dummy
This Boolean function has 12 of 16 true spots. It is similar to medusa, but without spot 3.
(See here.)
2D Euler diagram with separated cell 0
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3D Euler diagram with one intersection point of three planes
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The Euler diagrams shown above are not good, because they hide the symmetry of this Boolean function.
2D Euler diagram with with rotational symmetry
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This code is part of a Python library called discrete helpers, which is not yet published.
from discretehelpers.boolf.examples import farofe
assert farofe.symmetric_spots.blocks_with_singletons() == [[0, 4], [1, 5], [2, 12], [6, 8], [7, 9], [10, 14]]
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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).
Euler diagram
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6 pairs
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![](//upload.wikimedia.org/wikipedia/commons/thumb/6/63/EuDi%3B_farofe_pair_01.png/230px-EuDi%3B_farofe_pair_01.png) A B
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![](//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/EuDi%3B_farofe_pair_02.png/230px-EuDi%3B_farofe_pair_02.png) A C
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/de/EuDi%3B_farofe_pair_03.png/230px-EuDi%3B_farofe_pair_03.png) A D
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![](//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/EuDi%3B_farofe_pair_23.png/230px-EuDi%3B_farofe_pair_23.png) C D
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![](//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/EuDi%3B_farofe_pair_13.png/230px-EuDi%3B_farofe_pair_13.png) B D
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![](//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/EuDi%3B_farofe_pair_12.png/230px-EuDi%3B_farofe_pair_12.png) B C
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4 triples
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/da/EuDi%3B_farofe_triple_123.png/230px-EuDi%3B_farofe_triple_123.png) B C D 8 cells
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/EuDi%3B_farofe_triple_023.png/230px-EuDi%3B_farofe_triple_023.png) A C D 7 cells
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![](//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/EuDi%3B_farofe_triple_013.png/230px-EuDi%3B_farofe_triple_013.png) A B D 7 cells
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![](//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/EuDi%3B_farofe_triple_012.png/230px-EuDi%3B_farofe_triple_012.png) A B C 7 cells
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graph
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complete
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6 pairs
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![](//upload.wikimedia.org/wikipedia/commons/thumb/7/77/EuDi%3B_farofe_graph%3B_pair_0_1.svg/300px-EuDi%3B_farofe_graph%3B_pair_0_1.svg.png) A B
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![](//upload.wikimedia.org/wikipedia/commons/thumb/7/72/EuDi%3B_farofe_graph%3B_pair_0_2.svg/300px-EuDi%3B_farofe_graph%3B_pair_0_2.svg.png) A C
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![](//upload.wikimedia.org/wikipedia/commons/thumb/7/71/EuDi%3B_farofe_graph%3B_pair_0_3.svg/300px-EuDi%3B_farofe_graph%3B_pair_0_3.svg.png) A D
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![](//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/EuDi%3B_farofe_graph%3B_pair_2_3.svg/300px-EuDi%3B_farofe_graph%3B_pair_2_3.svg.png) C D
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/db/EuDi%3B_farofe_graph%3B_pair_1_3.svg/300px-EuDi%3B_farofe_graph%3B_pair_1_3.svg.png) B D
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![](//upload.wikimedia.org/wikipedia/commons/thumb/4/44/EuDi%3B_farofe_graph%3B_pair_1_2.svg/300px-EuDi%3B_farofe_graph%3B_pair_1_2.svg.png) B C
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4 triples
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![](//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/EuDi%3B_farofe_graph%3B_triple_1_2_3.svg/300px-EuDi%3B_farofe_graph%3B_triple_1_2_3.svg.png) B C D
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/EuDi%3B_farofe_graph%3B_triple_0_2_3.svg/300px-EuDi%3B_farofe_graph%3B_triple_0_2_3.svg.png) A C D
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![](//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/EuDi%3B_farofe_graph%3B_triple_0_1_3.svg/300px-EuDi%3B_farofe_graph%3B_triple_0_1_3.svg.png) A B D
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![](//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/EuDi%3B_farofe_graph%3B_triple_0_1_2.svg/300px-EuDi%3B_farofe_graph%3B_triple_0_1_2.svg.png) A B C
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blue and green (top)
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7 ABC_
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6 _BC_
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14 _BCD
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either blue or green (middle)
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5 A_C_
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4 __C_
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2 _B__
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12 __CD
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10 _B_D
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neither blue nor green (bottom)
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0 ____
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8 ___D
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1 A___
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9 A__D
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