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 is part of a Python library called discrete helpers, which is not yet published. 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 is part of a Python library called discrete helpers, which is not yet published. 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__