 pairs is a 2-split (with all 4 quadrants). Only one of the 4 triples is a 3-split (with all 8 octants).

4 sets
A	B	C	D

6 pairs
A B	A C	A D	B C	B D	C D

4 triples
A B C 7 cells	A B D 6 cells	A C D 6 cells	B C D 7 cells

cells

middle
14      _BCD	6      _BC_	7      ABC_
	0      ____

top or bottom   (either blue or green)
12      __CD	4      __C_	5      A_C_
10      _B_D	2      _B__	3      AB__